# 有限群共軛類基礎 · 脈衝 R03

本批已通過 Schema、去重、來源快照與獨立答案重算；仍未標記為人工審定。

本題庫已有對應的中英逐步詳解。原題的 candidate 與英文 ai_candidate 狀態保留；AI 覆核、有限計算與 Lean 形式證明分開標示。

batch-20261015-advance-20261114-r03-finite-group-conjugacy-class-foundations · 2026-10-15 · 100 題

欄序為來源綁定的呈現補充；原始 JSONL 與數學答案不變。

[欄序與來源綁定資料](https://ocme.evemisslab.com/data/i18n/question-output-protocols.json)



## 1. 有限群共軛類

由完整Cayley table導出全部conjugation action與orbits。操作=conjugacy-action-table；資料={"group_table":[[0,1,2,3,4,5],[1,2,0,4,5,3],[2,0,1,5,3,4],[3,5,4,0,2,1],[4,3,5,1,0,2],[5,4,3,2,1,0]],"identity":0}。請依 [conjugation_action, identity_action, composition_action, certificate] 欄序回答。

查看答案與解釋([[0, 1, 2, 3, 4, 5], [0, 1, 2, 5, 3, 4], [0, 1, 2, 4, 5, 3], [0, 2, 1, 3, 5, 4], [0, 2, 1, 5, 4, 3], [0, 2, 1, 4, 3, 5]], 是, 是, g_dot_x_equals_g_x_g_inverse_is_a_complete_left_action)

Wave6第八層核對=([[0, 1, 2, 3, 4, 5], [0, 1, 2, 5, 3, 4], [0, 1, 2, 4, 5, 3], [0, 2, 1, 3, 5, 4], [0, 2, 1, 5, 4, 3], [0, 2, 1, 4, 3, 5]], 是, 是, g_dot_x_equals_g_x_g_inverse_is_a_complete_left_action)；依完整明示資料獨立重算；共軛類是element orbit並形成完整partition；singleton以forall g commute核對；共軛類不是coset或conjugate subgroup；不使用centralizer、class-size公式或類方程。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r03-finite-group-conjugacy-class-0001/)

有限群共軛類 · qf-mod45-conjugacy-action-table · candidate





## 2. 有限群共軛類

由完整Cayley table導出全部conjugation action與orbits。操作=conjugacy-action-table；資料={"group_table":[[0,1,2,3,4,5,6,7],[1,2,3,0,5,6,7,4],[2,3,0,1,6,7,4,5],[3,0,1,2,7,4,5,6],[4,7,6,5,0,3,2,1],[5,4,7,6,1,0,3,2],[6,5,4,7,2,1,0,3],[7,6,5,4,3,2,1,0]],"identity":0}。請依 [conjugation_action, identity_action, composition_action, certificate] 欄序回答。

查看答案與解釋([[0, 1, 2, 3, 4, 5, 6, 7], [0, 1, 2, 3, 6, 7, 4, 5], [0, 1, 2, 3, 4, 5, 6, 7], [0, 1, 2, 3, 6, 7, 4, 5], [0, 3, 2, 1, 4, 7, 6, 5], [0, 3, 2, 1, 6, 5, 4, 7], [0, 3, 2, 1, 4, 7, 6, 5], [0, 3, 2, 1, 6, 5, 4, 7]], 是, 是, g_dot_x_equals_g_x_g_inverse_is_a_complete_left_action)

Wave6第八層核對=([[0, 1, 2, 3, 4, 5, 6, 7], [0, 1, 2, 3, 6, 7, 4, 5], [0, 1, 2, 3, 4, 5, 6, 7], [0, 1, 2, 3, 6, 7, 4, 5], [0, 3, 2, 1, 4, 7, 6, 5], [0, 3, 2, 1, 6, 5, 4, 7], [0, 3, 2, 1, 4, 7, 6, 5], [0, 3, 2, 1, 6, 5, 4, 7]], 是, 是, g_dot_x_equals_g_x_g_inverse_is_a_complete_left_action)；依完整明示資料獨立重算；共軛類是element orbit並形成完整partition；singleton以forall g commute核對；共軛類不是coset或conjugate subgroup；不使用centralizer、class-size公式或類方程。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r03-finite-group-conjugacy-class-0002/)

有限群共軛類 · qf-mod45-conjugacy-action-table · candidate





## 3. 有限群共軛類

由完整Cayley table導出全部conjugation action與orbits。操作=conjugacy-action-table；資料={"group_table":[[0,1,2,3,4,5,6,7,8,9],[1,2,3,4,0,6,7,8,9,5],[2,3,4,0,1,7,8,9,5,6],[3,4,0,1,2,8,9,5,6,7],[4,0,1,2,3,9,5,6,7,8],[5,9,8,7,6,0,4,3,2,1],[6,5,9,8,7,1,0,4,3,2],[7,6,5,9,8,2,1,0,4,3],[8,7,6,5,9,3,2,1,0,4],[9,8,7,6,5,4,3,2,1,0]],"identity":0}。請依 [conjugation_action, identity_action, composition_action, certificate] 欄序回答。

查看答案與解釋([[0, 1, 2, 3, 4, 5, 6, 7, 8, 9], [0, 1, 2, 3, 4, 7, 8, 9, 5, 6], [0, 1, 2, 3, 4, 9, 5, 6, 7, 8], [0, 1, 2, 3, 4, 6, 7, 8, 9, 5], [0, 1, 2, 3, 4, 8, 9, 5, 6, 7], [0, 4, 3, 2, 1, 5, 9, 8, 7, 6], [0, 4, 3, 2, 1, 7, 6, 5, 9, 8], [0, 4, 3, 2, 1, 9, 8, 7, 6, 5], [0, 4, 3, 2, 1, 6, 5, 9, 8, 7], [0, 4, 3, 2, 1, 8, 7, 6, 5, 9]], 是, 是, g_dot_x_equals_g_x_g_inverse_is_a_complete_left_action)

Wave6第八層核對=([[0, 1, 2, 3, 4, 5, 6, 7, 8, 9], [0, 1, 2, 3, 4, 7, 8, 9, 5, 6], [0, 1, 2, 3, 4, 9, 5, 6, 7, 8], [0, 1, 2, 3, 4, 6, 7, 8, 9, 5], [0, 1, 2, 3, 4, 8, 9, 5, 6, 7], [0, 4, 3, 2, 1, 5, 9, 8, 7, 6], [0, 4, 3, 2, 1, 7, 6, 5, 9, 8], [0, 4, 3, 2, 1, 9, 8, 7, 6, 5], [0, 4, 3, 2, 1, 6, 5, 9, 8, 7], [0, 4, 3, 2, 1, 8, 7, 6, 5, 9]], 是, 是, g_dot_x_equals_g_x_g_inverse_is_a_complete_left_action)；依完整明示資料獨立重算；共軛類是element orbit並形成完整partition；singleton以forall g commute核對；共軛類不是coset或conjugate subgroup；不使用centralizer、class-size公式或類方程。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r03-finite-group-conjugacy-class-0003/)

有限群共軛類 · qf-mod45-conjugacy-action-table · candidate





## 4. 有限群共軛類

由完整Cayley table導出全部conjugation action與orbits。操作=conjugacy-action-table；資料={"group_table":[[0,1,2,3,4,5,6,7,8,9,10,11],[1,2,3,4,5,0,7,8,9,10,11,6],[2,3,4,5,0,1,8,9,10,11,6,7],[3,4,5,0,1,2,9,10,11,6,7,8],[4,5,0,1,2,3,10,11,6,7,8,9],[5,0,1,2,3,4,11,6,7,8,9,10],[6,11,10,9,8,7,0,5,4,3,2,1],[7,6,11,10,9,8,1,0,5,4,3,2],[8,7,6,11,10,9,2,1,0,5,4,3],[9,8,7,6,11,10,3,2,1,0,5,4],[10,9,8,7,6,11,4,3,2,1,0,5],[11,10,9,8,7,6,5,4,3,2,1,0]],"identity":0}。請依 [conjugation_action, identity_action, composition_action, certificate] 欄序回答。

查看答案與解釋([[0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11], [0, 1, 2, 3, 4, 5, 8, 9, 10, 11, 6, 7], [0, 1, 2, 3, 4, 5, 10, 11, 6, 7, 8, 9], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11], [0, 1, 2, 3, 4, 5, 8, 9, 10, 11, 6, 7], [0, 1, 2, 3, 4, 5, 10, 11, 6, 7, 8, 9], [0, 5, 4, 3, 2, 1, 6, 11, 10, 9, 8, 7], [0, 5, 4, 3, 2, 1, 8, 7, 6, 11, 10, 9], [0, 5, 4, 3, 2, 1, 10, 9, 8, 7, 6, 11], [0, 5, 4, 3, 2, 1, 6, 11, 10, 9, 8, 7], [0, 5, 4, 3, 2, 1, 8, 7, 6, 11, 10, 9], [0, 5, 4, 3, 2, 1, 10, 9, 8, 7, 6, 11]], 是, 是, g_dot_x_equals_g_x_g_inverse_is_a_complete_left_action)

Wave6第八層核對=([[0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11], [0, 1, 2, 3, 4, 5, 8, 9, 10, 11, 6, 7], [0, 1, 2, 3, 4, 5, 10, 11, 6, 7, 8, 9], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11], [0, 1, 2, 3, 4, 5, 8, 9, 10, 11, 6, 7], [0, 1, 2, 3, 4, 5, 10, 11, 6, 7, 8, 9], [0, 5, 4, 3, 2, 1, 6, 11, 10, 9, 8, 7], [0, 5, 4, 3, 2, 1, 8, 7, 6, 11, 10, 9], [0, 5, 4, 3, 2, 1, 10, 9, 8, 7, 6, 11], [0, 5, 4, 3, 2, 1, 6, 11, 10, 9, 8, 7], [0, 5, 4, 3, 2, 1, 8, 7, 6, 11, 10, 9], [0, 5, 4, 3, 2, 1, 10, 9, 8, 7, 6, 11]], 是, 是, g_dot_x_equals_g_x_g_inverse_is_a_complete_left_action)；依完整明示資料獨立重算；共軛類是element orbit並形成完整partition；singleton以forall g commute核對；共軛類不是coset或conjugate subgroup；不使用centralizer、class-size公式或類方程。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r03-finite-group-conjugacy-class-0004/)

有限群共軛類 · qf-mod45-conjugacy-action-table · candidate





## 5. 有限群共軛類

由完整Cayley table導出全部conjugation action與orbits。操作=conjugacy-action-table；資料={"group_table":[[0,1,2,3,4,5,6,7,8,9,10,11,12,13],[1,2,3,4,5,6,0,8,9,10,11,12,13,7],[2,3,4,5,6,0,1,9,10,11,12,13,7,8],[3,4,5,6,0,1,2,10,11,12,13,7,8,9],[4,5,6,0,1,2,3,11,12,13,7,8,9,10],[5,6,0,1,2,3,4,12,13,7,8,9,10,11],[6,0,1,2,3,4,5,13,7,8,9,10,11,12],[7,13,12,11,10,9,8,0,6,5,4,3,2,1],[8,7,13,12,11,10,9,1,0,6,5,4,3,2],[9,8,7,13,12,11,10,2,1,0,6,5,4,3],[10,9,8,7,13,12,11,3,2,1,0,6,5,4],[11,10,9,8,7,13,12,4,3,2,1,0,6,5],[12,11,10,9,8,7,13,5,4,3,2,1,0,6],[13,12,11,10,9,8,7,6,5,4,3,2,1,0]],"identity":0}。請依 [conjugation_action, identity_action, composition_action, certificate] 欄序回答。

查看答案與解釋([[0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13], [0, 1, 2, 3, 4, 5, 6, 9, 10, 11, 12, 13, 7, 8], [0, 1, 2, 3, 4, 5, 6, 11, 12, 13, 7, 8, 9, 10], [0, 1, 2, 3, 4, 5, 6, 13, 7, 8, 9, 10, 11, 12], [0, 1, 2, 3, 4, 5, 6, 8, 9, 10, 11, 12, 13, 7], [0, 1, 2, 3, 4, 5, 6, 10, 11, 12, 13, 7, 8, 9], [0, 1, 2, 3, 4, 5, 6, 12, 13, 7, 8, 9, 10, 11], [0, 6, 5, 4, 3, 2, 1, 7, 13, 12, 11, 10, 9, 8], [0, 6, 5, 4, 3, 2, 1, 9, 8, 7, 13, 12, 11, 10], [0, 6, 5, 4, 3, 2, 1, 11, 10, 9, 8, 7, 13, 12], [0, 6, 5, 4, 3, 2, 1, 13, 12, 11, 10, 9, 8, 7], [0, 6, 5, 4, 3, 2, 1, 8, 7, 13, 12, 11, 10, 9], [0, 6, 5, 4, 3, 2, 1, 10, 9, 8, 7, 13, 12, 11], [0, 6, 5, 4, 3, 2, 1, 12, 11, 10, 9, 8, 7, 13]], 是, 是, g_dot_x_equals_g_x_g_inverse_is_a_complete_left_action)

Wave6第八層核對=([[0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13], [0, 1, 2, 3, 4, 5, 6, 9, 10, 11, 12, 13, 7, 8], [0, 1, 2, 3, 4, 5, 6, 11, 12, 13, 7, 8, 9, 10], [0, 1, 2, 3, 4, 5, 6, 13, 7, 8, 9, 10, 11, 12], [0, 1, 2, 3, 4, 5, 6, 8, 9, 10, 11, 12, 13, 7], [0, 1, 2, 3, 4, 5, 6, 10, 11, 12, 13, 7, 8, 9], [0, 1, 2, 3, 4, 5, 6, 12, 13, 7, 8, 9, 10, 11], [0, 6, 5, 4, 3, 2, 1, 7, 13, 12, 11, 10, 9, 8], [0, 6, 5, 4, 3, 2, 1, 9, 8, 7, 13, 12, 11, 10], [0, 6, 5, 4, 3, 2, 1, 11, 10, 9, 8, 7, 13, 12], [0, 6, 5, 4, 3, 2, 1, 13, 12, 11, 10, 9, 8, 7], [0, 6, 5, 4, 3, 2, 1, 8, 7, 13, 12, 11, 10, 9], [0, 6, 5, 4, 3, 2, 1, 10, 9, 8, 7, 13, 12, 11], [0, 6, 5, 4, 3, 2, 1, 12, 11, 10, 9, 8, 7, 13]], 是, 是, g_dot_x_equals_g_x_g_inverse_is_a_complete_left_action)；依完整明示資料獨立重算；共軛類是element orbit並形成完整partition；singleton以forall g commute核對；共軛類不是coset或conjugate subgroup；不使用centralizer、class-size公式或類方程。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r03-finite-group-conjugacy-class-0005/)

有限群共軛類 · qf-mod45-conjugacy-action-table · candidate





## 6. 有限群共軛類

由完整Cayley table導出全部conjugation action與orbits。操作=conjugacy-action-table；資料={"group_table":[[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15],[1,2,3,4,5,6,7,0,9,10,11,12,13,14,15,8],[2,3,4,5,6,7,0,1,10,11,12,13,14,15,8,9],[3,4,5,6,7,0,1,2,11,12,13,14,15,8,9,10],[4,5,6,7,0,1,2,3,12,13,14,15,8,9,10,11],[5,6,7,0,1,2,3,4,13,14,15,8,9,10,11,12],[6,7,0,1,2,3,4,5,14,15,8,9,10,11,12,13],[7,0,1,2,3,4,5,6,15,8,9,10,11,12,13,14],[8,15,14,13,12,11,10,9,0,7,6,5,4,3,2,1],[9,8,15,14,13,12,11,10,1,0,7,6,5,4,3,2],[10,9,8,15,14,13,12,11,2,1,0,7,6,5,4,3],[11,10,9,8,15,14,13,12,3,2,1,0,7,6,5,4],[12,11,10,9,8,15,14,13,4,3,2,1,0,7,6,5],[13,12,11,10,9,8,15,14,5,4,3,2,1,0,7,6],[14,13,12,11,10,9,8,15,6,5,4,3,2,1,0,7],[15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0]],"identity":0}。請依 [conjugation_action, identity_action, composition_action, certificate] 欄序回答。

查看答案與解釋([[0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15], [0, 1, 2, 3, 4, 5, 6, 7, 10, 11, 12, 13, 14, 15, 8, 9], [0, 1, 2, 3, 4, 5, 6, 7, 12, 13, 14, 15, 8, 9, 10, 11], [0, 1, 2, 3, 4, 5, 6, 7, 14, 15, 8, 9, 10, 11, 12, 13], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15], [0, 1, 2, 3, 4, 5, 6, 7, 10, 11, 12, 13, 14, 15, 8, 9], [0, 1, 2, 3, 4, 5, 6, 7, 12, 13, 14, 15, 8, 9, 10, 11], [0, 1, 2, 3, 4, 5, 6, 7, 14, 15, 8, 9, 10, 11, 12, 13], [0, 7, 6, 5, 4, 3, 2, 1, 8, 15, 14, 13, 12, 11, 10, 9], [0, 7, 6, 5, 4, 3, 2, 1, 10, 9, 8, 15, 14, 13, 12, 11], [0, 7, 6, 5, 4, 3, 2, 1, 12, 11, 10, 9, 8, 15, 14, 13], [0, 7, 6, 5, 4, 3, 2, 1, 14, 13, 12, 11, 10, 9, 8, 15], [0, 7, 6, 5, 4, 3, 2, 1, 8, 15, 14, 13, 12, 11, 10, 9], [0, 7, 6, 5, 4, 3, 2, 1, 10, 9, 8, 15, 14, 13, 12, 11], [0, 7, 6, 5, 4, 3, 2, 1, 12, 11, 10, 9, 8, 15, 14, 13], [0, 7, 6, 5, 4, 3, 2, 1, 14, 13, 12, 11, 10, 9, 8, 15]], 是, 是, g_dot_x_equals_g_x_g_inverse_is_a_complete_left_action)

Wave6第八層核對=([[0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15], [0, 1, 2, 3, 4, 5, 6, 7, 10, 11, 12, 13, 14, 15, 8, 9], [0, 1, 2, 3, 4, 5, 6, 7, 12, 13, 14, 15, 8, 9, 10, 11], [0, 1, 2, 3, 4, 5, 6, 7, 14, 15, 8, 9, 10, 11, 12, 13], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15], [0, 1, 2, 3, 4, 5, 6, 7, 10, 11, 12, 13, 14, 15, 8, 9], [0, 1, 2, 3, 4, 5, 6, 7, 12, 13, 14, 15, 8, 9, 10, 11], [0, 1, 2, 3, 4, 5, 6, 7, 14, 15, 8, 9, 10, 11, 12, 13], [0, 7, 6, 5, 4, 3, 2, 1, 8, 15, 14, 13, 12, 11, 10, 9], [0, 7, 6, 5, 4, 3, 2, 1, 10, 9, 8, 15, 14, 13, 12, 11], [0, 7, 6, 5, 4, 3, 2, 1, 12, 11, 10, 9, 8, 15, 14, 13], [0, 7, 6, 5, 4, 3, 2, 1, 14, 13, 12, 11, 10, 9, 8, 15], [0, 7, 6, 5, 4, 3, 2, 1, 8, 15, 14, 13, 12, 11, 10, 9], [0, 7, 6, 5, 4, 3, 2, 1, 10, 9, 8, 15, 14, 13, 12, 11], [0, 7, 6, 5, 4, 3, 2, 1, 12, 11, 10, 9, 8, 15, 14, 13], [0, 7, 6, 5, 4, 3, 2, 1, 14, 13, 12, 11, 10, 9, 8, 15]], 是, 是, g_dot_x_equals_g_x_g_inverse_is_a_complete_left_action)；依完整明示資料獨立重算；共軛類是element orbit並形成完整partition；singleton以forall g commute核對；共軛類不是coset或conjugate subgroup；不使用centralizer、class-size公式或類方程。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r03-finite-group-conjugacy-class-0006/)

有限群共軛類 · qf-mod45-conjugacy-action-table · candidate





## 7. 有限群共軛類

由完整Cayley table導出全部conjugation action與orbits。操作=conjugacy-action-table；資料={"group_table":[[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17],[1,2,3,4,5,6,7,8,0,10,11,12,13,14,15,16,17,9],[2,3,4,5,6,7,8,0,1,11,12,13,14,15,16,17,9,10],[3,4,5,6,7,8,0,1,2,12,13,14,15,16,17,9,10,11],[4,5,6,7,8,0,1,2,3,13,14,15,16,17,9,10,11,12],[5,6,7,8,0,1,2,3,4,14,15,16,17,9,10,11,12,13],[6,7,8,0,1,2,3,4,5,15,16,17,9,10,11,12,13,14],[7,8,0,1,2,3,4,5,6,16,17,9,10,11,12,13,14,15],[8,0,1,2,3,4,5,6,7,17,9,10,11,12,13,14,15,16],[9,17,16,15,14,13,12,11,10,0,8,7,6,5,4,3,2,1],[10,9,17,16,15,14,13,12,11,1,0,8,7,6,5,4,3,2],[11,10,9,17,16,15,14,13,12,2,1,0,8,7,6,5,4,3],[12,11,10,9,17,16,15,14,13,3,2,1,0,8,7,6,5,4],[13,12,11,10,9,17,16,15,14,4,3,2,1,0,8,7,6,5],[14,13,12,11,10,9,17,16,15,5,4,3,2,1,0,8,7,6],[15,14,13,12,11,10,9,17,16,6,5,4,3,2,1,0,8,7],[16,15,14,13,12,11,10,9,17,7,6,5,4,3,2,1,0,8],[17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0]],"identity":0}。請依 [conjugation_action, identity_action, composition_action, certificate] 欄序回答。

查看答案與解釋([[0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17], [0, 1, 2, 3, 4, 5, 6, 7, 8, 11, 12, 13, 14, 15, 16, 17, 9, 10], [0, 1, 2, 3, 4, 5, 6, 7, 8, 13, 14, 15, 16, 17, 9, 10, 11, 12], [0, 1, 2, 3, 4, 5, 6, 7, 8, 15, 16, 17, 9, 10, 11, 12, 13, 14], [0, 1, 2, 3, 4, 5, 6, 7, 8, 17, 9, 10, 11, 12, 13, 14, 15, 16], [0, 1, 2, 3, 4, 5, 6, 7, 8, 10, 11, 12, 13, 14, 15, 16, 17, 9], [0, 1, 2, 3, 4, 5, 6, 7, 8, 12, 13, 14, 15, 16, 17, 9, 10, 11], [0, 1, 2, 3, 4, 5, 6, 7, 8, 14, 15, 16, 17, 9, 10, 11, 12, 13], [0, 1, 2, 3, 4, 5, 6, 7, 8, 16, 17, 9, 10, 11, 12, 13, 14, 15], [0, 8, 7, 6, 5, 4, 3, 2, 1, 9, 17, 16, 15, 14, 13, 12, 11, 10], [0, 8, 7, 6, 5, 4, 3, 2, 1, 11, 10, 9, 17, 16, 15, 14, 13, 12], [0, 8, 7, 6, 5, 4, 3, 2, 1, 13, 12, 11, 10, 9, 17, 16, 15, 14], [0, 8, 7, 6, 5, 4, 3, 2, 1, 15, 14, 13, 12, 11, 10, 9, 17, 16], [0, 8, 7, 6, 5, 4, 3, 2, 1, 17, 16, 15, 14, 13, 12, 11, 10, 9], [0, 8, 7, 6, 5, 4, 3, 2, 1, 10, 9, 17, 16, 15, 14, 13, 12, 11], [0, 8, 7, 6, 5, 4, 3, 2, 1, 12, 11, 10, 9, 17, 16, 15, 14, 13], [0, 8, 7, 6, 5, 4, 3, 2, 1, 14, 13, 12, 11, 10, 9, 17, 16, 15], [0, 8, 7, 6, 5, 4, 3, 2, 1, 16, 15, 14, 13, 12, 11, 10, 9, 17]], 是, 是, g_dot_x_equals_g_x_g_inverse_is_a_complete_left_action)

Wave6第八層核對=([[0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17], [0, 1, 2, 3, 4, 5, 6, 7, 8, 11, 12, 13, 14, 15, 16, 17, 9, 10], [0, 1, 2, 3, 4, 5, 6, 7, 8, 13, 14, 15, 16, 17, 9, 10, 11, 12], [0, 1, 2, 3, 4, 5, 6, 7, 8, 15, 16, 17, 9, 10, 11, 12, 13, 14], [0, 1, 2, 3, 4, 5, 6, 7, 8, 17, 9, 10, 11, 12, 13, 14, 15, 16], [0, 1, 2, 3, 4, 5, 6, 7, 8, 10, 11, 12, 13, 14, 15, 16, 17, 9], [0, 1, 2, 3, 4, 5, 6, 7, 8, 12, 13, 14, 15, 16, 17, 9, 10, 11], [0, 1, 2, 3, 4, 5, 6, 7, 8, 14, 15, 16, 17, 9, 10, 11, 12, 13], [0, 1, 2, 3, 4, 5, 6, 7, 8, 16, 17, 9, 10, 11, 12, 13, 14, 15], [0, 8, 7, 6, 5, 4, 3, 2, 1, 9, 17, 16, 15, 14, 13, 12, 11, 10], [0, 8, 7, 6, 5, 4, 3, 2, 1, 11, 10, 9, 17, 16, 15, 14, 13, 12], [0, 8, 7, 6, 5, 4, 3, 2, 1, 13, 12, 11, 10, 9, 17, 16, 15, 14], [0, 8, 7, 6, 5, 4, 3, 2, 1, 15, 14, 13, 12, 11, 10, 9, 17, 16], [0, 8, 7, 6, 5, 4, 3, 2, 1, 17, 16, 15, 14, 13, 12, 11, 10, 9], [0, 8, 7, 6, 5, 4, 3, 2, 1, 10, 9, 17, 16, 15, 14, 13, 12, 11], [0, 8, 7, 6, 5, 4, 3, 2, 1, 12, 11, 10, 9, 17, 16, 15, 14, 13], [0, 8, 7, 6, 5, 4, 3, 2, 1, 14, 13, 12, 11, 10, 9, 17, 16, 15], [0, 8, 7, 6, 5, 4, 3, 2, 1, 16, 15, 14, 13, 12, 11, 10, 9, 17]], 是, 是, g_dot_x_equals_g_x_g_inverse_is_a_complete_left_action)；依完整明示資料獨立重算；共軛類是element orbit並形成完整partition；singleton以forall g commute核對；共軛類不是coset或conjugate subgroup；不使用centralizer、class-size公式或類方程。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r03-finite-group-conjugacy-class-0007/)

有限群共軛類 · qf-mod45-conjugacy-action-table · candidate





## 8. 有限群共軛類

由完整Cayley table導出全部conjugation action與orbits。操作=conjugacy-action-table；資料={"group_table":[[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19],[1,2,3,4,5,6,7,8,9,0,11,12,13,14,15,16,17,18,19,10],[2,3,4,5,6,7,8,9,0,1,12,13,14,15,16,17,18,19,10,11],[3,4,5,6,7,8,9,0,1,2,13,14,15,16,17,18,19,10,11,12],[4,5,6,7,8,9,0,1,2,3,14,15,16,17,18,19,10,11,12,13],[5,6,7,8,9,0,1,2,3,4,15,16,17,18,19,10,11,12,13,14],[6,7,8,9,0,1,2,3,4,5,16,17,18,19,10,11,12,13,14,15],[7,8,9,0,1,2,3,4,5,6,17,18,19,10,11,12,13,14,15,16],[8,9,0,1,2,3,4,5,6,7,18,19,10,11,12,13,14,15,16,17],[9,0,1,2,3,4,5,6,7,8,19,10,11,12,13,14,15,16,17,18],[10,19,18,17,16,15,14,13,12,11,0,9,8,7,6,5,4,3,2,1],[11,10,19,18,17,16,15,14,13,12,1,0,9,8,7,6,5,4,3,2],[12,11,10,19,18,17,16,15,14,13,2,1,0,9,8,7,6,5,4,3],[13,12,11,10,19,18,17,16,15,14,3,2,1,0,9,8,7,6,5,4],[14,13,12,11,10,19,18,17,16,15,4,3,2,1,0,9,8,7,6,5],[15,14,13,12,11,10,19,18,17,16,5,4,3,2,1,0,9,8,7,6],[16,15,14,13,12,11,10,19,18,17,6,5,4,3,2,1,0,9,8,7],[17,16,15,14,13,12,11,10,19,18,7,6,5,4,3,2,1,0,9,8],[18,17,16,15,14,13,12,11,10,19,8,7,6,5,4,3,2,1,0,9],[19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0]],"identity":0}。請依 [conjugation_action, identity_action, composition_action, certificate] 欄序回答。

查看答案與解釋([[0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 12, 13, 14, 15, 16, 17, 18, 19, 10, 11], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 14, 15, 16, 17, 18, 19, 10, 11, 12, 13], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 16, 17, 18, 19, 10, 11, 12, 13, 14, 15], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 18, 19, 10, 11, 12, 13, 14, 15, 16, 17], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 12, 13, 14, 15, 16, 17, 18, 19, 10, 11], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 14, 15, 16, 17, 18, 19, 10, 11, 12, 13], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 16, 17, 18, 19, 10, 11, 12, 13, 14, 15], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 18, 19, 10, 11, 12, 13, 14, 15, 16, 17], [0, 9, 8, 7, 6, 5, 4, 3, 2, 1, 10, 19, 18, 17, 16, 15, 14, 13, 12, 11], [0, 9, 8, 7, 6, 5, 4, 3, 2, 1, 12, 11, 10, 19, 18, 17, 16, 15, 14, 13], [0, 9, 8, 7, 6, 5, 4, 3, 2, 1, 14, 13, 12, 11, 10, 19, 18, 17, 16, 15], [0, 9, 8, 7, 6, 5, 4, 3, 2, 1, 16, 15, 14, 13, 12, 11, 10, 19, 18, 17], [0, 9, 8, 7, 6, 5, 4, 3, 2, 1, 18, 17, 16, 15, 14, 13, 12, 11, 10, 19], [0, 9, 8, 7, 6, 5, 4, 3, 2, 1, 10, 19, 18, 17, 16, 15, 14, 13, 12, 11], [0, 9, 8, 7, 6, 5, 4, 3, 2, 1, 12, 11, 10, 19, 18, 17, 16, 15, 14, 13], [0, 9, 8, 7, 6, 5, 4, 3, 2, 1, 14, 13, 12, 11, 10, 19, 18, 17, 16, 15], [0, 9, 8, 7, 6, 5, 4, 3, 2, 1, 16, 15, 14, 13, 12, 11, 10, 19, 18, 17], [0, 9, 8, 7, 6, 5, 4, 3, 2, 1, 18, 17, 16, 15, 14, 13, 12, 11, 10, 19]], 是, 是, g_dot_x_equals_g_x_g_inverse_is_a_complete_left_action)

Wave6第八層核對=([[0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 12, 13, 14, 15, 16, 17, 18, 19, 10, 11], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 14, 15, 16, 17, 18, 19, 10, 11, 12, 13], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 16, 17, 18, 19, 10, 11, 12, 13, 14, 15], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 18, 19, 10, 11, 12, 13, 14, 15, 16, 17], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 12, 13, 14, 15, 16, 17, 18, 19, 10, 11], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 14, 15, 16, 17, 18, 19, 10, 11, 12, 13], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 16, 17, 18, 19, 10, 11, 12, 13, 14, 15], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 18, 19, 10, 11, 12, 13, 14, 15, 16, 17], [0, 9, 8, 7, 6, 5, 4, 3, 2, 1, 10, 19, 18, 17, 16, 15, 14, 13, 12, 11], [0, 9, 8, 7, 6, 5, 4, 3, 2, 1, 12, 11, 10, 19, 18, 17, 16, 15, 14, 13], [0, 9, 8, 7, 6, 5, 4, 3, 2, 1, 14, 13, 12, 11, 10, 19, 18, 17, 16, 15], [0, 9, 8, 7, 6, 5, 4, 3, 2, 1, 16, 15, 14, 13, 12, 11, 10, 19, 18, 17], [0, 9, 8, 7, 6, 5, 4, 3, 2, 1, 18, 17, 16, 15, 14, 13, 12, 11, 10, 19], [0, 9, 8, 7, 6, 5, 4, 3, 2, 1, 10, 19, 18, 17, 16, 15, 14, 13, 12, 11], [0, 9, 8, 7, 6, 5, 4, 3, 2, 1, 12, 11, 10, 19, 18, 17, 16, 15, 14, 13], [0, 9, 8, 7, 6, 5, 4, 3, 2, 1, 14, 13, 12, 11, 10, 19, 18, 17, 16, 15], [0, 9, 8, 7, 6, 5, 4, 3, 2, 1, 16, 15, 14, 13, 12, 11, 10, 19, 18, 17], [0, 9, 8, 7, 6, 5, 4, 3, 2, 1, 18, 17, 16, 15, 14, 13, 12, 11, 10, 19]], 是, 是, g_dot_x_equals_g_x_g_inverse_is_a_complete_left_action)；依完整明示資料獨立重算；共軛類是element orbit並形成完整partition；singleton以forall g commute核對；共軛類不是coset或conjugate subgroup；不使用centralizer、class-size公式或類方程。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r03-finite-group-conjugacy-class-0008/)

有限群共軛類 · qf-mod45-conjugacy-action-table · candidate





## 9. 有限群共軛類

由完整Cayley table導出全部conjugation action與orbits。操作=conjugacy-action-table；資料={"group_table":[[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21],[1,2,3,4,5,6,7,8,9,10,0,12,13,14,15,16,17,18,19,20,21,11],[2,3,4,5,6,7,8,9,10,0,1,13,14,15,16,17,18,19,20,21,11,12],[3,4,5,6,7,8,9,10,0,1,2,14,15,16,17,18,19,20,21,11,12,13],[4,5,6,7,8,9,10,0,1,2,3,15,16,17,18,19,20,21,11,12,13,14],[5,6,7,8,9,10,0,1,2,3,4,16,17,18,19,20,21,11,12,13,14,15],[6,7,8,9,10,0,1,2,3,4,5,17,18,19,20,21,11,12,13,14,15,16],[7,8,9,10,0,1,2,3,4,5,6,18,19,20,21,11,12,13,14,15,16,17],[8,9,10,0,1,2,3,4,5,6,7,19,20,21,11,12,13,14,15,16,17,18],[9,10,0,1,2,3,4,5,6,7,8,20,21,11,12,13,14,15,16,17,18,19],[10,0,1,2,3,4,5,6,7,8,9,21,11,12,13,14,15,16,17,18,19,20],[11,21,20,19,18,17,16,15,14,13,12,0,10,9,8,7,6,5,4,3,2,1],[12,11,21,20,19,18,17,16,15,14,13,1,0,10,9,8,7,6,5,4,3,2],[13,12,11,21,20,19,18,17,16,15,14,2,1,0,10,9,8,7,6,5,4,3],[14,13,12,11,21,20,19,18,17,16,15,3,2,1,0,10,9,8,7,6,5,4],[15,14,13,12,11,21,20,19,18,17,16,4,3,2,1,0,10,9,8,7,6,5],[16,15,14,13,12,11,21,20,19,18,17,5,4,3,2,1,0,10,9,8,7,6],[17,16,15,14,13,12,11,21,20,19,18,6,5,4,3,2,1,0,10,9,8,7],[18,17,16,15,14,13,12,11,21,20,19,7,6,5,4,3,2,1,0,10,9,8],[19,18,17,16,15,14,13,12,11,21,20,8,7,6,5,4,3,2,1,0,10,9],[20,19,18,17,16,15,14,13,12,11,21,9,8,7,6,5,4,3,2,1,0,10],[21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0]],"identity":0}。請依 [conjugation_action, identity_action, composition_action, certificate] 欄序回答。

查看答案與解釋([[0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 13, 14, 15, 16, 17, 18, 19, 20, 21, 11, 12], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 15, 16, 17, 18, 19, 20, 21, 11, 12, 13, 14], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 17, 18, 19, 20, 21, 11, 12, 13, 14, 15, 16], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 19, 20, 21, 11, 12, 13, 14, 15, 16, 17, 18], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 21, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 11], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 14, 15, 16, 17, 18, 19, 20, 21, 11, 12, 13], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 16, 17, 18, 19, 20, 21, 11, 12, 13, 14, 15], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 18, 19, 20, 21, 11, 12, 13, 14, 15, 16, 17], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 20, 21, 11, 12, 13, 14, 15, 16, 17, 18, 19], [0, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 11, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12], [0, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 13, 12, 11, 21, 20, 19, 18, 17, 16, 15, 14], [0, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 15, 14, 13, 12, 11, 21, 20, 19, 18, 17, 16], [0, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 17, 16, 15, 14, 13, 12, 11, 21, 20, 19, 18], [0, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 19, 18, 17, 16, 15, 14, 13, 12, 11, 21, 20], [0, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11], [0, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 12, 11, 21, 20, 19, 18, 17, 16, 15, 14, 13], [0, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 14, 13, 12, 11, 21, 20, 19, 18, 17, 16, 15], [0, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 16, 15, 14, 13, 12, 11, 21, 20, 19, 18, 17], [0, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 18, 17, 16, 15, 14, 13, 12, 11, 21, 20, 19], [0, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 21]], 是, 是, g_dot_x_equals_g_x_g_inverse_is_a_complete_left_action)

Wave6第八層核對=([[0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 13, 14, 15, 16, 17, 18, 19, 20, 21, 11, 12], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 15, 16, 17, 18, 19, 20, 21, 11, 12, 13, 14], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 17, 18, 19, 20, 21, 11, 12, 13, 14, 15, 16], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 19, 20, 21, 11, 12, 13, 14, 15, 16, 17, 18], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 21, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 11], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 14, 15, 16, 17, 18, 19, 20, 21, 11, 12, 13], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 16, 17, 18, 19, 20, 21, 11, 12, 13, 14, 15], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 18, 19, 20, 21, 11, 12, 13, 14, 15, 16, 17], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 20, 21, 11, 12, 13, 14, 15, 16, 17, 18, 19], [0, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 11, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12], [0, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 13, 12, 11, 21, 20, 19, 18, 17, 16, 15, 14], [0, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 15, 14, 13, 12, 11, 21, 20, 19, 18, 17, 16], [0, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 17, 16, 15, 14, 13, 12, 11, 21, 20, 19, 18], [0, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 19, 18, 17, 16, 15, 14, 13, 12, 11, 21, 20], [0, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11], [0, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 12, 11, 21, 20, 19, 18, 17, 16, 15, 14, 13], [0, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 14, 13, 12, 11, 21, 20, 19, 18, 17, 16, 15], [0, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 16, 15, 14, 13, 12, 11, 21, 20, 19, 18, 17], [0, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 18, 17, 16, 15, 14, 13, 12, 11, 21, 20, 19], [0, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 21]], 是, 是, g_dot_x_equals_g_x_g_inverse_is_a_complete_left_action)；依完整明示資料獨立重算；共軛類是element orbit並形成完整partition；singleton以forall g commute核對；共軛類不是coset或conjugate subgroup；不使用centralizer、class-size公式或類方程。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r03-finite-group-conjugacy-class-0009/)

有限群共軛類 · qf-mod45-conjugacy-action-table · candidate





## 10. 有限群共軛類

由完整Cayley table導出全部conjugation action與orbits。操作=conjugacy-action-table；資料={"group_table":[[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23],[1,2,3,4,5,6,7,8,9,10,11,0,13,14,15,16,17,18,19,20,21,22,23,12],[2,3,4,5,6,7,8,9,10,11,0,1,14,15,16,17,18,19,20,21,22,23,12,13],[3,4,5,6,7,8,9,10,11,0,1,2,15,16,17,18,19,20,21,22,23,12,13,14],[4,5,6,7,8,9,10,11,0,1,2,3,16,17,18,19,20,21,22,23,12,13,14,15],[5,6,7,8,9,10,11,0,1,2,3,4,17,18,19,20,21,22,23,12,13,14,15,16],[6,7,8,9,10,11,0,1,2,3,4,5,18,19,20,21,22,23,12,13,14,15,16,17],[7,8,9,10,11,0,1,2,3,4,5,6,19,20,21,22,23,12,13,14,15,16,17,18],[8,9,10,11,0,1,2,3,4,5,6,7,20,21,22,23,12,13,14,15,16,17,18,19],[9,10,11,0,1,2,3,4,5,6,7,8,21,22,23,12,13,14,15,16,17,18,19,20],[10,11,0,1,2,3,4,5,6,7,8,9,22,23,12,13,14,15,16,17,18,19,20,21],[11,0,1,2,3,4,5,6,7,8,9,10,23,12,13,14,15,16,17,18,19,20,21,22],[12,23,22,21,20,19,18,17,16,15,14,13,0,11,10,9,8,7,6,5,4,3,2,1],[13,12,23,22,21,20,19,18,17,16,15,14,1,0,11,10,9,8,7,6,5,4,3,2],[14,13,12,23,22,21,20,19,18,17,16,15,2,1,0,11,10,9,8,7,6,5,4,3],[15,14,13,12,23,22,21,20,19,18,17,16,3,2,1,0,11,10,9,8,7,6,5,4],[16,15,14,13,12,23,22,21,20,19,18,17,4,3,2,1,0,11,10,9,8,7,6,5],[17,16,15,14,13,12,23,22,21,20,19,18,5,4,3,2,1,0,11,10,9,8,7,6],[18,17,16,15,14,13,12,23,22,21,20,19,6,5,4,3,2,1,0,11,10,9,8,7],[19,18,17,16,15,14,13,12,23,22,21,20,7,6,5,4,3,2,1,0,11,10,9,8],[20,19,18,17,16,15,14,13,12,23,22,21,8,7,6,5,4,3,2,1,0,11,10,9],[21,20,19,18,17,16,15,14,13,12,23,22,9,8,7,6,5,4,3,2,1,0,11,10],[22,21,20,19,18,17,16,15,14,13,12,23,10,9,8,7,6,5,4,3,2,1,0,11],[23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0]],"identity":0}。請依 [conjugation_action, identity_action, composition_action, certificate] 欄序回答。

查看答案與解釋([[0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 12, 13], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 16, 17, 18, 19, 20, 21, 22, 23, 12, 13, 14, 15], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 18, 19, 20, 21, 22, 23, 12, 13, 14, 15, 16, 17], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 20, 21, 22, 23, 12, 13, 14, 15, 16, 17, 18, 19], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 22, 23, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 12, 13], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 16, 17, 18, 19, 20, 21, 22, 23, 12, 13, 14, 15], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 18, 19, 20, 21, 22, 23, 12, 13, 14, 15, 16, 17], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 20, 21, 22, 23, 12, 13, 14, 15, 16, 17, 18, 19], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 22, 23, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21], [0, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 12, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13], [0, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 14, 13, 12, 23, 22, 21, 20, 19, 18, 17, 16, 15], [0, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 16, 15, 14, 13, 12, 23, 22, 21, 20, 19, 18, 17], [0, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 18, 17, 16, 15, 14, 13, 12, 23, 22, 21, 20, 19], [0, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 20, 19, 18, 17, 16, 15, 14, 13, 12, 23, 22, 21], [0, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 23], [0, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 12, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13], [0, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 14, 13, 12, 23, 22, 21, 20, 19, 18, 17, 16, 15], [0, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 16, 15, 14, 13, 12, 23, 22, 21, 20, 19, 18, 17], [0, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 18, 17, 16, 15, 14, 13, 12, 23, 22, 21, 20, 19], [0, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 20, 19, 18, 17, 16, 15, 14, 13, 12, 23, 22, 21], [0, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 23]], 是, 是, g_dot_x_equals_g_x_g_inverse_is_a_complete_left_action)

Wave6第八層核對=([[0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 12, 13], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 16, 17, 18, 19, 20, 21, 22, 23, 12, 13, 14, 15], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 18, 19, 20, 21, 22, 23, 12, 13, 14, 15, 16, 17], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 20, 21, 22, 23, 12, 13, 14, 15, 16, 17, 18, 19], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 22, 23, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 12, 13], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 16, 17, 18, 19, 20, 21, 22, 23, 12, 13, 14, 15], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 18, 19, 20, 21, 22, 23, 12, 13, 14, 15, 16, 17], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 20, 21, 22, 23, 12, 13, 14, 15, 16, 17, 18, 19], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 22, 23, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21], [0, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 12, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13], [0, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 14, 13, 12, 23, 22, 21, 20, 19, 18, 17, 16, 15], [0, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 16, 15, 14, 13, 12, 23, 22, 21, 20, 19, 18, 17], [0, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 18, 17, 16, 15, 14, 13, 12, 23, 22, 21, 20, 19], [0, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 20, 19, 18, 17, 16, 15, 14, 13, 12, 23, 22, 21], [0, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 23], [0, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 12, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13], [0, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 14, 13, 12, 23, 22, 21, 20, 19, 18, 17, 16, 15], [0, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 16, 15, 14, 13, 12, 23, 22, 21, 20, 19, 18, 17], [0, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 18, 17, 16, 15, 14, 13, 12, 23, 22, 21, 20, 19], [0, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 20, 19, 18, 17, 16, 15, 14, 13, 12, 23, 22, 21], [0, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 23]], 是, 是, g_dot_x_equals_g_x_g_inverse_is_a_complete_left_action)；依完整明示資料獨立重算；共軛類是element orbit並形成完整partition；singleton以forall g commute核對；共軛類不是coset或conjugate subgroup；不使用centralizer、class-size公式或類方程。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r03-finite-group-conjugacy-class-0010/)

有限群共軛類 · qf-mod45-conjugacy-action-table · candidate





## 11. 有限群共軛類

由完整Cayley table導出全部conjugation action與orbits。操作=conjugacy-action-table；資料={"group_table":[[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25],[1,2,3,4,5,6,7,8,9,10,11,12,0,14,15,16,17,18,19,20,21,22,23,24,25,13],[2,3,4,5,6,7,8,9,10,11,12,0,1,15,16,17,18,19,20,21,22,23,24,25,13,14],[3,4,5,6,7,8,9,10,11,12,0,1,2,16,17,18,19,20,21,22,23,24,25,13,14,15],[4,5,6,7,8,9,10,11,12,0,1,2,3,17,18,19,20,21,22,23,24,25,13,14,15,16],[5,6,7,8,9,10,11,12,0,1,2,3,4,18,19,20,21,22,23,24,25,13,14,15,16,17],[6,7,8,9,10,11,12,0,1,2,3,4,5,19,20,21,22,23,24,25,13,14,15,16,17,18],[7,8,9,10,11,12,0,1,2,3,4,5,6,20,21,22,23,24,25,13,14,15,16,17,18,19],[8,9,10,11,12,0,1,2,3,4,5,6,7,21,22,23,24,25,13,14,15,16,17,18,19,20],[9,10,11,12,0,1,2,3,4,5,6,7,8,22,23,24,25,13,14,15,16,17,18,19,20,21],[10,11,12,0,1,2,3,4,5,6,7,8,9,23,24,25,13,14,15,16,17,18,19,20,21,22],[11,12,0,1,2,3,4,5,6,7,8,9,10,24,25,13,14,15,16,17,18,19,20,21,22,23],[12,0,1,2,3,4,5,6,7,8,9,10,11,25,13,14,15,16,17,18,19,20,21,22,23,24],[13,25,24,23,22,21,20,19,18,17,16,15,14,0,12,11,10,9,8,7,6,5,4,3,2,1],[14,13,25,24,23,22,21,20,19,18,17,16,15,1,0,12,11,10,9,8,7,6,5,4,3,2],[15,14,13,25,24,23,22,21,20,19,18,17,16,2,1,0,12,11,10,9,8,7,6,5,4,3],[16,15,14,13,25,24,23,22,21,20,19,18,17,3,2,1,0,12,11,10,9,8,7,6,5,4],[17,16,15,14,13,25,24,23,22,21,20,19,18,4,3,2,1,0,12,11,10,9,8,7,6,5],[18,17,16,15,14,13,25,24,23,22,21,20,19,5,4,3,2,1,0,12,11,10,9,8,7,6],[19,18,17,16,15,14,13,25,24,23,22,21,20,6,5,4,3,2,1,0,12,11,10,9,8,7],[20,19,18,17,16,15,14,13,25,24,23,22,21,7,6,5,4,3,2,1,0,12,11,10,9,8],[21,20,19,18,17,16,15,14,13,25,24,23,22,8,7,6,5,4,3,2,1,0,12,11,10,9],[22,21,20,19,18,17,16,15,14,13,25,24,23,9,8,7,6,5,4,3,2,1,0,12,11,10],[23,22,21,20,19,18,17,16,15,14,13,25,24,10,9,8,7,6,5,4,3,2,1,0,12,11],[24,23,22,21,20,19,18,17,16,15,14,13,25,11,10,9,8,7,6,5,4,3,2,1,0,12],[25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0]],"identity":0}。請依 [conjugation_action, identity_action, composition_action, certificate] 欄序回答。

查看答案與解釋([[0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 13, 14], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 17, 18, 19, 20, 21, 22, 23, 24, 25, 13, 14, 15, 16], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 19, 20, 21, 22, 23, 24, 25, 13, 14, 15, 16, 17, 18], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 21, 22, 23, 24, 25, 13, 14, 15, 16, 17, 18, 19, 20], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 23, 24, 25, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 25, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 13], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 13, 14, 15], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 18, 19, 20, 21, 22, 23, 24, 25, 13, 14, 15, 16, 17], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 20, 21, 22, 23, 24, 25, 13, 14, 15, 16, 17, 18, 19], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 22, 23, 24, 25, 13, 14, 15, 16, 17, 18, 19, 20, 21], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 24, 25, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23], [0, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 13, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14], [0, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 15, 14, 13, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16], [0, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 17, 16, 15, 14, 13, 25, 24, 23, 22, 21, 20, 19, 18], [0, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 19, 18, 17, 16, 15, 14, 13, 25, 24, 23, 22, 21, 20], [0, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 21, 20, 19, 18, 17, 16, 15, 14, 13, 25, 24, 23, 22], [0, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 25, 24], [0, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13], [0, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 14, 13, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15], [0, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 16, 15, 14, 13, 25, 24, 23, 22, 21, 20, 19, 18, 17], [0, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 18, 17, 16, 15, 14, 13, 25, 24, 23, 22, 21, 20, 19], [0, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 20, 19, 18, 17, 16, 15, 14, 13, 25, 24, 23, 22, 21], [0, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 25, 24, 23], [0, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 25]], 是, 是, g_dot_x_equals_g_x_g_inverse_is_a_complete_left_action)

Wave6第八層核對=([[0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 13, 14], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 17, 18, 19, 20, 21, 22, 23, 24, 25, 13, 14, 15, 16], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 19, 20, 21, 22, 23, 24, 25, 13, 14, 15, 16, 17, 18], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 21, 22, 23, 24, 25, 13, 14, 15, 16, 17, 18, 19, 20], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 23, 24, 25, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 25, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 13], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 13, 14, 15], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 18, 19, 20, 21, 22, 23, 24, 25, 13, 14, 15, 16, 17], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 20, 21, 22, 23, 24, 25, 13, 14, 15, 16, 17, 18, 19], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 22, 23, 24, 25, 13, 14, 15, 16, 17, 18, 19, 20, 21], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 24, 25, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23], [0, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 13, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14], [0, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 15, 14, 13, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16], [0, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 17, 16, 15, 14, 13, 25, 24, 23, 22, 21, 20, 19, 18], [0, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 19, 18, 17, 16, 15, 14, 13, 25, 24, 23, 22, 21, 20], [0, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 21, 20, 19, 18, 17, 16, 15, 14, 13, 25, 24, 23, 22], [0, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 25, 24], [0, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13], [0, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 14, 13, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15], [0, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 16, 15, 14, 13, 25, 24, 23, 22, 21, 20, 19, 18, 17], [0, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 18, 17, 16, 15, 14, 13, 25, 24, 23, 22, 21, 20, 19], [0, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 20, 19, 18, 17, 16, 15, 14, 13, 25, 24, 23, 22, 21], [0, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 25, 24, 23], [0, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 25]], 是, 是, g_dot_x_equals_g_x_g_inverse_is_a_complete_left_action)；依完整明示資料獨立重算；共軛類是element orbit並形成完整partition；singleton以forall g commute核對；共軛類不是coset或conjugate subgroup；不使用centralizer、class-size公式或類方程。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r03-finite-group-conjugacy-class-0011/)

有限群共軛類 · qf-mod45-conjugacy-action-table · candidate





## 12. 有限群共軛類

由完整Cayley table導出全部conjugation action與orbits。操作=conjugacy-action-table；資料={"group_table":[[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27],[1,2,3,4,5,6,7,8,9,10,11,12,13,0,15,16,17,18,19,20,21,22,23,24,25,26,27,14],[2,3,4,5,6,7,8,9,10,11,12,13,0,1,16,17,18,19,20,21,22,23,24,25,26,27,14,15],[3,4,5,6,7,8,9,10,11,12,13,0,1,2,17,18,19,20,21,22,23,24,25,26,27,14,15,16],[4,5,6,7,8,9,10,11,12,13,0,1,2,3,18,19,20,21,22,23,24,25,26,27,14,15,16,17],[5,6,7,8,9,10,11,12,13,0,1,2,3,4,19,20,21,22,23,24,25,26,27,14,15,16,17,18],[6,7,8,9,10,11,12,13,0,1,2,3,4,5,20,21,22,23,24,25,26,27,14,15,16,17,18,19],[7,8,9,10,11,12,13,0,1,2,3,4,5,6,21,22,23,24,25,26,27,14,15,16,17,18,19,20],[8,9,10,11,12,13,0,1,2,3,4,5,6,7,22,23,24,25,26,27,14,15,16,17,18,19,20,21],[9,10,11,12,13,0,1,2,3,4,5,6,7,8,23,24,25,26,27,14,15,16,17,18,19,20,21,22],[10,11,12,13,0,1,2,3,4,5,6,7,8,9,24,25,26,27,14,15,16,17,18,19,20,21,22,23],[11,12,13,0,1,2,3,4,5,6,7,8,9,10,25,26,27,14,15,16,17,18,19,20,21,22,23,24],[12,13,0,1,2,3,4,5,6,7,8,9,10,11,26,27,14,15,16,17,18,19,20,21,22,23,24,25],[13,0,1,2,3,4,5,6,7,8,9,10,11,12,27,14,15,16,17,18,19,20,21,22,23,24,25,26],[14,27,26,25,24,23,22,21,20,19,18,17,16,15,0,13,12,11,10,9,8,7,6,5,4,3,2,1],[15,14,27,26,25,24,23,22,21,20,19,18,17,16,1,0,13,12,11,10,9,8,7,6,5,4,3,2],[16,15,14,27,26,25,24,23,22,21,20,19,18,17,2,1,0,13,12,11,10,9,8,7,6,5,4,3],[17,16,15,14,27,26,25,24,23,22,21,20,19,18,3,2,1,0,13,12,11,10,9,8,7,6,5,4],[18,17,16,15,14,27,26,25,24,23,22,21,20,19,4,3,2,1,0,13,12,11,10,9,8,7,6,5],[19,18,17,16,15,14,27,26,25,24,23,22,21,20,5,4,3,2,1,0,13,12,11,10,9,8,7,6],[20,19,18,17,16,15,14,27,26,25,24,23,22,21,6,5,4,3,2,1,0,13,12,11,10,9,8,7],[21,20,19,18,17,16,15,14,27,26,25,24,23,22,7,6,5,4,3,2,1,0,13,12,11,10,9,8],[22,21,20,19,18,17,16,15,14,27,26,25,24,23,8,7,6,5,4,3,2,1,0,13,12,11,10,9],[23,22,21,20,19,18,17,16,15,14,27,26,25,24,9,8,7,6,5,4,3,2,1,0,13,12,11,10],[24,23,22,21,20,19,18,17,16,15,14,27,26,25,10,9,8,7,6,5,4,3,2,1,0,13,12,11],[25,24,23,22,21,20,19,18,17,16,15,14,27,26,11,10,9,8,7,6,5,4,3,2,1,0,13,12],[26,25,24,23,22,21,20,19,18,17,16,15,14,27,12,11,10,9,8,7,6,5,4,3,2,1,0,13],[27,26,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0]],"identity":0}。請依 [conjugation_action, identity_action, composition_action, certificate] 欄序回答。

查看答案與解釋([[0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 14, 15], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 14, 15, 16, 17], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 20, 21, 22, 23, 24, 25, 26, 27, 14, 15, 16, 17, 18, 19], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 22, 23, 24, 25, 26, 27, 14, 15, 16, 17, 18, 19, 20, 21], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 24, 25, 26, 27, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 26, 27, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 14, 15], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 14, 15, 16, 17], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 20, 21, 22, 23, 24, 25, 26, 27, 14, 15, 16, 17, 18, 19], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 22, 23, 24, 25, 26, 27, 14, 15, 16, 17, 18, 19, 20, 21], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 24, 25, 26, 27, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 26, 27, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25], [0, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 14, 27, 26, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15], [0, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 16, 15, 14, 27, 26, 25, 24, 23, 22, 21, 20, 19, 18, 17], [0, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 18, 17, 16, 15, 14, 27, 26, 25, 24, 23, 22, 21, 20, 19], [0, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 20, 19, 18, 17, 16, 15, 14, 27, 26, 25, 24, 23, 22, 21], [0, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 22, 21, 20, 19, 18, 17, 16, 15, 14, 27, 26, 25, 24, 23], [0, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 27, 26, 25], [0, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 26, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 27], [0, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 14, 27, 26, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15], [0, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 16, 15, 14, 27, 26, 25, 24, 23, 22, 21, 20, 19, 18, 17], [0, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 18, 17, 16, 15, 14, 27, 26, 25, 24, 23, 22, 21, 20, 19], [0, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 20, 19, 18, 17, 16, 15, 14, 27, 26, 25, 24, 23, 22, 21], [0, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 22, 21, 20, 19, 18, 17, 16, 15, 14, 27, 26, 25, 24, 23], [0, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 27, 26, 25], [0, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 26, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 27]], 是, 是, g_dot_x_equals_g_x_g_inverse_is_a_complete_left_action)

Wave6第八層核對=([[0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 14, 15], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 14, 15, 16, 17], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 20, 21, 22, 23, 24, 25, 26, 27, 14, 15, 16, 17, 18, 19], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 22, 23, 24, 25, 26, 27, 14, 15, 16, 17, 18, 19, 20, 21], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 24, 25, 26, 27, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 26, 27, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 14, 15], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 14, 15, 16, 17], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 20, 21, 22, 23, 24, 25, 26, 27, 14, 15, 16, 17, 18, 19], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 22, 23, 24, 25, 26, 27, 14, 15, 16, 17, 18, 19, 20, 21], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 24, 25, 26, 27, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 26, 27, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25], [0, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 14, 27, 26, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15], [0, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 16, 15, 14, 27, 26, 25, 24, 23, 22, 21, 20, 19, 18, 17], [0, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 18, 17, 16, 15, 14, 27, 26, 25, 24, 23, 22, 21, 20, 19], [0, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 20, 19, 18, 17, 16, 15, 14, 27, 26, 25, 24, 23, 22, 21], [0, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 22, 21, 20, 19, 18, 17, 16, 15, 14, 27, 26, 25, 24, 23], [0, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 27, 26, 25], [0, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 26, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 27], [0, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 14, 27, 26, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15], [0, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 16, 15, 14, 27, 26, 25, 24, 23, 22, 21, 20, 19, 18, 17], [0, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 18, 17, 16, 15, 14, 27, 26, 25, 24, 23, 22, 21, 20, 19], [0, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 20, 19, 18, 17, 16, 15, 14, 27, 26, 25, 24, 23, 22, 21], [0, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 22, 21, 20, 19, 18, 17, 16, 15, 14, 27, 26, 25, 24, 23], [0, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 27, 26, 25], [0, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 26, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 27]], 是, 是, g_dot_x_equals_g_x_g_inverse_is_a_complete_left_action)；依完整明示資料獨立重算；共軛類是element orbit並形成完整partition；singleton以forall g commute核對；共軛類不是coset或conjugate subgroup；不使用centralizer、class-size公式或類方程。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r03-finite-group-conjugacy-class-0012/)

有限群共軛類 · qf-mod45-conjugacy-action-table · candidate





## 13. 有限群共軛類

由完整Cayley table導出全部conjugation action與orbits。操作=conjugacy-action-table；資料={"group_table":[[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,0,16,17,18,19,20,21,22,23,24,25,26,27,28,29,15],[2,3,4,5,6,7,8,9,10,11,12,13,14,0,1,17,18,19,20,21,22,23,24,25,26,27,28,29,15,16],[3,4,5,6,7,8,9,10,11,12,13,14,0,1,2,18,19,20,21,22,23,24,25,26,27,28,29,15,16,17],[4,5,6,7,8,9,10,11,12,13,14,0,1,2,3,19,20,21,22,23,24,25,26,27,28,29,15,16,17,18],[5,6,7,8,9,10,11,12,13,14,0,1,2,3,4,20,21,22,23,24,25,26,27,28,29,15,16,17,18,19],[6,7,8,9,10,11,12,13,14,0,1,2,3,4,5,21,22,23,24,25,26,27,28,29,15,16,17,18,19,20],[7,8,9,10,11,12,13,14,0,1,2,3,4,5,6,22,23,24,25,26,27,28,29,15,16,17,18,19,20,21],[8,9,10,11,12,13,14,0,1,2,3,4,5,6,7,23,24,25,26,27,28,29,15,16,17,18,19,20,21,22],[9,10,11,12,13,14,0,1,2,3,4,5,6,7,8,24,25,26,27,28,29,15,16,17,18,19,20,21,22,23],[10,11,12,13,14,0,1,2,3,4,5,6,7,8,9,25,26,27,28,29,15,16,17,18,19,20,21,22,23,24],[11,12,13,14,0,1,2,3,4,5,6,7,8,9,10,26,27,28,29,15,16,17,18,19,20,21,22,23,24,25],[12,13,14,0,1,2,3,4,5,6,7,8,9,10,11,27,28,29,15,16,17,18,19,20,21,22,23,24,25,26],[13,14,0,1,2,3,4,5,6,7,8,9,10,11,12,28,29,15,16,17,18,19,20,21,22,23,24,25,26,27],[14,0,1,2,3,4,5,6,7,8,9,10,11,12,13,29,15,16,17,18,19,20,21,22,23,24,25,26,27,28],[15,29,28,27,26,25,24,23,22,21,20,19,18,17,16,0,14,13,12,11,10,9,8,7,6,5,4,3,2,1],[16,15,29,28,27,26,25,24,23,22,21,20,19,18,17,1,0,14,13,12,11,10,9,8,7,6,5,4,3,2],[17,16,15,29,28,27,26,25,24,23,22,21,20,19,18,2,1,0,14,13,12,11,10,9,8,7,6,5,4,3],[18,17,16,15,29,28,27,26,25,24,23,22,21,20,19,3,2,1,0,14,13,12,11,10,9,8,7,6,5,4],[19,18,17,16,15,29,28,27,26,25,24,23,22,21,20,4,3,2,1,0,14,13,12,11,10,9,8,7,6,5],[20,19,18,17,16,15,29,28,27,26,25,24,23,22,21,5,4,3,2,1,0,14,13,12,11,10,9,8,7,6],[21,20,19,18,17,16,15,29,28,27,26,25,24,23,22,6,5,4,3,2,1,0,14,13,12,11,10,9,8,7],[22,21,20,19,18,17,16,15,29,28,27,26,25,24,23,7,6,5,4,3,2,1,0,14,13,12,11,10,9,8],[23,22,21,20,19,18,17,16,15,29,28,27,26,25,24,8,7,6,5,4,3,2,1,0,14,13,12,11,10,9],[24,23,22,21,20,19,18,17,16,15,29,28,27,26,25,9,8,7,6,5,4,3,2,1,0,14,13,12,11,10],[25,24,23,22,21,20,19,18,17,16,15,29,28,27,26,10,9,8,7,6,5,4,3,2,1,0,14,13,12,11],[26,25,24,23,22,21,20,19,18,17,16,15,29,28,27,11,10,9,8,7,6,5,4,3,2,1,0,14,13,12],[27,26,25,24,23,22,21,20,19,18,17,16,15,29,28,12,11,10,9,8,7,6,5,4,3,2,1,0,14,13],[28,27,26,25,24,23,22,21,20,19,18,17,16,15,29,13,12,11,10,9,8,7,6,5,4,3,2,1,0,14],[29,28,27,26,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0]],"identity":0}。請依 [conjugation_action, identity_action, composition_action, certificate] 欄序回答。

查看答案與解釋([[0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 15, 16], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 15, 16, 17, 18], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 21, 22, 23, 24, 25, 26, 27, 28, 29, 15, 16, 17, 18, 19, 20], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 23, 24, 25, 26, 27, 28, 29, 15, 16, 17, 18, 19, 20, 21, 22], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 25, 26, 27, 28, 29, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 27, 28, 29, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 29, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 15], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 15, 16, 17], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 15, 16, 17, 18, 19], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 22, 23, 24, 25, 26, 27, 28, 29, 15, 16, 17, 18, 19, 20, 21], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 24, 25, 26, 27, 28, 29, 15, 16, 17, 18, 19, 20, 21, 22, 23], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 26, 27, 28, 29, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 28, 29, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27], [0, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 15, 29, 28, 27, 26, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16], [0, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 17, 16, 15, 29, 28, 27, 26, 25, 24, 23, 22, 21, 20, 19, 18], [0, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 19, 18, 17, 16, 15, 29, 28, 27, 26, 25, 24, 23, 22, 21, 20], [0, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 21, 20, 19, 18, 17, 16, 15, 29, 28, 27, 26, 25, 24, 23, 22], [0, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 23, 22, 21, 20, 19, 18, 17, 16, 15, 29, 28, 27, 26, 25, 24], [0, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 29, 28, 27, 26], [0, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 27, 26, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 29, 28], [0, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 29, 28, 27, 26, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15], [0, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 16, 15, 29, 28, 27, 26, 25, 24, 23, 22, 21, 20, 19, 18, 17], [0, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 18, 17, 16, 15, 29, 28, 27, 26, 25, 24, 23, 22, 21, 20, 19], [0, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 20, 19, 18, 17, 16, 15, 29, 28, 27, 26, 25, 24, 23, 22, 21], [0, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 22, 21, 20, 19, 18, 17, 16, 15, 29, 28, 27, 26, 25, 24, 23], [0, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 29, 28, 27, 26, 25], [0, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 26, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 29, 28, 27], [0, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 28, 27, 26, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 29]], 是, 是, g_dot_x_equals_g_x_g_inverse_is_a_complete_left_action)

Wave6第八層核對=([[0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 15, 16], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 15, 16, 17, 18], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 21, 22, 23, 24, 25, 26, 27, 28, 29, 15, 16, 17, 18, 19, 20], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 23, 24, 25, 26, 27, 28, 29, 15, 16, 17, 18, 19, 20, 21, 22], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 25, 26, 27, 28, 29, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 27, 28, 29, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 29, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 15], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 15, 16, 17], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 15, 16, 17, 18, 19], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 22, 23, 24, 25, 26, 27, 28, 29, 15, 16, 17, 18, 19, 20, 21], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 24, 25, 26, 27, 28, 29, 15, 16, 17, 18, 19, 20, 21, 22, 23], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 26, 27, 28, 29, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 28, 29, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27], [0, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 15, 29, 28, 27, 26, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16], [0, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 17, 16, 15, 29, 28, 27, 26, 25, 24, 23, 22, 21, 20, 19, 18], [0, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 19, 18, 17, 16, 15, 29, 28, 27, 26, 25, 24, 23, 22, 21, 20], [0, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 21, 20, 19, 18, 17, 16, 15, 29, 28, 27, 26, 25, 24, 23, 22], [0, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 23, 22, 21, 20, 19, 18, 17, 16, 15, 29, 28, 27, 26, 25, 24], [0, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 29, 28, 27, 26], [0, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 27, 26, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 29, 28], [0, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 29, 28, 27, 26, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15], [0, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 16, 15, 29, 28, 27, 26, 25, 24, 23, 22, 21, 20, 19, 18, 17], [0, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 18, 17, 16, 15, 29, 28, 27, 26, 25, 24, 23, 22, 21, 20, 19], [0, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 20, 19, 18, 17, 16, 15, 29, 28, 27, 26, 25, 24, 23, 22, 21], [0, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 22, 21, 20, 19, 18, 17, 16, 15, 29, 28, 27, 26, 25, 24, 23], [0, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 29, 28, 27, 26, 25], [0, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 26, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 29, 28, 27], [0, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 28, 27, 26, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 29]], 是, 是, g_dot_x_equals_g_x_g_inverse_is_a_complete_left_action)；依完整明示資料獨立重算；共軛類是element orbit並形成完整partition；singleton以forall g commute核對；共軛類不是coset或conjugate subgroup；不使用centralizer、class-size公式或類方程。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r03-finite-group-conjugacy-class-0013/)

有限群共軛類 · qf-mod45-conjugacy-action-table · candidate





## 14. 有限群共軛類

由完整Cayley table導出全部conjugation action與orbits。操作=conjugacy-action-table；資料={"group_table":[[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,0,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,16],[2,3,4,5,6,7,8,9,10,11,12,13,14,15,0,1,18,19,20,21,22,23,24,25,26,27,28,29,30,31,16,17],[3,4,5,6,7,8,9,10,11,12,13,14,15,0,1,2,19,20,21,22,23,24,25,26,27,28,29,30,31,16,17,18],[4,5,6,7,8,9,10,11,12,13,14,15,0,1,2,3,20,21,22,23,24,25,26,27,28,29,30,31,16,17,18,19],[5,6,7,8,9,10,11,12,13,14,15,0,1,2,3,4,21,22,23,24,25,26,27,28,29,30,31,16,17,18,19,20],[6,7,8,9,10,11,12,13,14,15,0,1,2,3,4,5,22,23,24,25,26,27,28,29,30,31,16,17,18,19,20,21],[7,8,9,10,11,12,13,14,15,0,1,2,3,4,5,6,23,24,25,26,27,28,29,30,31,16,17,18,19,20,21,22],[8,9,10,11,12,13,14,15,0,1,2,3,4,5,6,7,24,25,26,27,28,29,30,31,16,17,18,19,20,21,22,23],[9,10,11,12,13,14,15,0,1,2,3,4,5,6,7,8,25,26,27,28,29,30,31,16,17,18,19,20,21,22,23,24],[10,11,12,13,14,15,0,1,2,3,4,5,6,7,8,9,26,27,28,29,30,31,16,17,18,19,20,21,22,23,24,25],[11,12,13,14,15,0,1,2,3,4,5,6,7,8,9,10,27,28,29,30,31,16,17,18,19,20,21,22,23,24,25,26],[12,13,14,15,0,1,2,3,4,5,6,7,8,9,10,11,28,29,30,31,16,17,18,19,20,21,22,23,24,25,26,27],[13,14,15,0,1,2,3,4,5,6,7,8,9,10,11,12,29,30,31,16,17,18,19,20,21,22,23,24,25,26,27,28],[14,15,0,1,2,3,4,5,6,7,8,9,10,11,12,13,30,31,16,17,18,19,20,21,22,23,24,25,26,27,28,29],[15,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,31,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30],[16,31,30,29,28,27,26,25,24,23,22,21,20,19,18,17,0,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1],[17,16,31,30,29,28,27,26,25,24,23,22,21,20,19,18,1,0,15,14,13,12,11,10,9,8,7,6,5,4,3,2],[18,17,16,31,30,29,28,27,26,25,24,23,22,21,20,19,2,1,0,15,14,13,12,11,10,9,8,7,6,5,4,3],[19,18,17,16,31,30,29,28,27,26,25,24,23,22,21,20,3,2,1,0,15,14,13,12,11,10,9,8,7,6,5,4],[20,19,18,17,16,31,30,29,28,27,26,25,24,23,22,21,4,3,2,1,0,15,14,13,12,11,10,9,8,7,6,5],[21,20,19,18,17,16,31,30,29,28,27,26,25,24,23,22,5,4,3,2,1,0,15,14,13,12,11,10,9,8,7,6],[22,21,20,19,18,17,16,31,30,29,28,27,26,25,24,23,6,5,4,3,2,1,0,15,14,13,12,11,10,9,8,7],[23,22,21,20,19,18,17,16,31,30,29,28,27,26,25,24,7,6,5,4,3,2,1,0,15,14,13,12,11,10,9,8],[24,23,22,21,20,19,18,17,16,31,30,29,28,27,26,25,8,7,6,5,4,3,2,1,0,15,14,13,12,11,10,9],[25,24,23,22,21,20,19,18,17,16,31,30,29,28,27,26,9,8,7,6,5,4,3,2,1,0,15,14,13,12,11,10],[26,25,24,23,22,21,20,19,18,17,16,31,30,29,28,27,10,9,8,7,6,5,4,3,2,1,0,15,14,13,12,11],[27,26,25,24,23,22,21,20,19,18,17,16,31,30,29,28,11,10,9,8,7,6,5,4,3,2,1,0,15,14,13,12],[28,27,26,25,24,23,22,21,20,19,18,17,16,31,30,29,12,11,10,9,8,7,6,5,4,3,2,1,0,15,14,13],[29,28,27,26,25,24,23,22,21,20,19,18,17,16,31,30,13,12,11,10,9,8,7,6,5,4,3,2,1,0,15,14],[30,29,28,27,26,25,24,23,22,21,20,19,18,17,16,31,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0,15],[31,30,29,28,27,26,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0]],"identity":0}。請依 [conjugation_action, identity_action, composition_action, certificate] 欄序回答。

查看答案與解釋([[0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 16, 17], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 16, 17, 18, 19], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 16, 17, 18, 19, 20, 21], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 24, 25, 26, 27, 28, 29, 30, 31, 16, 17, 18, 19, 20, 21, 22, 23], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 26, 27, 28, 29, 30, 31, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 28, 29, 30, 31, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 30, 31, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 16, 17], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 16, 17, 18, 19], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 16, 17, 18, 19, 20, 21], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 24, 25, 26, 27, 28, 29, 30, 31, 16, 17, 18, 19, 20, 21, 22, 23], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 26, 27, 28, 29, 30, 31, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 28, 29, 30, 31, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 30, 31, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29], [0, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 16, 31, 30, 29, 28, 27, 26, 25, 24, 23, 22, 21, 20, 19, 18, 17], [0, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 18, 17, 16, 31, 30, 29, 28, 27, 26, 25, 24, 23, 22, 21, 20, 19], [0, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 20, 19, 18, 17, 16, 31, 30, 29, 28, 27, 26, 25, 24, 23, 22, 21], [0, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 22, 21, 20, 19, 18, 17, 16, 31, 30, 29, 28, 27, 26, 25, 24, 23], [0, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 24, 23, 22, 21, 20, 19, 18, 17, 16, 31, 30, 29, 28, 27, 26, 25], [0, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 26, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 31, 30, 29, 28, 27], [0, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 28, 27, 26, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 31, 30, 29], [0, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 30, 29, 28, 27, 26, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 31], [0, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 16, 31, 30, 29, 28, 27, 26, 25, 24, 23, 22, 21, 20, 19, 18, 17], [0, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 18, 17, 16, 31, 30, 29, 28, 27, 26, 25, 24, 23, 22, 21, 20, 19], [0, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 20, 19, 18, 17, 16, 31, 30, 29, 28, 27, 26, 25, 24, 23, 22, 21], [0, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 22, 21, 20, 19, 18, 17, 16, 31, 30, 29, 28, 27, 26, 25, 24, 23], [0, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 24, 23, 22, 21, 20, 19, 18, 17, 16, 31, 30, 29, 28, 27, 26, 25], [0, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 26, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 31, 30, 29, 28, 27], [0, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 28, 27, 26, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 31, 30, 29], [0, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 30, 29, 28, 27, 26, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 31]], 是, 是, g_dot_x_equals_g_x_g_inverse_is_a_complete_left_action)

Wave6第八層核對=([[0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 16, 17], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 16, 17, 18, 19], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 16, 17, 18, 19, 20, 21], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 24, 25, 26, 27, 28, 29, 30, 31, 16, 17, 18, 19, 20, 21, 22, 23], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 26, 27, 28, 29, 30, 31, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 28, 29, 30, 31, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 30, 31, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 16, 17], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 16, 17, 18, 19], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 16, 17, 18, 19, 20, 21], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 24, 25, 26, 27, 28, 29, 30, 31, 16, 17, 18, 19, 20, 21, 22, 23], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 26, 27, 28, 29, 30, 31, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 28, 29, 30, 31, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 30, 31, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29], [0, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 16, 31, 30, 29, 28, 27, 26, 25, 24, 23, 22, 21, 20, 19, 18, 17], [0, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 18, 17, 16, 31, 30, 29, 28, 27, 26, 25, 24, 23, 22, 21, 20, 19], [0, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 20, 19, 18, 17, 16, 31, 30, 29, 28, 27, 26, 25, 24, 23, 22, 21], [0, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 22, 21, 20, 19, 18, 17, 16, 31, 30, 29, 28, 27, 26, 25, 24, 23], [0, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 24, 23, 22, 21, 20, 19, 18, 17, 16, 31, 30, 29, 28, 27, 26, 25], [0, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 26, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 31, 30, 29, 28, 27], [0, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 28, 27, 26, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 31, 30, 29], [0, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 30, 29, 28, 27, 26, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 31], [0, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 16, 31, 30, 29, 28, 27, 26, 25, 24, 23, 22, 21, 20, 19, 18, 17], [0, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 18, 17, 16, 31, 30, 29, 28, 27, 26, 25, 24, 23, 22, 21, 20, 19], [0, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 20, 19, 18, 17, 16, 31, 30, 29, 28, 27, 26, 25, 24, 23, 22, 21], [0, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 22, 21, 20, 19, 18, 17, 16, 31, 30, 29, 28, 27, 26, 25, 24, 23], [0, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 24, 23, 22, 21, 20, 19, 18, 17, 16, 31, 30, 29, 28, 27, 26, 25], [0, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 26, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 31, 30, 29, 28, 27], [0, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 28, 27, 26, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 31, 30, 29], [0, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 30, 29, 28, 27, 26, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 31]], 是, 是, g_dot_x_equals_g_x_g_inverse_is_a_complete_left_action)；依完整明示資料獨立重算；共軛類是element orbit並形成完整partition；singleton以forall g commute核對；共軛類不是coset或conjugate subgroup；不使用centralizer、class-size公式或類方程。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r03-finite-group-conjugacy-class-0014/)

有限群共軛類 · qf-mod45-conjugacy-action-table · candidate





## 15. 有限群共軛類

由完整Cayley table導出全部conjugation action與orbits。操作=conjugacy-action-table；資料={"group_table":[[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,0,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,17],[2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,0,1,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,17,18],[3,4,5,6,7,8,9,10,11,12,13,14,15,16,0,1,2,20,21,22,23,24,25,26,27,28,29,30,31,32,33,17,18,19],[4,5,6,7,8,9,10,11,12,13,14,15,16,0,1,2,3,21,22,23,24,25,26,27,28,29,30,31,32,33,17,18,19,20],[5,6,7,8,9,10,11,12,13,14,15,16,0,1,2,3,4,22,23,24,25,26,27,28,29,30,31,32,33,17,18,19,20,21],[6,7,8,9,10,11,12,13,14,15,16,0,1,2,3,4,5,23,24,25,26,27,28,29,30,31,32,33,17,18,19,20,21,22],[7,8,9,10,11,12,13,14,15,16,0,1,2,3,4,5,6,24,25,26,27,28,29,30,31,32,33,17,18,19,20,21,22,23],[8,9,10,11,12,13,14,15,16,0,1,2,3,4,5,6,7,25,26,27,28,29,30,31,32,33,17,18,19,20,21,22,23,24],[9,10,11,12,13,14,15,16,0,1,2,3,4,5,6,7,8,26,27,28,29,30,31,32,33,17,18,19,20,21,22,23,24,25],[10,11,12,13,14,15,16,0,1,2,3,4,5,6,7,8,9,27,28,29,30,31,32,33,17,18,19,20,21,22,23,24,25,26],[11,12,13,14,15,16,0,1,2,3,4,5,6,7,8,9,10,28,29,30,31,32,33,17,18,19,20,21,22,23,24,25,26,27],[12,13,14,15,16,0,1,2,3,4,5,6,7,8,9,10,11,29,30,31,32,33,17,18,19,20,21,22,23,24,25,26,27,28],[13,14,15,16,0,1,2,3,4,5,6,7,8,9,10,11,12,30,31,32,33,17,18,19,20,21,22,23,24,25,26,27,28,29],[14,15,16,0,1,2,3,4,5,6,7,8,9,10,11,12,13,31,32,33,17,18,19,20,21,22,23,24,25,26,27,28,29,30],[15,16,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,32,33,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31],[16,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,33,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32],[17,33,32,31,30,29,28,27,26,25,24,23,22,21,20,19,18,0,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1],[18,17,33,32,31,30,29,28,27,26,25,24,23,22,21,20,19,1,0,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2],[19,18,17,33,32,31,30,29,28,27,26,25,24,23,22,21,20,2,1,0,16,15,14,13,12,11,10,9,8,7,6,5,4,3],[20,19,18,17,33,32,31,30,29,28,27,26,25,24,23,22,21,3,2,1,0,16,15,14,13,12,11,10,9,8,7,6,5,4],[21,20,19,18,17,33,32,31,30,29,28,27,26,25,24,23,22,4,3,2,1,0,16,15,14,13,12,11,10,9,8,7,6,5],[22,21,20,19,18,17,33,32,31,30,29,28,27,26,25,24,23,5,4,3,2,1,0,16,15,14,13,12,11,10,9,8,7,6],[23,22,21,20,19,18,17,33,32,31,30,29,28,27,26,25,24,6,5,4,3,2,1,0,16,15,14,13,12,11,10,9,8,7],[24,23,22,21,20,19,18,17,33,32,31,30,29,28,27,26,25,7,6,5,4,3,2,1,0,16,15,14,13,12,11,10,9,8],[25,24,23,22,21,20,19,18,17,33,32,31,30,29,28,27,26,8,7,6,5,4,3,2,1,0,16,15,14,13,12,11,10,9],[26,25,24,23,22,21,20,19,18,17,33,32,31,30,29,28,27,9,8,7,6,5,4,3,2,1,0,16,15,14,13,12,11,10],[27,26,25,24,23,22,21,20,19,18,17,33,32,31,30,29,28,10,9,8,7,6,5,4,3,2,1,0,16,15,14,13,12,11],[28,27,26,25,24,23,22,21,20,19,18,17,33,32,31,30,29,11,10,9,8,7,6,5,4,3,2,1,0,16,15,14,13,12],[29,28,27,26,25,24,23,22,21,20,19,18,17,33,32,31,30,12,11,10,9,8,7,6,5,4,3,2,1,0,16,15,14,13],[30,29,28,27,26,25,24,23,22,21,20,19,18,17,33,32,31,13,12,11,10,9,8,7,6,5,4,3,2,1,0,16,15,14],[31,30,29,28,27,26,25,24,23,22,21,20,19,18,17,33,32,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0,16,15],[32,31,30,29,28,27,26,25,24,23,22,21,20,19,18,17,33,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0,16],[33,32,31,30,29,28,27,26,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0]],"identity":0}。請依 [conjugation_action, identity_action, composition_action, certificate] 欄序回答。

查看答案與解釋([[0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 17, 18], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 17, 18, 19, 20], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 17, 18, 19, 20, 21, 22], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 25, 26, 27, 28, 29, 30, 31, 32, 33, 17, 18, 19, 20, 21, 22, 23, 24], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 27, 28, 29, 30, 31, 32, 33, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 29, 30, 31, 32, 33, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 31, 32, 33, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 33, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 17], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 17, 18, 19], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 17, 18, 19, 20, 21], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 17, 18, 19, 20, 21, 22, 23], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 26, 27, 28, 29, 30, 31, 32, 33, 17, 18, 19, 20, 21, 22, 23, 24, 25], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 28, 29, 30, 31, 32, 33, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 30, 31, 32, 33, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 32, 33, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31], [0, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 17, 33, 32, 31, 30, 29, 28, 27, 26, 25, 24, 23, 22, 21, 20, 19, 18], [0, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 19, 18, 17, 33, 32, 31, 30, 29, 28, 27, 26, 25, 24, 23, 22, 21, 20], [0, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 21, 20, 19, 18, 17, 33, 32, 31, 30, 29, 28, 27, 26, 25, 24, 23, 22], [0, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 23, 22, 21, 20, 19, 18, 17, 33, 32, 31, 30, 29, 28, 27, 26, 25, 24], [0, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 25, 24, 23, 22, 21, 20, 19, 18, 17, 33, 32, 31, 30, 29, 28, 27, 26], [0, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 27, 26, 25, 24, 23, 22, 21, 20, 19, 18, 17, 33, 32, 31, 30, 29, 28], [0, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 29, 28, 27, 26, 25, 24, 23, 22, 21, 20, 19, 18, 17, 33, 32, 31, 30], [0, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 31, 30, 29, 28, 27, 26, 25, 24, 23, 22, 21, 20, 19, 18, 17, 33, 32], [0, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 33, 32, 31, 30, 29, 28, 27, 26, 25, 24, 23, 22, 21, 20, 19, 18, 17], [0, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 18, 17, 33, 32, 31, 30, 29, 28, 27, 26, 25, 24, 23, 22, 21, 20, 19], [0, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 20, 19, 18, 17, 33, 32, 31, 30, 29, 28, 27, 26, 25, 24, 23, 22, 21], [0, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 22, 21, 20, 19, 18, 17, 33, 32, 31, 30, 29, 28, 27, 26, 25, 24, 23], [0, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 24, 23, 22, 21, 20, 19, 18, 17, 33, 32, 31, 30, 29, 28, 27, 26, 25], [0, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 26, 25, 24, 23, 22, 21, 20, 19, 18, 17, 33, 32, 31, 30, 29, 28, 27], [0, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 28, 27, 26, 25, 24, 23, 22, 21, 20, 19, 18, 17, 33, 32, 31, 30, 29], [0, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 30, 29, 28, 27, 26, 25, 24, 23, 22, 21, 20, 19, 18, 17, 33, 32, 31], [0, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 32, 31, 30, 29, 28, 27, 26, 25, 24, 23, 22, 21, 20, 19, 18, 17, 33]], 是, 是, g_dot_x_equals_g_x_g_inverse_is_a_complete_left_action)

Wave6第八層核對=([[0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 17, 18], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 17, 18, 19, 20], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 17, 18, 19, 20, 21, 22], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 25, 26, 27, 28, 29, 30, 31, 32, 33, 17, 18, 19, 20, 21, 22, 23, 24], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 27, 28, 29, 30, 31, 32, 33, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 29, 30, 31, 32, 33, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 31, 32, 33, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 33, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 17], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 17, 18, 19], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 17, 18, 19, 20, 21], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 17, 18, 19, 20, 21, 22, 23], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 26, 27, 28, 29, 30, 31, 32, 33, 17, 18, 19, 20, 21, 22, 23, 24, 25], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 28, 29, 30, 31, 32, 33, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 30, 31, 32, 33, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 32, 33, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31], [0, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 17, 33, 32, 31, 30, 29, 28, 27, 26, 25, 24, 23, 22, 21, 20, 19, 18], [0, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 19, 18, 17, 33, 32, 31, 30, 29, 28, 27, 26, 25, 24, 23, 22, 21, 20], [0, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 21, 20, 19, 18, 17, 33, 32, 31, 30, 29, 28, 27, 26, 25, 24, 23, 22], [0, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 23, 22, 21, 20, 19, 18, 17, 33, 32, 31, 30, 29, 28, 27, 26, 25, 24], [0, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 25, 24, 23, 22, 21, 20, 19, 18, 17, 33, 32, 31, 30, 29, 28, 27, 26], [0, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 27, 26, 25, 24, 23, 22, 21, 20, 19, 18, 17, 33, 32, 31, 30, 29, 28], [0, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 29, 28, 27, 26, 25, 24, 23, 22, 21, 20, 19, 18, 17, 33, 32, 31, 30], [0, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 31, 30, 29, 28, 27, 26, 25, 24, 23, 22, 21, 20, 19, 18, 17, 33, 32], [0, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 33, 32, 31, 30, 29, 28, 27, 26, 25, 24, 23, 22, 21, 20, 19, 18, 17], [0, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 18, 17, 33, 32, 31, 30, 29, 28, 27, 26, 25, 24, 23, 22, 21, 20, 19], [0, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 20, 19, 18, 17, 33, 32, 31, 30, 29, 28, 27, 26, 25, 24, 23, 22, 21], [0, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 22, 21, 20, 19, 18, 17, 33, 32, 31, 30, 29, 28, 27, 26, 25, 24, 23], [0, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 24, 23, 22, 21, 20, 19, 18, 17, 33, 32, 31, 30, 29, 28, 27, 26, 25], [0, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 26, 25, 24, 23, 22, 21, 20, 19, 18, 17, 33, 32, 31, 30, 29, 28, 27], [0, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 28, 27, 26, 25, 24, 23, 22, 21, 20, 19, 18, 17, 33, 32, 31, 30, 29], [0, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 30, 29, 28, 27, 26, 25, 24, 23, 22, 21, 20, 19, 18, 17, 33, 32, 31], [0, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 32, 31, 30, 29, 28, 27, 26, 25, 24, 23, 22, 21, 20, 19, 18, 17, 33]], 是, 是, g_dot_x_equals_g_x_g_inverse_is_a_complete_left_action)；依完整明示資料獨立重算；共軛類是element orbit並形成完整partition；singleton以forall g commute核對；共軛類不是coset或conjugate subgroup；不使用centralizer、class-size公式或類方程。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r03-finite-group-conjugacy-class-0015/)

有限群共軛類 · qf-mod45-conjugacy-action-table · candidate





## 16. 有限群共軛類

由完整Cayley table導出全部conjugation action與orbits。操作=conjugacy-action-table；資料={"group_table":[[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,0,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,18],[2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,0,1,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,18,19],[3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,0,1,2,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,18,19,20],[4,5,6,7,8,9,10,11,12,13,14,15,16,17,0,1,2,3,22,23,24,25,26,27,28,29,30,31,32,33,34,35,18,19,20,21],[5,6,7,8,9,10,11,12,13,14,15,16,17,0,1,2,3,4,23,24,25,26,27,28,29,30,31,32,33,34,35,18,19,20,21,22],[6,7,8,9,10,11,12,13,14,15,16,17,0,1,2,3,4,5,24,25,26,27,28,29,30,31,32,33,34,35,18,19,20,21,22,23],[7,8,9,10,11,12,13,14,15,16,17,0,1,2,3,4,5,6,25,26,27,28,29,30,31,32,33,34,35,18,19,20,21,22,23,24],[8,9,10,11,12,13,14,15,16,17,0,1,2,3,4,5,6,7,26,27,28,29,30,31,32,33,34,35,18,19,20,21,22,23,24,25],[9,10,11,12,13,14,15,16,17,0,1,2,3,4,5,6,7,8,27,28,29,30,31,32,33,34,35,18,19,20,21,22,23,24,25,26],[10,11,12,13,14,15,16,17,0,1,2,3,4,5,6,7,8,9,28,29,30,31,32,33,34,35,18,19,20,21,22,23,24,25,26,27],[11,12,13,14,15,16,17,0,1,2,3,4,5,6,7,8,9,10,29,30,31,32,33,34,35,18,19,20,21,22,23,24,25,26,27,28],[12,13,14,15,16,17,0,1,2,3,4,5,6,7,8,9,10,11,30,31,32,33,34,35,18,19,20,21,22,23,24,25,26,27,28,29],[13,14,15,16,17,0,1,2,3,4,5,6,7,8,9,10,11,12,31,32,33,34,35,18,19,20,21,22,23,24,25,26,27,28,29,30],[14,15,16,17,0,1,2,3,4,5,6,7,8,9,10,11,12,13,32,33,34,35,18,19,20,21,22,23,24,25,26,27,28,29,30,31],[15,16,17,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,33,34,35,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32],[16,17,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,34,35,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33],[17,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,35,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34],[18,35,34,33,32,31,30,29,28,27,26,25,24,23,22,21,20,19,0,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1],[19,18,35,34,33,32,31,30,29,28,27,26,25,24,23,22,21,20,1,0,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2],[20,19,18,35,34,33,32,31,30,29,28,27,26,25,24,23,22,21,2,1,0,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3],[21,20,19,18,35,34,33,32,31,30,29,28,27,26,25,24,23,22,3,2,1,0,17,16,15,14,13,12,11,10,9,8,7,6,5,4],[22,21,20,19,18,35,34,33,32,31,30,29,28,27,26,25,24,23,4,3,2,1,0,17,16,15,14,13,12,11,10,9,8,7,6,5],[23,22,21,20,19,18,35,34,33,32,31,30,29,28,27,26,25,24,5,4,3,2,1,0,17,16,15,14,13,12,11,10,9,8,7,6],[24,23,22,21,20,19,18,35,34,33,32,31,30,29,28,27,26,25,6,5,4,3,2,1,0,17,16,15,14,13,12,11,10,9,8,7],[25,24,23,22,21,20,19,18,35,34,33,32,31,30,29,28,27,26,7,6,5,4,3,2,1,0,17,16,15,14,13,12,11,10,9,8],[26,25,24,23,22,21,20,19,18,35,34,33,32,31,30,29,28,27,8,7,6,5,4,3,2,1,0,17,16,15,14,13,12,11,10,9],[27,26,25,24,23,22,21,20,19,18,35,34,33,32,31,30,29,28,9,8,7,6,5,4,3,2,1,0,17,16,15,14,13,12,11,10],[28,27,26,25,24,23,22,21,20,19,18,35,34,33,32,31,30,29,10,9,8,7,6,5,4,3,2,1,0,17,16,15,14,13,12,11],[29,28,27,26,25,24,23,22,21,20,19,18,35,34,33,32,31,30,11,10,9,8,7,6,5,4,3,2,1,0,17,16,15,14,13,12],[30,29,28,27,26,25,24,23,22,21,20,19,18,35,34,33,32,31,12,11,10,9,8,7,6,5,4,3,2,1,0,17,16,15,14,13],[31,30,29,28,27,26,25,24,23,22,21,20,19,18,35,34,33,32,13,12,11,10,9,8,7,6,5,4,3,2,1,0,17,16,15,14],[32,31,30,29,28,27,26,25,24,23,22,21,20,19,18,35,34,33,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0,17,16,15],[33,32,31,30,29,28,27,26,25,24,23,22,21,20,19,18,35,34,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0,17,16],[34,33,32,31,30,29,28,27,26,25,24,23,22,21,20,19,18,35,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0,17],[35,34,33,32,31,30,29,28,27,26,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0]],"identity":0}。請依 [conjugation_action, identity_action, composition_action, certificate] 欄序回答。

查看答案與解釋([[0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 18, 19], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 18, 19, 20, 21], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 18, 19, 20, 21, 22, 23], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 18, 19, 20, 21, 22, 23, 24, 25], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 28, 29, 30, 31, 32, 33, 34, 35, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 30, 31, 32, 33, 34, 35, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 32, 33, 34, 35, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 34, 35, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 18, 19], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 18, 19, 20, 21], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 18, 19, 20, 21, 22, 23], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 18, 19, 20, 21, 22, 23, 24, 25], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 28, 29, 30, 31, 32, 33, 34, 35, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 30, 31, 32, 33, 34, 35, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 32, 33, 34, 35, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 34, 35, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33], [0, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 18, 35, 34, 33, 32, 31, 30, 29, 28, 27, 26, 25, 24, 23, 22, 21, 20, 19], [0, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 20, 19, 18, 35, 34, 33, 32, 31, 30, 29, 28, 27, 26, 25, 24, 23, 22, 21], [0, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 22, 21, 20, 19, 18, 35, 34, 33, 32, 31, 30, 29, 28, 27, 26, 25, 24, 23], [0, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 24, 23, 22, 21, 20, 19, 18, 35, 34, 33, 32, 31, 30, 29, 28, 27, 26, 25], [0, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 26, 25, 24, 23, 22, 21, 20, 19, 18, 35, 34, 33, 32, 31, 30, 29, 28, 27], [0, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 28, 27, 26, 25, 24, 23, 22, 21, 20, 19, 18, 35, 34, 33, 32, 31, 30, 29], [0, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 30, 29, 28, 27, 26, 25, 24, 23, 22, 21, 20, 19, 18, 35, 34, 33, 32, 31], [0, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 32, 31, 30, 29, 28, 27, 26, 25, 24, 23, 22, 21, 20, 19, 18, 35, 34, 33], [0, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 34, 33, 32, 31, 30, 29, 28, 27, 26, 25, 24, 23, 22, 21, 20, 19, 18, 35], [0, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 18, 35, 34, 33, 32, 31, 30, 29, 28, 27, 26, 25, 24, 23, 22, 21, 20, 19], [0, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 20, 19, 18, 35, 34, 33, 32, 31, 30, 29, 28, 27, 26, 25, 24, 23, 22, 21], [0, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 22, 21, 20, 19, 18, 35, 34, 33, 32, 31, 30, 29, 28, 27, 26, 25, 24, 23], [0, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 24, 23, 22, 21, 20, 19, 18, 35, 34, 33, 32, 31, 30, 29, 28, 27, 26, 25], [0, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 26, 25, 24, 23, 22, 21, 20, 19, 18, 35, 34, 33, 32, 31, 30, 29, 28, 27], [0, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 28, 27, 26, 25, 24, 23, 22, 21, 20, 19, 18, 35, 34, 33, 32, 31, 30, 29], [0, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 30, 29, 28, 27, 26, 25, 24, 23, 22, 21, 20, 19, 18, 35, 34, 33, 32, 31], [0, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 32, 31, 30, 29, 28, 27, 26, 25, 24, 23, 22, 21, 20, 19, 18, 35, 34, 33], [0, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 34, 33, 32, 31, 30, 29, 28, 27, 26, 25, 24, 23, 22, 21, 20, 19, 18, 35]], 是, 是, g_dot_x_equals_g_x_g_inverse_is_a_complete_left_action)

Wave6第八層核對=([[0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 18, 19], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 18, 19, 20, 21], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 18, 19, 20, 21, 22, 23], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 18, 19, 20, 21, 22, 23, 24, 25], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 28, 29, 30, 31, 32, 33, 34, 35, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 30, 31, 32, 33, 34, 35, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 32, 33, 34, 35, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 34, 35, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 18, 19], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 18, 19, 20, 21], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 18, 19, 20, 21, 22, 23], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 18, 19, 20, 21, 22, 23, 24, 25], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 28, 29, 30, 31, 32, 33, 34, 35, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 30, 31, 32, 33, 34, 35, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 32, 33, 34, 35, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 34, 35, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33], [0, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 18, 35, 34, 33, 32, 31, 30, 29, 28, 27, 26, 25, 24, 23, 22, 21, 20, 19], [0, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 20, 19, 18, 35, 34, 33, 32, 31, 30, 29, 28, 27, 26, 25, 24, 23, 22, 21], [0, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 22, 21, 20, 19, 18, 35, 34, 33, 32, 31, 30, 29, 28, 27, 26, 25, 24, 23], [0, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 24, 23, 22, 21, 20, 19, 18, 35, 34, 33, 32, 31, 30, 29, 28, 27, 26, 25], [0, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 26, 25, 24, 23, 22, 21, 20, 19, 18, 35, 34, 33, 32, 31, 30, 29, 28, 27], [0, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 28, 27, 26, 25, 24, 23, 22, 21, 20, 19, 18, 35, 34, 33, 32, 31, 30, 29], [0, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 30, 29, 28, 27, 26, 25, 24, 23, 22, 21, 20, 19, 18, 35, 34, 33, 32, 31], [0, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 32, 31, 30, 29, 28, 27, 26, 25, 24, 23, 22, 21, 20, 19, 18, 35, 34, 33], [0, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 34, 33, 32, 31, 30, 29, 28, 27, 26, 25, 24, 23, 22, 21, 20, 19, 18, 35], [0, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 18, 35, 34, 33, 32, 31, 30, 29, 28, 27, 26, 25, 24, 23, 22, 21, 20, 19], [0, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 20, 19, 18, 35, 34, 33, 32, 31, 30, 29, 28, 27, 26, 25, 24, 23, 22, 21], [0, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 22, 21, 20, 19, 18, 35, 34, 33, 32, 31, 30, 29, 28, 27, 26, 25, 24, 23], [0, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 24, 23, 22, 21, 20, 19, 18, 35, 34, 33, 32, 31, 30, 29, 28, 27, 26, 25], [0, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 26, 25, 24, 23, 22, 21, 20, 19, 18, 35, 34, 33, 32, 31, 30, 29, 28, 27], [0, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 28, 27, 26, 25, 24, 23, 22, 21, 20, 19, 18, 35, 34, 33, 32, 31, 30, 29], [0, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 30, 29, 28, 27, 26, 25, 24, 23, 22, 21, 20, 19, 18, 35, 34, 33, 32, 31], [0, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 32, 31, 30, 29, 28, 27, 26, 25, 24, 23, 22, 21, 20, 19, 18, 35, 34, 33], [0, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 34, 33, 32, 31, 30, 29, 28, 27, 26, 25, 24, 23, 22, 21, 20, 19, 18, 35]], 是, 是, g_dot_x_equals_g_x_g_inverse_is_a_complete_left_action)；依完整明示資料獨立重算；共軛類是element orbit並形成完整partition；singleton以forall g commute核對；共軛類不是coset或conjugate subgroup；不使用centralizer、class-size公式或類方程。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r03-finite-group-conjugacy-class-0016/)

有限群共軛類 · qf-mod45-conjugacy-action-table · candidate





## 17. 有限群共軛類

由完整Cayley table導出全部conjugation action與orbits。操作=conjugacy-action-table；資料={"group_table":[[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,0,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,19],[2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,0,1,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,19,20],[3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,0,1,2,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,19,20,21],[4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,0,1,2,3,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,19,20,21,22],[5,6,7,8,9,10,11,12,13,14,15,16,17,18,0,1,2,3,4,24,25,26,27,28,29,30,31,32,33,34,35,36,37,19,20,21,22,23],[6,7,8,9,10,11,12,13,14,15,16,17,18,0,1,2,3,4,5,25,26,27,28,29,30,31,32,33,34,35,36,37,19,20,21,22,23,24],[7,8,9,10,11,12,13,14,15,16,17,18,0,1,2,3,4,5,6,26,27,28,29,30,31,32,33,34,35,36,37,19,20,21,22,23,24,25],[8,9,10,11,12,13,14,15,16,17,18,0,1,2,3,4,5,6,7,27,28,29,30,31,32,33,34,35,36,37,19,20,21,22,23,24,25,26],[9,10,11,12,13,14,15,16,17,18,0,1,2,3,4,5,6,7,8,28,29,30,31,32,33,34,35,36,37,19,20,21,22,23,24,25,26,27],[10,11,12,13,14,15,16,17,18,0,1,2,3,4,5,6,7,8,9,29,30,31,32,33,34,35,36,37,19,20,21,22,23,24,25,26,27,28],[11,12,13,14,15,16,17,18,0,1,2,3,4,5,6,7,8,9,10,30,31,32,33,34,35,36,37,19,20,21,22,23,24,25,26,27,28,29],[12,13,14,15,16,17,18,0,1,2,3,4,5,6,7,8,9,10,11,31,32,33,34,35,36,37,19,20,21,22,23,24,25,26,27,28,29,30],[13,14,15,16,17,18,0,1,2,3,4,5,6,7,8,9,10,11,12,32,33,34,35,36,37,19,20,21,22,23,24,25,26,27,28,29,30,31],[14,15,16,17,18,0,1,2,3,4,5,6,7,8,9,10,11,12,13,33,34,35,36,37,19,20,21,22,23,24,25,26,27,28,29,30,31,32],[15,16,17,18,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,34,35,36,37,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33],[16,17,18,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,35,36,37,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34],[17,18,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,36,37,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35],[18,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,37,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36],[19,37,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,21,20,0,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1],[20,19,37,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,21,1,0,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2],[21,20,19,37,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,2,1,0,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3],[22,21,20,19,37,36,35,34,33,32,31,30,29,28,27,26,25,24,23,3,2,1,0,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4],[23,22,21,20,19,37,36,35,34,33,32,31,30,29,28,27,26,25,24,4,3,2,1,0,18,17,16,15,14,13,12,11,10,9,8,7,6,5],[24,23,22,21,20,19,37,36,35,34,33,32,31,30,29,28,27,26,25,5,4,3,2,1,0,18,17,16,15,14,13,12,11,10,9,8,7,6],[25,24,23,22,21,20,19,37,36,35,34,33,32,31,30,29,28,27,26,6,5,4,3,2,1,0,18,17,16,15,14,13,12,11,10,9,8,7],[26,25,24,23,22,21,20,19,37,36,35,34,33,32,31,30,29,28,27,7,6,5,4,3,2,1,0,18,17,16,15,14,13,12,11,10,9,8],[27,26,25,24,23,22,21,20,19,37,36,35,34,33,32,31,30,29,28,8,7,6,5,4,3,2,1,0,18,17,16,15,14,13,12,11,10,9],[28,27,26,25,24,23,22,21,20,19,37,36,35,34,33,32,31,30,29,9,8,7,6,5,4,3,2,1,0,18,17,16,15,14,13,12,11,10],[29,28,27,26,25,24,23,22,21,20,19,37,36,35,34,33,32,31,30,10,9,8,7,6,5,4,3,2,1,0,18,17,16,15,14,13,12,11],[30,29,28,27,26,25,24,23,22,21,20,19,37,36,35,34,33,32,31,11,10,9,8,7,6,5,4,3,2,1,0,18,17,16,15,14,13,12],[31,30,29,28,27,26,25,24,23,22,21,20,19,37,36,35,34,33,32,12,11,10,9,8,7,6,5,4,3,2,1,0,18,17,16,15,14,13],[32,31,30,29,28,27,26,25,24,23,22,21,20,19,37,36,35,34,33,13,12,11,10,9,8,7,6,5,4,3,2,1,0,18,17,16,15,14],[33,32,31,30,29,28,27,26,25,24,23,22,21,20,19,37,36,35,34,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0,18,17,16,15],[34,33,32,31,30,29,28,27,26,25,24,23,22,21,20,19,37,36,35,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0,18,17,16],[35,34,33,32,31,30,29,28,27,26,25,24,23,22,21,20,19,37,36,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0,18,17],[36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,21,20,19,37,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0,18],[37,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0]],"identity":0}。請依 [conjugation_action, identity_action, composition_action, certificate] 欄序回答。

查看答案與解釋([[0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 19, 20], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 19, 20, 21, 22], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 19, 20, 21, 22, 23, 24], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 19, 20, 21, 22, 23, 24, 25, 26], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 29, 30, 31, 32, 33, 34, 35, 36, 37, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 31, 32, 33, 34, 35, 36, 37, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 33, 34, 35, 36, 37, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 35, 36, 37, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 37, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 19], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 19, 20, 21], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 19, 20, 21, 22, 23], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 19, 20, 21, 22, 23, 24, 25], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 19, 20, 21, 22, 23, 24, 25, 26, 27], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 30, 31, 32, 33, 34, 35, 36, 37, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 32, 33, 34, 35, 36, 37, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 34, 35, 36, 37, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 36, 37, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35], [0, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 19, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 26, 25, 24, 23, 22, 21, 20], [0, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 21, 20, 19, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 26, 25, 24, 23, 22], [0, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 23, 22, 21, 20, 19, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 26, 25, 24], [0, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 25, 24, 23, 22, 21, 20, 19, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 26], [0, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 27, 26, 25, 24, 23, 22, 21, 20, 19, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28], [0, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 29, 28, 27, 26, 25, 24, 23, 22, 21, 20, 19, 37, 36, 35, 34, 33, 32, 31, 30], [0, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 31, 30, 29, 28, 27, 26, 25, 24, 23, 22, 21, 20, 19, 37, 36, 35, 34, 33, 32], [0, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 33, 32, 31, 30, 29, 28, 27, 26, 25, 24, 23, 22, 21, 20, 19, 37, 36, 35, 34], [0, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 35, 34, 33, 32, 31, 30, 29, 28, 27, 26, 25, 24, 23, 22, 21, 20, 19, 37, 36], [0, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 26, 25, 24, 23, 22, 21, 20, 19], [0, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 20, 19, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 26, 25, 24, 23, 22, 21], [0, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 22, 21, 20, 19, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 26, 25, 24, 23], [0, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 24, 23, 22, 21, 20, 19, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 26, 25], [0, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 26, 25, 24, 23, 22, 21, 20, 19, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27], [0, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 28, 27, 26, 25, 24, 23, 22, 21, 20, 19, 37, 36, 35, 34, 33, 32, 31, 30, 29], [0, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 30, 29, 28, 27, 26, 25, 24, 23, 22, 21, 20, 19, 37, 36, 35, 34, 33, 32, 31], [0, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 32, 31, 30, 29, 28, 27, 26, 25, 24, 23, 22, 21, 20, 19, 37, 36, 35, 34, 33], [0, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 34, 33, 32, 31, 30, 29, 28, 27, 26, 25, 24, 23, 22, 21, 20, 19, 37, 36, 35], [0, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 26, 25, 24, 23, 22, 21, 20, 19, 37]], 是, 是, g_dot_x_equals_g_x_g_inverse_is_a_complete_left_action)

Wave6第八層核對=([[0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 19, 20], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 19, 20, 21, 22], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 19, 20, 21, 22, 23, 24], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 19, 20, 21, 22, 23, 24, 25, 26], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 29, 30, 31, 32, 33, 34, 35, 36, 37, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 31, 32, 33, 34, 35, 36, 37, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 33, 34, 35, 36, 37, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 35, 36, 37, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 37, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 19], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 19, 20, 21], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 19, 20, 21, 22, 23], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 19, 20, 21, 22, 23, 24, 25], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 19, 20, 21, 22, 23, 24, 25, 26, 27], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 30, 31, 32, 33, 34, 35, 36, 37, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 32, 33, 34, 35, 36, 37, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 34, 35, 36, 37, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 36, 37, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35], [0, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 19, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 26, 25, 24, 23, 22, 21, 20], [0, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 21, 20, 19, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 26, 25, 24, 23, 22], [0, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 23, 22, 21, 20, 19, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 26, 25, 24], [0, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 25, 24, 23, 22, 21, 20, 19, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 26], [0, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 27, 26, 25, 24, 23, 22, 21, 20, 19, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28], [0, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 29, 28, 27, 26, 25, 24, 23, 22, 21, 20, 19, 37, 36, 35, 34, 33, 32, 31, 30], [0, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 31, 30, 29, 28, 27, 26, 25, 24, 23, 22, 21, 20, 19, 37, 36, 35, 34, 33, 32], [0, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 33, 32, 31, 30, 29, 28, 27, 26, 25, 24, 23, 22, 21, 20, 19, 37, 36, 35, 34], [0, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 35, 34, 33, 32, 31, 30, 29, 28, 27, 26, 25, 24, 23, 22, 21, 20, 19, 37, 36], [0, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 26, 25, 24, 23, 22, 21, 20, 19], [0, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 20, 19, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 26, 25, 24, 23, 22, 21], [0, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 22, 21, 20, 19, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 26, 25, 24, 23], [0, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 24, 23, 22, 21, 20, 19, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 26, 25], [0, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 26, 25, 24, 23, 22, 21, 20, 19, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27], [0, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 28, 27, 26, 25, 24, 23, 22, 21, 20, 19, 37, 36, 35, 34, 33, 32, 31, 30, 29], [0, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 30, 29, 28, 27, 26, 25, 24, 23, 22, 21, 20, 19, 37, 36, 35, 34, 33, 32, 31], [0, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 32, 31, 30, 29, 28, 27, 26, 25, 24, 23, 22, 21, 20, 19, 37, 36, 35, 34, 33], [0, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 34, 33, 32, 31, 30, 29, 28, 27, 26, 25, 24, 23, 22, 21, 20, 19, 37, 36, 35], [0, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 26, 25, 24, 23, 22, 21, 20, 19, 37]], 是, 是, g_dot_x_equals_g_x_g_inverse_is_a_complete_left_action)；依完整明示資料獨立重算；共軛類是element orbit並形成完整partition；singleton以forall g commute核對；共軛類不是coset或conjugate subgroup；不使用centralizer、class-size公式或類方程。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r03-finite-group-conjugacy-class-0017/)

有限群共軛類 · qf-mod45-conjugacy-action-table · candidate





## 18. 有限群共軛類

由完整Cayley table導出全部conjugation action與orbits。操作=conjugacy-action-table；資料={"group_table":[[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,0,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,20],[2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,0,1,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,20,21],[3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,0,1,2,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,20,21,22],[4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,0,1,2,3,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,20,21,22,23],[5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,0,1,2,3,4,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,20,21,22,23,24],[6,7,8,9,10,11,12,13,14,15,16,17,18,19,0,1,2,3,4,5,26,27,28,29,30,31,32,33,34,35,36,37,38,39,20,21,22,23,24,25],[7,8,9,10,11,12,13,14,15,16,17,18,19,0,1,2,3,4,5,6,27,28,29,30,31,32,33,34,35,36,37,38,39,20,21,22,23,24,25,26],[8,9,10,11,12,13,14,15,16,17,18,19,0,1,2,3,4,5,6,7,28,29,30,31,32,33,34,35,36,37,38,39,20,21,22,23,24,25,26,27],[9,10,11,12,13,14,15,16,17,18,19,0,1,2,3,4,5,6,7,8,29,30,31,32,33,34,35,36,37,38,39,20,21,22,23,24,25,26,27,28],[10,11,12,13,14,15,16,17,18,19,0,1,2,3,4,5,6,7,8,9,30,31,32,33,34,35,36,37,38,39,20,21,22,23,24,25,26,27,28,29],[11,12,13,14,15,16,17,18,19,0,1,2,3,4,5,6,7,8,9,10,31,32,33,34,35,36,37,38,39,20,21,22,23,24,25,26,27,28,29,30],[12,13,14,15,16,17,18,19,0,1,2,3,4,5,6,7,8,9,10,11,32,33,34,35,36,37,38,39,20,21,22,23,24,25,26,27,28,29,30,31],[13,14,15,16,17,18,19,0,1,2,3,4,5,6,7,8,9,10,11,12,33,34,35,36,37,38,39,20,21,22,23,24,25,26,27,28,29,30,31,32],[14,15,16,17,18,19,0,1,2,3,4,5,6,7,8,9,10,11,12,13,34,35,36,37,38,39,20,21,22,23,24,25,26,27,28,29,30,31,32,33],[15,16,17,18,19,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,35,36,37,38,39,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34],[16,17,18,19,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,36,37,38,39,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35],[17,18,19,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,37,38,39,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36],[18,19,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,38,39,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37],[19,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,39,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38],[20,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,21,0,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1],[21,20,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,1,0,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2],[22,21,20,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,23,2,1,0,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3],[23,22,21,20,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,3,2,1,0,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4],[24,23,22,21,20,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,4,3,2,1,0,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5],[25,24,23,22,21,20,39,38,37,36,35,34,33,32,31,30,29,28,27,26,5,4,3,2,1,0,19,18,17,16,15,14,13,12,11,10,9,8,7,6],[26,25,24,23,22,21,20,39,38,37,36,35,34,33,32,31,30,29,28,27,6,5,4,3,2,1,0,19,18,17,16,15,14,13,12,11,10,9,8,7],[27,26,25,24,23,22,21,20,39,38,37,36,35,34,33,32,31,30,29,28,7,6,5,4,3,2,1,0,19,18,17,16,15,14,13,12,11,10,9,8],[28,27,26,25,24,23,22,21,20,39,38,37,36,35,34,33,32,31,30,29,8,7,6,5,4,3,2,1,0,19,18,17,16,15,14,13,12,11,10,9],[29,28,27,26,25,24,23,22,21,20,39,38,37,36,35,34,33,32,31,30,9,8,7,6,5,4,3,2,1,0,19,18,17,16,15,14,13,12,11,10],[30,29,28,27,26,25,24,23,22,21,20,39,38,37,36,35,34,33,32,31,10,9,8,7,6,5,4,3,2,1,0,19,18,17,16,15,14,13,12,11],[31,30,29,28,27,26,25,24,23,22,21,20,39,38,37,36,35,34,33,32,11,10,9,8,7,6,5,4,3,2,1,0,19,18,17,16,15,14,13,12],[32,31,30,29,28,27,26,25,24,23,22,21,20,39,38,37,36,35,34,33,12,11,10,9,8,7,6,5,4,3,2,1,0,19,18,17,16,15,14,13],[33,32,31,30,29,28,27,26,25,24,23,22,21,20,39,38,37,36,35,34,13,12,11,10,9,8,7,6,5,4,3,2,1,0,19,18,17,16,15,14],[34,33,32,31,30,29,28,27,26,25,24,23,22,21,20,39,38,37,36,35,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0,19,18,17,16,15],[35,34,33,32,31,30,29,28,27,26,25,24,23,22,21,20,39,38,37,36,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0,19,18,17,16],[36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,21,20,39,38,37,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0,19,18,17],[37,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,21,20,39,38,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0,19,18],[38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,21,20,39,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0,19],[39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0]],"identity":0}。請依 [conjugation_action, identity_action, composition_action, certificate] 欄序回答。

查看答案與解釋([[0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 20, 21], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 20, 21, 22, 23], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 20, 21, 22, 23, 24, 25], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 20, 21, 22, 23, 24, 25, 26, 27], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 32, 33, 34, 35, 36, 37, 38, 39, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 34, 35, 36, 37, 38, 39, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 36, 37, 38, 39, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 38, 39, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 20, 21], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 20, 21, 22, 23], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 20, 21, 22, 23, 24, 25], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 20, 21, 22, 23, 24, 25, 26, 27], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 32, 33, 34, 35, 36, 37, 38, 39, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 34, 35, 36, 37, 38, 39, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 36, 37, 38, 39, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 38, 39, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37], [0, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 20, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 26, 25, 24, 23, 22, 21], [0, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 22, 21, 20, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 26, 25, 24, 23], [0, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 24, 23, 22, 21, 20, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 26, 25], [0, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 26, 25, 24, 23, 22, 21, 20, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27], [0, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 28, 27, 26, 25, 24, 23, 22, 21, 20, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29], [0, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 30, 29, 28, 27, 26, 25, 24, 23, 22, 21, 20, 39, 38, 37, 36, 35, 34, 33, 32, 31], [0, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 32, 31, 30, 29, 28, 27, 26, 25, 24, 23, 22, 21, 20, 39, 38, 37, 36, 35, 34, 33], [0, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 34, 33, 32, 31, 30, 29, 28, 27, 26, 25, 24, 23, 22, 21, 20, 39, 38, 37, 36, 35], [0, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 26, 25, 24, 23, 22, 21, 20, 39, 38, 37], [0, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 26, 25, 24, 23, 22, 21, 20, 39], [0, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 20, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 26, 25, 24, 23, 22, 21], [0, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 22, 21, 20, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 26, 25, 24, 23], [0, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 24, 23, 22, 21, 20, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 26, 25], [0, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 26, 25, 24, 23, 22, 21, 20, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27], [0, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 28, 27, 26, 25, 24, 23, 22, 21, 20, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29], [0, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 30, 29, 28, 27, 26, 25, 24, 23, 22, 21, 20, 39, 38, 37, 36, 35, 34, 33, 32, 31], [0, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 32, 31, 30, 29, 28, 27, 26, 25, 24, 23, 22, 21, 20, 39, 38, 37, 36, 35, 34, 33], [0, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 34, 33, 32, 31, 30, 29, 28, 27, 26, 25, 24, 23, 22, 21, 20, 39, 38, 37, 36, 35], [0, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 26, 25, 24, 23, 22, 21, 20, 39, 38, 37], [0, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 26, 25, 24, 23, 22, 21, 20, 39]], 是, 是, g_dot_x_equals_g_x_g_inverse_is_a_complete_left_action)

Wave6第八層核對=([[0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 20, 21], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 20, 21, 22, 23], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 20, 21, 22, 23, 24, 25], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 20, 21, 22, 23, 24, 25, 26, 27], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 32, 33, 34, 35, 36, 37, 38, 39, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 34, 35, 36, 37, 38, 39, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 36, 37, 38, 39, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 38, 39, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 20, 21], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 20, 21, 22, 23], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 20, 21, 22, 23, 24, 25], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 20, 21, 22, 23, 24, 25, 26, 27], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 32, 33, 34, 35, 36, 37, 38, 39, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 34, 35, 36, 37, 38, 39, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 36, 37, 38, 39, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 38, 39, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37], [0, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 20, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 26, 25, 24, 23, 22, 21], [0, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 22, 21, 20, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 26, 25, 24, 23], [0, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 24, 23, 22, 21, 20, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 26, 25], [0, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 26, 25, 24, 23, 22, 21, 20, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27], [0, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 28, 27, 26, 25, 24, 23, 22, 21, 20, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29], [0, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 30, 29, 28, 27, 26, 25, 24, 23, 22, 21, 20, 39, 38, 37, 36, 35, 34, 33, 32, 31], [0, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 32, 31, 30, 29, 28, 27, 26, 25, 24, 23, 22, 21, 20, 39, 38, 37, 36, 35, 34, 33], [0, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 34, 33, 32, 31, 30, 29, 28, 27, 26, 25, 24, 23, 22, 21, 20, 39, 38, 37, 36, 35], [0, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 26, 25, 24, 23, 22, 21, 20, 39, 38, 37], [0, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 26, 25, 24, 23, 22, 21, 20, 39], [0, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 20, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 26, 25, 24, 23, 22, 21], [0, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 22, 21, 20, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 26, 25, 24, 23], [0, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 24, 23, 22, 21, 20, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 26, 25], [0, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 26, 25, 24, 23, 22, 21, 20, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27], [0, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 28, 27, 26, 25, 24, 23, 22, 21, 20, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29], [0, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 30, 29, 28, 27, 26, 25, 24, 23, 22, 21, 20, 39, 38, 37, 36, 35, 34, 33, 32, 31], [0, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 32, 31, 30, 29, 28, 27, 26, 25, 24, 23, 22, 21, 20, 39, 38, 37, 36, 35, 34, 33], [0, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 34, 33, 32, 31, 30, 29, 28, 27, 26, 25, 24, 23, 22, 21, 20, 39, 38, 37, 36, 35], [0, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 26, 25, 24, 23, 22, 21, 20, 39, 38, 37], [0, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 26, 25, 24, 23, 22, 21, 20, 39]], 是, 是, g_dot_x_equals_g_x_g_inverse_is_a_complete_left_action)；依完整明示資料獨立重算；共軛類是element orbit並形成完整partition；singleton以forall g commute核對；共軛類不是coset或conjugate subgroup；不使用centralizer、class-size公式或類方程。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r03-finite-group-conjugacy-class-0018/)

有限群共軛類 · qf-mod45-conjugacy-action-table · candidate





## 19. 有限群共軛類

由完整Cayley table導出全部conjugation action與orbits。操作=conjugacy-action-table；資料={"group_table":[[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,0,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,21],[2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,0,1,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,21,22],[3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,0,1,2,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,21,22,23],[4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,0,1,2,3,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,21,22,23,24],[5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,0,1,2,3,4,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,21,22,23,24,25],[6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,0,1,2,3,4,5,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,21,22,23,24,25,26],[7,8,9,10,11,12,13,14,15,16,17,18,19,20,0,1,2,3,4,5,6,28,29,30,31,32,33,34,35,36,37,38,39,40,41,21,22,23,24,25,26,27],[8,9,10,11,12,13,14,15,16,17,18,19,20,0,1,2,3,4,5,6,7,29,30,31,32,33,34,35,36,37,38,39,40,41,21,22,23,24,25,26,27,28],[9,10,11,12,13,14,15,16,17,18,19,20,0,1,2,3,4,5,6,7,8,30,31,32,33,34,35,36,37,38,39,40,41,21,22,23,24,25,26,27,28,29],[10,11,12,13,14,15,16,17,18,19,20,0,1,2,3,4,5,6,7,8,9,31,32,33,34,35,36,37,38,39,40,41,21,22,23,24,25,26,27,28,29,30],[11,12,13,14,15,16,17,18,19,20,0,1,2,3,4,5,6,7,8,9,10,32,33,34,35,36,37,38,39,40,41,21,22,23,24,25,26,27,28,29,30,31],[12,13,14,15,16,17,18,19,20,0,1,2,3,4,5,6,7,8,9,10,11,33,34,35,36,37,38,39,40,41,21,22,23,24,25,26,27,28,29,30,31,32],[13,14,15,16,17,18,19,20,0,1,2,3,4,5,6,7,8,9,10,11,12,34,35,36,37,38,39,40,41,21,22,23,24,25,26,27,28,29,30,31,32,33],[14,15,16,17,18,19,20,0,1,2,3,4,5,6,7,8,9,10,11,12,13,35,36,37,38,39,40,41,21,22,23,24,25,26,27,28,29,30,31,32,33,34],[15,16,17,18,19,20,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,36,37,38,39,40,41,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35],[16,17,18,19,20,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,37,38,39,40,41,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36],[17,18,19,20,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,38,39,40,41,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37],[18,19,20,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,39,40,41,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38],[19,20,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,40,41,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39],[20,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,41,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40],[21,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,0,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1],[22,21,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,23,1,0,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2],[23,22,21,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,2,1,0,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3],[24,23,22,21,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,3,2,1,0,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4],[25,24,23,22,21,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,4,3,2,1,0,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5],[26,25,24,23,22,21,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,5,4,3,2,1,0,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6],[27,26,25,24,23,22,21,41,40,39,38,37,36,35,34,33,32,31,30,29,28,6,5,4,3,2,1,0,20,19,18,17,16,15,14,13,12,11,10,9,8,7],[28,27,26,25,24,23,22,21,41,40,39,38,37,36,35,34,33,32,31,30,29,7,6,5,4,3,2,1,0,20,19,18,17,16,15,14,13,12,11,10,9,8],[29,28,27,26,25,24,23,22,21,41,40,39,38,37,36,35,34,33,32,31,30,8,7,6,5,4,3,2,1,0,20,19,18,17,16,15,14,13,12,11,10,9],[30,29,28,27,26,25,24,23,22,21,41,40,39,38,37,36,35,34,33,32,31,9,8,7,6,5,4,3,2,1,0,20,19,18,17,16,15,14,13,12,11,10],[31,30,29,28,27,26,25,24,23,22,21,41,40,39,38,37,36,35,34,33,32,10,9,8,7,6,5,4,3,2,1,0,20,19,18,17,16,15,14,13,12,11],[32,31,30,29,28,27,26,25,24,23,22,21,41,40,39,38,37,36,35,34,33,11,10,9,8,7,6,5,4,3,2,1,0,20,19,18,17,16,15,14,13,12],[33,32,31,30,29,28,27,26,25,24,23,22,21,41,40,39,38,37,36,35,34,12,11,10,9,8,7,6,5,4,3,2,1,0,20,19,18,17,16,15,14,13],[34,33,32,31,30,29,28,27,26,25,24,23,22,21,41,40,39,38,37,36,35,13,12,11,10,9,8,7,6,5,4,3,2,1,0,20,19,18,17,16,15,14],[35,34,33,32,31,30,29,28,27,26,25,24,23,22,21,41,40,39,38,37,36,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0,20,19,18,17,16,15],[36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,21,41,40,39,38,37,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0,20,19,18,17,16],[37,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,21,41,40,39,38,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0,20,19,18,17],[38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,21,41,40,39,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0,20,19,18],[39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,21,41,40,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0,20,19],[40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,21,41,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0,20],[41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0]],"identity":0}。請依 [conjugation_action, identity_action, composition_action, certificate] 欄序回答。

查看答案與解釋([[0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 21, 22], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 21, 22, 23, 24], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 21, 22, 23, 24, 25, 26], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 21, 22, 23, 24, 25, 26, 27, 28], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 33, 34, 35, 36, 37, 38, 39, 40, 41, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 35, 36, 37, 38, 39, 40, 41, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 37, 38, 39, 40, 41, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 39, 40, 41, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 41, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 21], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 21, 22, 23], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 21, 22, 23, 24, 25], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 21, 22, 23, 24, 25, 26, 27], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 21, 22, 23, 24, 25, 26, 27, 28, 29], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 34, 35, 36, 37, 38, 39, 40, 41, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 36, 37, 38, 39, 40, 41, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 38, 39, 40, 41, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 40, 41, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39], [0, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 21, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 26, 25, 24, 23, 22], [0, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 23, 22, 21, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 26, 25, 24], [0, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 25, 24, 23, 22, 21, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 26], [0, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 27, 26, 25, 24, 23, 22, 21, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28], [0, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 29, 28, 27, 26, 25, 24, 23, 22, 21, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30], [0, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 31, 30, 29, 28, 27, 26, 25, 24, 23, 22, 21, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32], [0, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 33, 32, 31, 30, 29, 28, 27, 26, 25, 24, 23, 22, 21, 41, 40, 39, 38, 37, 36, 35, 34], [0, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 35, 34, 33, 32, 31, 30, 29, 28, 27, 26, 25, 24, 23, 22, 21, 41, 40, 39, 38, 37, 36], [0, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 26, 25, 24, 23, 22, 21, 41, 40, 39, 38], [0, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 26, 25, 24, 23, 22, 21, 41, 40], [0, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 26, 25, 24, 23, 22, 21], [0, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 22, 21, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 26, 25, 24, 23], [0, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 24, 23, 22, 21, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 26, 25], [0, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 26, 25, 24, 23, 22, 21, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27], [0, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 28, 27, 26, 25, 24, 23, 22, 21, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29], [0, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 30, 29, 28, 27, 26, 25, 24, 23, 22, 21, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31], [0, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 32, 31, 30, 29, 28, 27, 26, 25, 24, 23, 22, 21, 41, 40, 39, 38, 37, 36, 35, 34, 33], [0, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 34, 33, 32, 31, 30, 29, 28, 27, 26, 25, 24, 23, 22, 21, 41, 40, 39, 38, 37, 36, 35], [0, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 26, 25, 24, 23, 22, 21, 41, 40, 39, 38, 37], [0, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 26, 25, 24, 23, 22, 21, 41, 40, 39], [0, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 26, 25, 24, 23, 22, 21, 41]], 是, 是, g_dot_x_equals_g_x_g_inverse_is_a_complete_left_action)

Wave6第八層核對=([[0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 21, 22], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 21, 22, 23, 24], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 21, 22, 23, 24, 25, 26], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 21, 22, 23, 24, 25, 26, 27, 28], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 33, 34, 35, 36, 37, 38, 39, 40, 41, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 35, 36, 37, 38, 39, 40, 41, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 37, 38, 39, 40, 41, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 39, 40, 41, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 41, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 21], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 21, 22, 23], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 21, 22, 23, 24, 25], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 21, 22, 23, 24, 25, 26, 27], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 21, 22, 23, 24, 25, 26, 27, 28, 29], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 34, 35, 36, 37, 38, 39, 40, 41, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 36, 37, 38, 39, 40, 41, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 38, 39, 40, 41, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 40, 41, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39], [0, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 21, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 26, 25, 24, 23, 22], [0, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 23, 22, 21, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 26, 25, 24], [0, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 25, 24, 23, 22, 21, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 26], [0, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 27, 26, 25, 24, 23, 22, 21, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28], [0, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 29, 28, 27, 26, 25, 24, 23, 22, 21, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30], [0, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 31, 30, 29, 28, 27, 26, 25, 24, 23, 22, 21, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32], [0, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 33, 32, 31, 30, 29, 28, 27, 26, 25, 24, 23, 22, 21, 41, 40, 39, 38, 37, 36, 35, 34], [0, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 35, 34, 33, 32, 31, 30, 29, 28, 27, 26, 25, 24, 23, 22, 21, 41, 40, 39, 38, 37, 36], [0, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 26, 25, 24, 23, 22, 21, 41, 40, 39, 38], [0, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 26, 25, 24, 23, 22, 21, 41, 40], [0, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 26, 25, 24, 23, 22, 21], [0, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 22, 21, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 26, 25, 24, 23], [0, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 24, 23, 22, 21, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 26, 25], [0, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 26, 25, 24, 23, 22, 21, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27], [0, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 28, 27, 26, 25, 24, 23, 22, 21, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29], [0, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 30, 29, 28, 27, 26, 25, 24, 23, 22, 21, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31], [0, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 32, 31, 30, 29, 28, 27, 26, 25, 24, 23, 22, 21, 41, 40, 39, 38, 37, 36, 35, 34, 33], [0, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 34, 33, 32, 31, 30, 29, 28, 27, 26, 25, 24, 23, 22, 21, 41, 40, 39, 38, 37, 36, 35], [0, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 26, 25, 24, 23, 22, 21, 41, 40, 39, 38, 37], [0, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 26, 25, 24, 23, 22, 21, 41, 40, 39], [0, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 26, 25, 24, 23, 22, 21, 41]], 是, 是, g_dot_x_equals_g_x_g_inverse_is_a_complete_left_action)；依完整明示資料獨立重算；共軛類是element orbit並形成完整partition；singleton以forall g commute核對；共軛類不是coset或conjugate subgroup；不使用centralizer、class-size公式或類方程。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r03-finite-group-conjugacy-class-0019/)

有限群共軛類 · qf-mod45-conjugacy-action-table · candidate





## 20. 有限群共軛類

由完整Cayley table導出全部conjugation action與orbits。操作=conjugacy-action-table；資料={"group_table":[[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,0,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,22],[2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,0,1,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,22,23],[3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,0,1,2,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,22,23,24],[4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,0,1,2,3,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,22,23,24,25],[5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,0,1,2,3,4,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,22,23,24,25,26],[6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,0,1,2,3,4,5,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,22,23,24,25,26,27],[7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,0,1,2,3,4,5,6,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,22,23,24,25,26,27,28],[8,9,10,11,12,13,14,15,16,17,18,19,20,21,0,1,2,3,4,5,6,7,30,31,32,33,34,35,36,37,38,39,40,41,42,43,22,23,24,25,26,27,28,29],[9,10,11,12,13,14,15,16,17,18,19,20,21,0,1,2,3,4,5,6,7,8,31,32,33,34,35,36,37,38,39,40,41,42,43,22,23,24,25,26,27,28,29,30],[10,11,12,13,14,15,16,17,18,19,20,21,0,1,2,3,4,5,6,7,8,9,32,33,34,35,36,37,38,39,40,41,42,43,22,23,24,25,26,27,28,29,30,31],[11,12,13,14,15,16,17,18,19,20,21,0,1,2,3,4,5,6,7,8,9,10,33,34,35,36,37,38,39,40,41,42,43,22,23,24,25,26,27,28,29,30,31,32],[12,13,14,15,16,17,18,19,20,21,0,1,2,3,4,5,6,7,8,9,10,11,34,35,36,37,38,39,40,41,42,43,22,23,24,25,26,27,28,29,30,31,32,33],[13,14,15,16,17,18,19,20,21,0,1,2,3,4,5,6,7,8,9,10,11,12,35,36,37,38,39,40,41,42,43,22,23,24,25,26,27,28,29,30,31,32,33,34],[14,15,16,17,18,19,20,21,0,1,2,3,4,5,6,7,8,9,10,11,12,13,36,37,38,39,40,41,42,43,22,23,24,25,26,27,28,29,30,31,32,33,34,35],[15,16,17,18,19,20,21,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,37,38,39,40,41,42,43,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36],[16,17,18,19,20,21,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,38,39,40,41,42,43,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37],[17,18,19,20,21,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,39,40,41,42,43,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38],[18,19,20,21,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,40,41,42,43,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39],[19,20,21,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,41,42,43,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40],[20,21,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,42,43,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41],[21,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,43,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42],[22,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,23,0,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1],[23,22,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,1,0,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2],[24,23,22,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,2,1,0,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3],[25,24,23,22,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,3,2,1,0,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4],[26,25,24,23,22,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,4,3,2,1,0,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5],[27,26,25,24,23,22,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,5,4,3,2,1,0,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6],[28,27,26,25,24,23,22,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,6,5,4,3,2,1,0,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7],[29,28,27,26,25,24,23,22,43,42,41,40,39,38,37,36,35,34,33,32,31,30,7,6,5,4,3,2,1,0,21,20,19,18,17,16,15,14,13,12,11,10,9,8],[30,29,28,27,26,25,24,23,22,43,42,41,40,39,38,37,36,35,34,33,32,31,8,7,6,5,4,3,2,1,0,21,20,19,18,17,16,15,14,13,12,11,10,9],[31,30,29,28,27,26,25,24,23,22,43,42,41,40,39,38,37,36,35,34,33,32,9,8,7,6,5,4,3,2,1,0,21,20,19,18,17,16,15,14,13,12,11,10],[32,31,30,29,28,27,26,25,24,23,22,43,42,41,40,39,38,37,36,35,34,33,10,9,8,7,6,5,4,3,2,1,0,21,20,19,18,17,16,15,14,13,12,11],[33,32,31,30,29,28,27,26,25,24,23,22,43,42,41,40,39,38,37,36,35,34,11,10,9,8,7,6,5,4,3,2,1,0,21,20,19,18,17,16,15,14,13,12],[34,33,32,31,30,29,28,27,26,25,24,23,22,43,42,41,40,39,38,37,36,35,12,11,10,9,8,7,6,5,4,3,2,1,0,21,20,19,18,17,16,15,14,13],[35,34,33,32,31,30,29,28,27,26,25,24,23,22,43,42,41,40,39,38,37,36,13,12,11,10,9,8,7,6,5,4,3,2,1,0,21,20,19,18,17,16,15,14],[36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,43,42,41,40,39,38,37,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0,21,20,19,18,17,16,15],[37,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,43,42,41,40,39,38,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0,21,20,19,18,17,16],[38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,43,42,41,40,39,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0,21,20,19,18,17],[39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,43,42,41,40,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0,21,20,19,18],[40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,43,42,41,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0,21,20,19],[41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,43,42,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0,21,20],[42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,43,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0,21],[43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0]],"identity":0}。請依 [conjugation_action, identity_action, composition_action, certificate] 欄序回答。

查看答案與解釋([[0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 22, 23], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 22, 23, 24, 25], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 22, 23, 24, 25, 26, 27], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 22, 23, 24, 25, 26, 27, 28, 29], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 36, 37, 38, 39, 40, 41, 42, 43, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 38, 39, 40, 41, 42, 43, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 40, 41, 42, 43, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 42, 43, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 22, 23], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 22, 23, 24, 25], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 22, 23, 24, 25, 26, 27], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 22, 23, 24, 25, 26, 27, 28, 29], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 36, 37, 38, 39, 40, 41, 42, 43, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 38, 39, 40, 41, 42, 43, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 40, 41, 42, 43, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 42, 43, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41], [0, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 22, 43, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 26, 25, 24, 23], [0, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 24, 23, 22, 43, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 26, 25], [0, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 26, 25, 24, 23, 22, 43, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27], [0, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 28, 27, 26, 25, 24, 23, 22, 43, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29], [0, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 30, 29, 28, 27, 26, 25, 24, 23, 22, 43, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31], [0, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 32, 31, 30, 29, 28, 27, 26, 25, 24, 23, 22, 43, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33], [0, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 34, 33, 32, 31, 30, 29, 28, 27, 26, 25, 24, 23, 22, 43, 42, 41, 40, 39, 38, 37, 36, 35], [0, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 26, 25, 24, 23, 22, 43, 42, 41, 40, 39, 38, 37], [0, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 26, 25, 24, 23, 22, 43, 42, 41, 40, 39], [0, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 26, 25, 24, 23, 22, 43, 42, 41], [0, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 26, 25, 24, 23, 22, 43], [0, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 22, 43, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 26, 25, 24, 23], [0, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 24, 23, 22, 43, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 26, 25], [0, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 26, 25, 24, 23, 22, 43, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27], [0, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 28, 27, 26, 25, 24, 23, 22, 43, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29], [0, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 30, 29, 28, 27, 26, 25, 24, 23, 22, 43, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31], [0, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 32, 31, 30, 29, 28, 27, 26, 25, 24, 23, 22, 43, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33], [0, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 34, 33, 32, 31, 30, 29, 28, 27, 26, 25, 24, 23, 22, 43, 42, 41, 40, 39, 38, 37, 36, 35], [0, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 26, 25, 24, 23, 22, 43, 42, 41, 40, 39, 38, 37], [0, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 26, 25, 24, 23, 22, 43, 42, 41, 40, 39], [0, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 26, 25, 24, 23, 22, 43, 42, 41], [0, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 26, 25, 24, 23, 22, 43]], 是, 是, g_dot_x_equals_g_x_g_inverse_is_a_complete_left_action)

Wave6第八層核對=([[0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 22, 23], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 22, 23, 24, 25], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 22, 23, 24, 25, 26, 27], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 22, 23, 24, 25, 26, 27, 28, 29], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 36, 37, 38, 39, 40, 41, 42, 43, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 38, 39, 40, 41, 42, 43, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 40, 41, 42, 43, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 42, 43, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 22, 23], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 22, 23, 24, 25], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 22, 23, 24, 25, 26, 27], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 22, 23, 24, 25, 26, 27, 28, 29], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 36, 37, 38, 39, 40, 41, 42, 43, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 38, 39, 40, 41, 42, 43, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 40, 41, 42, 43, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 42, 43, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41], [0, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 22, 43, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 26, 25, 24, 23], [0, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 24, 23, 22, 43, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 26, 25], [0, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 26, 25, 24, 23, 22, 43, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27], [0, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 28, 27, 26, 25, 24, 23, 22, 43, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29], [0, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 30, 29, 28, 27, 26, 25, 24, 23, 22, 43, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31], [0, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 32, 31, 30, 29, 28, 27, 26, 25, 24, 23, 22, 43, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33], [0, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 34, 33, 32, 31, 30, 29, 28, 27, 26, 25, 24, 23, 22, 43, 42, 41, 40, 39, 38, 37, 36, 35], [0, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 26, 25, 24, 23, 22, 43, 42, 41, 40, 39, 38, 37], [0, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 26, 25, 24, 23, 22, 43, 42, 41, 40, 39], [0, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 26, 25, 24, 23, 22, 43, 42, 41], [0, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 26, 25, 24, 23, 22, 43], [0, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 22, 43, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 26, 25, 24, 23], [0, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 24, 23, 22, 43, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 26, 25], [0, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 26, 25, 24, 23, 22, 43, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27], [0, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 28, 27, 26, 25, 24, 23, 22, 43, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29], [0, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 30, 29, 28, 27, 26, 25, 24, 23, 22, 43, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31], [0, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 32, 31, 30, 29, 28, 27, 26, 25, 24, 23, 22, 43, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33], [0, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 34, 33, 32, 31, 30, 29, 28, 27, 26, 25, 24, 23, 22, 43, 42, 41, 40, 39, 38, 37, 36, 35], [0, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 26, 25, 24, 23, 22, 43, 42, 41, 40, 39, 38, 37], [0, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 26, 25, 24, 23, 22, 43, 42, 41, 40, 39], [0, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 26, 25, 24, 23, 22, 43, 42, 41], [0, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 26, 25, 24, 23, 22, 43]], 是, 是, g_dot_x_equals_g_x_g_inverse_is_a_complete_left_action)；依完整明示資料獨立重算；共軛類是element orbit並形成完整partition；singleton以forall g commute核對；共軛類不是coset或conjugate subgroup；不使用centralizer、class-size公式或類方程。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r03-finite-group-conjugacy-class-0020/)

有限群共軛類 · qf-mod45-conjugacy-action-table · candidate





## 21. 有限群共軛類

由完整Cayley table導出全部conjugation action與orbits。操作=conjugacy-action-table；資料={"group_table":[[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,0,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,23],[2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,0,1,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,23,24],[3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,0,1,2,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,23,24,25],[4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,0,1,2,3,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,23,24,25,26],[5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,0,1,2,3,4,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,23,24,25,26,27],[6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,0,1,2,3,4,5,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,23,24,25,26,27,28],[7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,0,1,2,3,4,5,6,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,23,24,25,26,27,28,29],[8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,0,1,2,3,4,5,6,7,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,23,24,25,26,27,28,29,30],[9,10,11,12,13,14,15,16,17,18,19,20,21,22,0,1,2,3,4,5,6,7,8,32,33,34,35,36,37,38,39,40,41,42,43,44,45,23,24,25,26,27,28,29,30,31],[10,11,12,13,14,15,16,17,18,19,20,21,22,0,1,2,3,4,5,6,7,8,9,33,34,35,36,37,38,39,40,41,42,43,44,45,23,24,25,26,27,28,29,30,31,32],[11,12,13,14,15,16,17,18,19,20,21,22,0,1,2,3,4,5,6,7,8,9,10,34,35,36,37,38,39,40,41,42,43,44,45,23,24,25,26,27,28,29,30,31,32,33],[12,13,14,15,16,17,18,19,20,21,22,0,1,2,3,4,5,6,7,8,9,10,11,35,36,37,38,39,40,41,42,43,44,45,23,24,25,26,27,28,29,30,31,32,33,34],[13,14,15,16,17,18,19,20,21,22,0,1,2,3,4,5,6,7,8,9,10,11,12,36,37,38,39,40,41,42,43,44,45,23,24,25,26,27,28,29,30,31,32,33,34,35],[14,15,16,17,18,19,20,21,22,0,1,2,3,4,5,6,7,8,9,10,11,12,13,37,38,39,40,41,42,43,44,45,23,24,25,26,27,28,29,30,31,32,33,34,35,36],[15,16,17,18,19,20,21,22,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,38,39,40,41,42,43,44,45,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37],[16,17,18,19,20,21,22,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,39,40,41,42,43,44,45,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38],[17,18,19,20,21,22,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,40,41,42,43,44,45,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39],[18,19,20,21,22,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,41,42,43,44,45,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40],[19,20,21,22,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,42,43,44,45,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41],[20,21,22,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,43,44,45,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42],[21,22,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,44,45,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],[22,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,45,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44],[23,45,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,0,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1],[24,23,45,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,1,0,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2],[25,24,23,45,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,2,1,0,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3],[26,25,24,23,45,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,3,2,1,0,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4],[27,26,25,24,23,45,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,4,3,2,1,0,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5],[28,27,26,25,24,23,45,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,5,4,3,2,1,0,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6],[29,28,27,26,25,24,23,45,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,6,5,4,3,2,1,0,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7],[30,29,28,27,26,25,24,23,45,44,43,42,41,40,39,38,37,36,35,34,33,32,31,7,6,5,4,3,2,1,0,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8],[31,30,29,28,27,26,25,24,23,45,44,43,42,41,40,39,38,37,36,35,34,33,32,8,7,6,5,4,3,2,1,0,22,21,20,19,18,17,16,15,14,13,12,11,10,9],[32,31,30,29,28,27,26,25,24,23,45,44,43,42,41,40,39,38,37,36,35,34,33,9,8,7,6,5,4,3,2,1,0,22,21,20,19,18,17,16,15,14,13,12,11,10],[33,32,31,30,29,28,27,26,25,24,23,45,44,43,42,41,40,39,38,37,36,35,34,10,9,8,7,6,5,4,3,2,1,0,22,21,20,19,18,17,16,15,14,13,12,11],[34,33,32,31,30,29,28,27,26,25,24,23,45,44,43,42,41,40,39,38,37,36,35,11,10,9,8,7,6,5,4,3,2,1,0,22,21,20,19,18,17,16,15,14,13,12],[35,34,33,32,31,30,29,28,27,26,25,24,23,45,44,43,42,41,40,39,38,37,36,12,11,10,9,8,7,6,5,4,3,2,1,0,22,21,20,19,18,17,16,15,14,13],[36,35,34,33,32,31,30,29,28,27,26,25,24,23,45,44,43,42,41,40,39,38,37,13,12,11,10,9,8,7,6,5,4,3,2,1,0,22,21,20,19,18,17,16,15,14],[37,36,35,34,33,32,31,30,29,28,27,26,25,24,23,45,44,43,42,41,40,39,38,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0,22,21,20,19,18,17,16,15],[38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,23,45,44,43,42,41,40,39,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0,22,21,20,19,18,17,16],[39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,23,45,44,43,42,41,40,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0,22,21,20,19,18,17],[40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,23,45,44,43,42,41,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0,22,21,20,19,18],[41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,23,45,44,43,42,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0,22,21,20,19],[42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,23,45,44,43,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0,22,21,20],[43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,23,45,44,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0,22,21],[44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,23,45,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0,22],[45,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0]],"identity":0}。請依 [conjugation_action, identity_action, composition_action, certificate] 欄序回答。

查看答案與解釋([[0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 23, 24], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 23, 24, 25, 26], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 23, 24, 25, 26, 27, 28], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 23, 24, 25, 26, 27, 28, 29, 30], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 37, 38, 39, 40, 41, 42, 43, 44, 45, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 39, 40, 41, 42, 43, 44, 45, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 41, 42, 43, 44, 45, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 43, 44, 45, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 45, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 23], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 23, 24, 25], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 23, 24, 25, 26, 27], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 23, 24, 25, 26, 27, 28, 29], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 23, 24, 25, 26, 27, 28, 29, 30, 31], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 38, 39, 40, 41, 42, 43, 44, 45, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 40, 41, 42, 43, 44, 45, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 42, 43, 44, 45, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 44, 45, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43], [0, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 23, 45, 44, 43, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 26, 25, 24], [0, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 25, 24, 23, 45, 44, 43, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 26], [0, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 27, 26, 25, 24, 23, 45, 44, 43, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28], [0, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 29, 28, 27, 26, 25, 24, 23, 45, 44, 43, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30], [0, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 31, 30, 29, 28, 27, 26, 25, 24, 23, 45, 44, 43, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32], [0, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 33, 32, 31, 30, 29, 28, 27, 26, 25, 24, 23, 45, 44, 43, 42, 41, 40, 39, 38, 37, 36, 35, 34], [0, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 35, 34, 33, 32, 31, 30, 29, 28, 27, 26, 25, 24, 23, 45, 44, 43, 42, 41, 40, 39, 38, 37, 36], [0, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 26, 25, 24, 23, 45, 44, 43, 42, 41, 40, 39, 38], [0, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 26, 25, 24, 23, 45, 44, 43, 42, 41, 40], [0, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 26, 25, 24, 23, 45, 44, 43, 42], [0, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 43, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 26, 25, 24, 23, 45, 44], [0, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 45, 44, 43, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 26, 25, 24, 23], [0, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 24, 23, 45, 44, 43, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 26, 25], [0, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 26, 25, 24, 23, 45, 44, 43, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27], [0, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 28, 27, 26, 25, 24, 23, 45, 44, 43, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29], [0, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 30, 29, 28, 27, 26, 25, 24, 23, 45, 44, 43, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31], [0, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 32, 31, 30, 29, 28, 27, 26, 25, 24, 23, 45, 44, 43, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33], [0, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 34, 33, 32, 31, 30, 29, 28, 27, 26, 25, 24, 23, 45, 44, 43, 42, 41, 40, 39, 38, 37, 36, 35], [0, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 26, 25, 24, 23, 45, 44, 43, 42, 41, 40, 39, 38, 37], [0, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 26, 25, 24, 23, 45, 44, 43, 42, 41, 40, 39], [0, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 26, 25, 24, 23, 45, 44, 43, 42, 41], [0, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 26, 25, 24, 23, 45, 44, 43], [0, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 44, 43, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 26, 25, 24, 23, 45]], 是, 是, g_dot_x_equals_g_x_g_inverse_is_a_complete_left_action)

Wave6第八層核對=([[0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 23, 24], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 23, 24, 25, 26], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 23, 24, 25, 26, 27, 28], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 23, 24, 25, 26, 27, 28, 29, 30], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 37, 38, 39, 40, 41, 42, 43, 44, 45, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 39, 40, 41, 42, 43, 44, 45, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 41, 42, 43, 44, 45, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 43, 44, 45, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 45, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 23], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 23, 24, 25], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 23, 24, 25, 26, 27], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 23, 24, 25, 26, 27, 28, 29], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 23, 24, 25, 26, 27, 28, 29, 30, 31], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 38, 39, 40, 41, 42, 43, 44, 45, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 40, 41, 42, 43, 44, 45, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 42, 43, 44, 45, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 44, 45, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43], [0, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 23, 45, 44, 43, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 26, 25, 24], [0, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 25, 24, 23, 45, 44, 43, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 26], [0, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 27, 26, 25, 24, 23, 45, 44, 43, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28], [0, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 29, 28, 27, 26, 25, 24, 23, 45, 44, 43, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30], [0, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 31, 30, 29, 28, 27, 26, 25, 24, 23, 45, 44, 43, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32], [0, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 33, 32, 31, 30, 29, 28, 27, 26, 25, 24, 23, 45, 44, 43, 42, 41, 40, 39, 38, 37, 36, 35, 34], [0, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 35, 34, 33, 32, 31, 30, 29, 28, 27, 26, 25, 24, 23, 45, 44, 43, 42, 41, 40, 39, 38, 37, 36], [0, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 26, 25, 24, 23, 45, 44, 43, 42, 41, 40, 39, 38], [0, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 26, 25, 24, 23, 45, 44, 43, 42, 41, 40], [0, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 26, 25, 24, 23, 45, 44, 43, 42], [0, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 43, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 26, 25, 24, 23, 45, 44], [0, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 45, 44, 43, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 26, 25, 24, 23], [0, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 24, 23, 45, 44, 43, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 26, 25], [0, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 26, 25, 24, 23, 45, 44, 43, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27], [0, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 28, 27, 26, 25, 24, 23, 45, 44, 43, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29], [0, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 30, 29, 28, 27, 26, 25, 24, 23, 45, 44, 43, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31], [0, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 32, 31, 30, 29, 28, 27, 26, 25, 24, 23, 45, 44, 43, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33], [0, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 34, 33, 32, 31, 30, 29, 28, 27, 26, 25, 24, 23, 45, 44, 43, 42, 41, 40, 39, 38, 37, 36, 35], [0, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 26, 25, 24, 23, 45, 44, 43, 42, 41, 40, 39, 38, 37], [0, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 26, 25, 24, 23, 45, 44, 43, 42, 41, 40, 39], [0, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 26, 25, 24, 23, 45, 44, 43, 42, 41], [0, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 26, 25, 24, 23, 45, 44, 43], [0, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 44, 43, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 26, 25, 24, 23, 45]], 是, 是, g_dot_x_equals_g_x_g_inverse_is_a_complete_left_action)；依完整明示資料獨立重算；共軛類是element orbit並形成完整partition；singleton以forall g commute核對；共軛類不是coset或conjugate subgroup；不使用centralizer、class-size公式或類方程。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r03-finite-group-conjugacy-class-0021/)

有限群共軛類 · qf-mod45-conjugacy-action-table · candidate





## 22. 有限群共軛類

由完整Cayley table導出全部conjugation action與orbits。操作=conjugacy-action-table；資料={"group_table":[[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,0,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,24],[2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,0,1,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,24,25],[3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,0,1,2,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,24,25,26],[4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,0,1,2,3,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,24,25,26,27],[5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,0,1,2,3,4,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,24,25,26,27,28],[6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,0,1,2,3,4,5,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,24,25,26,27,28,29],[7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,0,1,2,3,4,5,6,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,24,25,26,27,28,29,30],[8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,0,1,2,3,4,5,6,7,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,24,25,26,27,28,29,30,31],[9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,0,1,2,3,4,5,6,7,8,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,24,25,26,27,28,29,30,31,32],[10,11,12,13,14,15,16,17,18,19,20,21,22,23,0,1,2,3,4,5,6,7,8,9,34,35,36,37,38,39,40,41,42,43,44,45,46,47,24,25,26,27,28,29,30,31,32,33],[11,12,13,14,15,16,17,18,19,20,21,22,23,0,1,2,3,4,5,6,7,8,9,10,35,36,37,38,39,40,41,42,43,44,45,46,47,24,25,26,27,28,29,30,31,32,33,34],[12,13,14,15,16,17,18,19,20,21,22,23,0,1,2,3,4,5,6,7,8,9,10,11,36,37,38,39,40,41,42,43,44,45,46,47,24,25,26,27,28,29,30,31,32,33,34,35],[13,14,15,16,17,18,19,20,21,22,23,0,1,2,3,4,5,6,7,8,9,10,11,12,37,38,39,40,41,42,43,44,45,46,47,24,25,26,27,28,29,30,31,32,33,34,35,36],[14,15,16,17,18,19,20,21,22,23,0,1,2,3,4,5,6,7,8,9,10,11,12,13,38,39,40,41,42,43,44,45,46,47,24,25,26,27,28,29,30,31,32,33,34,35,36,37],[15,16,17,18,19,20,21,22,23,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,39,40,41,42,43,44,45,46,47,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38],[16,17,18,19,20,21,22,23,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,40,41,42,43,44,45,46,47,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39],[17,18,19,20,21,22,23,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,41,42,43,44,45,46,47,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40],[18,19,20,21,22,23,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,42,43,44,45,46,47,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41],[19,20,21,22,23,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,43,44,45,46,47,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42],[20,21,22,23,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,44,45,46,47,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],[21,22,23,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,45,46,47,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44],[22,23,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,46,47,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45],[23,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,47,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46],[24,47,46,45,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,0,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1],[25,24,47,46,45,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,1,0,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2],[26,25,24,47,46,45,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,2,1,0,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3],[27,26,25,24,47,46,45,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,3,2,1,0,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4],[28,27,26,25,24,47,46,45,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,4,3,2,1,0,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5],[29,28,27,26,25,24,47,46,45,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,5,4,3,2,1,0,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6],[30,29,28,27,26,25,24,47,46,45,44,43,42,41,40,39,38,37,36,35,34,33,32,31,6,5,4,3,2,1,0,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7],[31,30,29,28,27,26,25,24,47,46,45,44,43,42,41,40,39,38,37,36,35,34,33,32,7,6,5,4,3,2,1,0,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8],[32,31,30,29,28,27,26,25,24,47,46,45,44,43,42,41,40,39,38,37,36,35,34,33,8,7,6,5,4,3,2,1,0,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9],[33,32,31,30,29,28,27,26,25,24,47,46,45,44,43,42,41,40,39,38,37,36,35,34,9,8,7,6,5,4,3,2,1,0,23,22,21,20,19,18,17,16,15,14,13,12,11,10],[34,33,32,31,30,29,28,27,26,25,24,47,46,45,44,43,42,41,40,39,38,37,36,35,10,9,8,7,6,5,4,3,2,1,0,23,22,21,20,19,18,17,16,15,14,13,12,11],[35,34,33,32,31,30,29,28,27,26,25,24,47,46,45,44,43,42,41,40,39,38,37,36,11,10,9,8,7,6,5,4,3,2,1,0,23,22,21,20,19,18,17,16,15,14,13,12],[36,35,34,33,32,31,30,29,28,27,26,25,24,47,46,45,44,43,42,41,40,39,38,37,12,11,10,9,8,7,6,5,4,3,2,1,0,23,22,21,20,19,18,17,16,15,14,13],[37,36,35,34,33,32,31,30,29,28,27,26,25,24,47,46,45,44,43,42,41,40,39,38,13,12,11,10,9,8,7,6,5,4,3,2,1,0,23,22,21,20,19,18,17,16,15,14],[38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,47,46,45,44,43,42,41,40,39,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0,23,22,21,20,19,18,17,16,15],[39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,47,46,45,44,43,42,41,40,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0,23,22,21,20,19,18,17,16],[40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,47,46,45,44,43,42,41,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0,23,22,21,20,19,18,17],[41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,47,46,45,44,43,42,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0,23,22,21,20,19,18],[42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,47,46,45,44,43,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0,23,22,21,20,19],[43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,47,46,45,44,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0,23,22,21,20],[44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,47,46,45,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0,23,22,21],[45,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,47,46,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0,23,22],[46,45,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,47,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0,23],[47,46,45,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0]],"identity":0}。請依 [conjugation_action, identity_action, composition_action, certificate] 欄序回答。

查看答案與解釋([[0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 24, 25], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 24, 25, 26, 27], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 24, 25, 26, 27, 28, 29], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 24, 25, 26, 27, 28, 29, 30, 31], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 40, 41, 42, 43, 44, 45, 46, 47, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 42, 43, 44, 45, 46, 47, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 44, 45, 46, 47, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 46, 47, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 24, 25], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 24, 25, 26, 27], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 24, 25, 26, 27, 28, 29], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 24, 25, 26, 27, 28, 29, 30, 31], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 40, 41, 42, 43, 44, 45, 46, 47, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 42, 43, 44, 45, 46, 47, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 44, 45, 46, 47, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 46, 47, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45], [0, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 24, 47, 46, 45, 44, 43, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 26, 25], [0, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 26, 25, 24, 47, 46, 45, 44, 43, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27], [0, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 28, 27, 26, 25, 24, 47, 46, 45, 44, 43, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29], [0, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 30, 29, 28, 27, 26, 25, 24, 47, 46, 45, 44, 43, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31], [0, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 32, 31, 30, 29, 28, 27, 26, 25, 24, 47, 46, 45, 44, 43, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33], [0, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 34, 33, 32, 31, 30, 29, 28, 27, 26, 25, 24, 47, 46, 45, 44, 43, 42, 41, 40, 39, 38, 37, 36, 35], [0, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 26, 25, 24, 47, 46, 45, 44, 43, 42, 41, 40, 39, 38, 37], [0, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 26, 25, 24, 47, 46, 45, 44, 43, 42, 41, 40, 39], [0, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 26, 25, 24, 47, 46, 45, 44, 43, 42, 41], [0, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 26, 25, 24, 47, 46, 45, 44, 43], [0, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 44, 43, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 26, 25, 24, 47, 46, 45], [0, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 46, 45, 44, 43, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 26, 25, 24, 47], [0, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 24, 47, 46, 45, 44, 43, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 26, 25], [0, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 26, 25, 24, 47, 46, 45, 44, 43, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27], [0, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 28, 27, 26, 25, 24, 47, 46, 45, 44, 43, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29], [0, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 30, 29, 28, 27, 26, 25, 24, 47, 46, 45, 44, 43, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31], [0, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 32, 31, 30, 29, 28, 27, 26, 25, 24, 47, 46, 45, 44, 43, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33], [0, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 34, 33, 32, 31, 30, 29, 28, 27, 26, 25, 24, 47, 46, 45, 44, 43, 42, 41, 40, 39, 38, 37, 36, 35], [0, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 26, 25, 24, 47, 46, 45, 44, 43, 42, 41, 40, 39, 38, 37], [0, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 26, 25, 24, 47, 46, 45, 44, 43, 42, 41, 40, 39], [0, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 26, 25, 24, 47, 46, 45, 44, 43, 42, 41], [0, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 26, 25, 24, 47, 46, 45, 44, 43], [0, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 44, 43, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 26, 25, 24, 47, 46, 45], [0, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 46, 45, 44, 43, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 26, 25, 24, 47]], 是, 是, g_dot_x_equals_g_x_g_inverse_is_a_complete_left_action)

Wave6第八層核對=([[0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 24, 25], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 24, 25, 26, 27], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 24, 25, 26, 27, 28, 29], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 24, 25, 26, 27, 28, 29, 30, 31], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 40, 41, 42, 43, 44, 45, 46, 47, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 42, 43, 44, 45, 46, 47, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 44, 45, 46, 47, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 46, 47, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 24, 25], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 24, 25, 26, 27], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 24, 25, 26, 27, 28, 29], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 24, 25, 26, 27, 28, 29, 30, 31], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 40, 41, 42, 43, 44, 45, 46, 47, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 42, 43, 44, 45, 46, 47, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 44, 45, 46, 47, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 46, 47, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45], [0, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 24, 47, 46, 45, 44, 43, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 26, 25], [0, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 26, 25, 24, 47, 46, 45, 44, 43, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27], [0, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 28, 27, 26, 25, 24, 47, 46, 45, 44, 43, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29], [0, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 30, 29, 28, 27, 26, 25, 24, 47, 46, 45, 44, 43, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31], [0, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 32, 31, 30, 29, 28, 27, 26, 25, 24, 47, 46, 45, 44, 43, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33], [0, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 34, 33, 32, 31, 30, 29, 28, 27, 26, 25, 24, 47, 46, 45, 44, 43, 42, 41, 40, 39, 38, 37, 36, 35], [0, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 26, 25, 24, 47, 46, 45, 44, 43, 42, 41, 40, 39, 38, 37], [0, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 26, 25, 24, 47, 46, 45, 44, 43, 42, 41, 40, 39], [0, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 26, 25, 24, 47, 46, 45, 44, 43, 42, 41], [0, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 26, 25, 24, 47, 46, 45, 44, 43], [0, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 44, 43, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 26, 25, 24, 47, 46, 45], [0, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 46, 45, 44, 43, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 26, 25, 24, 47], [0, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 24, 47, 46, 45, 44, 43, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 26, 25], [0, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 26, 25, 24, 47, 46, 45, 44, 43, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27], [0, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 28, 27, 26, 25, 24, 47, 46, 45, 44, 43, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29], [0, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 30, 29, 28, 27, 26, 25, 24, 47, 46, 45, 44, 43, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31], [0, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 32, 31, 30, 29, 28, 27, 26, 25, 24, 47, 46, 45, 44, 43, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33], [0, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 34, 33, 32, 31, 30, 29, 28, 27, 26, 25, 24, 47, 46, 45, 44, 43, 42, 41, 40, 39, 38, 37, 36, 35], [0, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 26, 25, 24, 47, 46, 45, 44, 43, 42, 41, 40, 39, 38, 37], [0, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 26, 25, 24, 47, 46, 45, 44, 43, 42, 41, 40, 39], [0, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 26, 25, 24, 47, 46, 45, 44, 43, 42, 41], [0, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 26, 25, 24, 47, 46, 45, 44, 43], [0, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 44, 43, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 26, 25, 24, 47, 46, 45], [0, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 46, 45, 44, 43, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 26, 25, 24, 47]], 是, 是, g_dot_x_equals_g_x_g_inverse_is_a_complete_left_action)；依完整明示資料獨立重算；共軛類是element orbit並形成完整partition；singleton以forall g commute核對；共軛類不是coset或conjugate subgroup；不使用centralizer、class-size公式或類方程。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r03-finite-group-conjugacy-class-0022/)

有限群共軛類 · qf-mod45-conjugacy-action-table · candidate





## 23. 有限群共軛類

由完整Cayley table導出全部conjugation action與orbits。操作=conjugacy-action-table；資料={"group_table":[[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,0,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,25],[2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,0,1,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,25,26],[3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,0,1,2,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,25,26,27],[4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,0,1,2,3,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,25,26,27,28],[5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,0,1,2,3,4,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,25,26,27,28,29],[6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,0,1,2,3,4,5,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,25,26,27,28,29,30],[7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,0,1,2,3,4,5,6,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,25,26,27,28,29,30,31],[8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,0,1,2,3,4,5,6,7,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,25,26,27,28,29,30,31,32],[9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,0,1,2,3,4,5,6,7,8,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,25,26,27,28,29,30,31,32,33],[10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,0,1,2,3,4,5,6,7,8,9,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,25,26,27,28,29,30,31,32,33,34],[11,12,13,14,15,16,17,18,19,20,21,22,23,24,0,1,2,3,4,5,6,7,8,9,10,36,37,38,39,40,41,42,43,44,45,46,47,48,49,25,26,27,28,29,30,31,32,33,34,35],[12,13,14,15,16,17,18,19,20,21,22,23,24,0,1,2,3,4,5,6,7,8,9,10,11,37,38,39,40,41,42,43,44,45,46,47,48,49,25,26,27,28,29,30,31,32,33,34,35,36],[13,14,15,16,17,18,19,20,21,22,23,24,0,1,2,3,4,5,6,7,8,9,10,11,12,38,39,40,41,42,43,44,45,46,47,48,49,25,26,27,28,29,30,31,32,33,34,35,36,37],[14,15,16,17,18,19,20,21,22,23,24,0,1,2,3,4,5,6,7,8,9,10,11,12,13,39,40,41,42,43,44,45,46,47,48,49,25,26,27,28,29,30,31,32,33,34,35,36,37,38],[15,16,17,18,19,20,21,22,23,24,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,40,41,42,43,44,45,46,47,48,49,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39],[16,17,18,19,20,21,22,23,24,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,41,42,43,44,45,46,47,48,49,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40],[17,18,19,20,21,22,23,24,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,42,43,44,45,46,47,48,49,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41],[18,19,20,21,22,23,24,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,43,44,45,46,47,48,49,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42],[19,20,21,22,23,24,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,44,45,46,47,48,49,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],[20,21,22,23,24,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,45,46,47,48,49,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44],[21,22,23,24,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,46,47,48,49,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45],[22,23,24,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,47,48,49,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46],[23,24,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,48,49,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47],[24,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,49,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48],[25,49,48,47,46,45,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,0,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1],[26,25,49,48,47,46,45,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,1,0,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2],[27,26,25,49,48,47,46,45,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,2,1,0,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3],[28,27,26,25,49,48,47,46,45,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,3,2,1,0,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4],[29,28,27,26,25,49,48,47,46,45,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,4,3,2,1,0,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5],[30,29,28,27,26,25,49,48,47,46,45,44,43,42,41,40,39,38,37,36,35,34,33,32,31,5,4,3,2,1,0,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6],[31,30,29,28,27,26,25,49,48,47,46,45,44,43,42,41,40,39,38,37,36,35,34,33,32,6,5,4,3,2,1,0,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7],[32,31,30,29,28,27,26,25,49,48,47,46,45,44,43,42,41,40,39,38,37,36,35,34,33,7,6,5,4,3,2,1,0,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8],[33,32,31,30,29,28,27,26,25,49,48,47,46,45,44,43,42,41,40,39,38,37,36,35,34,8,7,6,5,4,3,2,1,0,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9],[34,33,32,31,30,29,28,27,26,25,49,48,47,46,45,44,43,42,41,40,39,38,37,36,35,9,8,7,6,5,4,3,2,1,0,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10],[35,34,33,32,31,30,29,28,27,26,25,49,48,47,46,45,44,43,42,41,40,39,38,37,36,10,9,8,7,6,5,4,3,2,1,0,24,23,22,21,20,19,18,17,16,15,14,13,12,11],[36,35,34,33,32,31,30,29,28,27,26,25,49,48,47,46,45,44,43,42,41,40,39,38,37,11,10,9,8,7,6,5,4,3,2,1,0,24,23,22,21,20,19,18,17,16,15,14,13,12],[37,36,35,34,33,32,31,30,29,28,27,26,25,49,48,47,46,45,44,43,42,41,40,39,38,12,11,10,9,8,7,6,5,4,3,2,1,0,24,23,22,21,20,19,18,17,16,15,14,13],[38,37,36,35,34,33,32,31,30,29,28,27,26,25,49,48,47,46,45,44,43,42,41,40,39,13,12,11,10,9,8,7,6,5,4,3,2,1,0,24,23,22,21,20,19,18,17,16,15,14],[39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,49,48,47,46,45,44,43,42,41,40,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0,24,23,22,21,20,19,18,17,16,15],[40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,49,48,47,46,45,44,43,42,41,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0,24,23,22,21,20,19,18,17,16],[41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,49,48,47,46,45,44,43,42,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0,24,23,22,21,20,19,18,17],[42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,49,48,47,46,45,44,43,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0,24,23,22,21,20,19,18],[43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,49,48,47,46,45,44,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0,24,23,22,21,20,19],[44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,49,48,47,46,45,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0,24,23,22,21,20],[45,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,49,48,47,46,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0,24,23,22,21],[46,45,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,49,48,47,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0,24,23,22],[47,46,45,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,49,48,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0,24,23],[48,47,46,45,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,49,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0,24],[49,48,47,46,45,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0]],"identity":0}。請依 [conjugation_action, identity_action, composition_action, certificate] 欄序回答。

查看答案與解釋([[0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 25, 26], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 25, 26, 27, 28], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 25, 26, 27, 28, 29, 30], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 25, 26, 27, 28, 29, 30, 31, 32], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 41, 42, 43, 44, 45, 46, 47, 48, 49, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 43, 44, 45, 46, 47, 48, 49, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 45, 46, 47, 48, 49, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 47, 48, 49, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 49, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 25], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 25, 26, 27], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 30, 31, 32, 33, 34, 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26, 25, 49, 48, 47, 46, 45, 44, 43, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33], [0, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 34, 33, 32, 31, 30, 29, 28, 27, 26, 25, 49, 48, 47, 46, 45, 44, 43, 42, 41, 40, 39, 38, 37, 36, 35], [0, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 26, 25, 49, 48, 47, 46, 45, 44, 43, 42, 41, 40, 39, 38, 37], [0, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 26, 25, 49, 48, 47, 46, 45, 44, 43, 42, 41, 40, 39], [0, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 26, 25, 49, 48, 47, 46, 45, 44, 43, 42, 41], [0, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 26, 25, 49, 48, 47, 46, 45, 44, 43], [0, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 44, 43, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 26, 25, 49, 48, 47, 46, 45], [0, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 46, 45, 44, 43, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 26, 25, 49, 48, 47], [0, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 48, 47, 46, 45, 44, 43, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 26, 25, 49]], 是, 是, g_dot_x_equals_g_x_g_inverse_is_a_complete_left_action)；依完整明示資料獨立重算；共軛類是element orbit並形成完整partition；singleton以forall g commute核對；共軛類不是coset或conjugate subgroup；不使用centralizer、class-size公式或類方程。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r03-finite-group-conjugacy-class-0023/)

有限群共軛類 · qf-mod45-conjugacy-action-table · candidate





## 24. 有限群共軛類

由完整Cayley table導出全部conjugation action與orbits。操作=conjugacy-action-table；資料={"group_table":[[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,0,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,26],[2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,0,1,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,26,27],[3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,0,1,2,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,26,27,28],[4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,0,1,2,3,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,26,27,28,29],[5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,0,1,2,3,4,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,26,27,28,29,30],[6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,0,1,2,3,4,5,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,26,27,28,29,30,31],[7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,0,1,2,3,4,5,6,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,26,27,28,29,30,31,32],[8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,0,1,2,3,4,5,6,7,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,26,27,28,29,30,31,32,33],[9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,0,1,2,3,4,5,6,7,8,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,26,27,28,29,30,31,32,33,34],[10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,0,1,2,3,4,5,6,7,8,9,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,26,27,28,29,30,31,32,33,34,35],[11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,0,1,2,3,4,5,6,7,8,9,10,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,26,27,28,29,30,31,32,33,34,35,36],[12,13,14,15,16,17,18,19,20,21,22,23,24,25,0,1,2,3,4,5,6,7,8,9,10,11,38,39,40,41,42,43,44,45,46,47,48,49,50,51,26,27,28,29,30,31,32,33,34,35,36,37],[13,14,15,16,17,18,19,20,21,22,23,24,25,0,1,2,3,4,5,6,7,8,9,10,11,12,39,40,41,42,43,44,45,46,47,48,49,50,51,26,27,28,29,30,31,32,33,34,35,36,37,38],[14,15,16,17,18,19,20,21,22,23,24,25,0,1,2,3,4,5,6,7,8,9,10,11,12,13,40,41,42,43,44,45,46,47,48,49,50,51,26,27,28,29,30,31,32,33,34,35,36,37,38,39],[15,16,17,18,19,20,21,22,23,24,25,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,41,42,43,44,45,46,47,48,49,50,51,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40],[16,17,18,19,20,21,22,23,24,25,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,42,43,44,45,46,47,48,49,50,51,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41],[17,18,19,20,21,22,23,24,25,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,43,44,45,46,47,48,49,50,51,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42],[18,19,20,21,22,23,24,25,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,44,45,46,47,48,49,50,51,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],[19,20,21,22,23,24,25,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,45,46,47,48,49,50,51,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44],[20,21,22,23,24,25,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,46,47,48,49,50,51,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45],[21,22,23,24,25,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,47,48,49,50,51,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46],[22,23,24,25,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,48,49,50,51,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47],[23,24,25,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,49,50,51,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48],[24,25,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,50,51,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49],[25,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,51,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50],[26,51,50,49,48,47,46,45,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,0,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1],[27,26,51,50,49,48,47,46,45,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,1,0,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2],[28,27,26,51,50,49,48,47,46,45,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,2,1,0,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3],[29,28,27,26,51,50,49,48,47,46,45,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,3,2,1,0,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4],[30,29,28,27,26,51,50,49,48,47,46,45,44,43,42,41,40,39,38,37,36,35,34,33,32,31,4,3,2,1,0,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5],[31,30,29,28,27,26,51,50,49,48,47,46,45,44,43,42,41,40,39,38,37,36,35,34,33,32,5,4,3,2,1,0,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6],[32,31,30,29,28,27,26,51,50,49,48,47,46,45,44,43,42,41,40,39,38,37,36,35,34,33,6,5,4,3,2,1,0,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7],[33,32,31,30,29,28,27,26,51,50,49,48,47,46,45,44,43,42,41,40,39,38,37,36,35,34,7,6,5,4,3,2,1,0,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8],[34,33,32,31,30,29,28,27,26,51,50,49,48,47,46,45,44,43,42,41,40,39,38,37,36,35,8,7,6,5,4,3,2,1,0,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9],[35,34,33,32,31,30,29,28,27,26,51,50,49,48,47,46,45,44,43,42,41,40,39,38,37,36,9,8,7,6,5,4,3,2,1,0,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10],[36,35,34,33,32,31,30,29,28,27,26,51,50,49,48,47,46,45,44,43,42,41,40,39,38,37,10,9,8,7,6,5,4,3,2,1,0,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11],[37,36,35,34,33,32,31,30,29,28,27,26,51,50,49,48,47,46,45,44,43,42,41,40,39,38,11,10,9,8,7,6,5,4,3,2,1,0,25,24,23,22,21,20,19,18,17,16,15,14,13,12],[38,37,36,35,34,33,32,31,30,29,28,27,26,51,50,49,48,47,46,45,44,43,42,41,40,39,12,11,10,9,8,7,6,5,4,3,2,1,0,25,24,23,22,21,20,19,18,17,16,15,14,13],[39,38,37,36,35,34,33,32,31,30,29,28,27,26,51,50,49,48,47,46,45,44,43,42,41,40,13,12,11,10,9,8,7,6,5,4,3,2,1,0,25,24,23,22,21,20,19,18,17,16,15,14],[40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,51,50,49,48,47,46,45,44,43,42,41,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0,25,24,23,22,21,20,19,18,17,16,15],[41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,51,50,49,48,47,46,45,44,43,42,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0,25,24,23,22,21,20,19,18,17,16],[42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,51,50,49,48,47,46,45,44,43,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0,25,24,23,22,21,20,19,18,17],[43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,51,50,49,48,47,46,45,44,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0,25,24,23,22,21,20,19,18],[44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,51,50,49,48,47,46,45,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0,25,24,23,22,21,20,19],[45,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,51,50,49,48,47,46,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0,25,24,23,22,21,20],[46,45,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,51,50,49,48,47,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0,25,24,23,22,21],[47,46,45,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,51,50,49,48,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0,25,24,23,22],[48,47,46,45,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,51,50,49,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0,25,24,23],[49,48,47,46,45,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,51,50,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0,25,24],[50,49,48,47,46,45,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,51,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0,25],[51,50,49,48,47,46,45,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0]],"identity":0}。請依 [conjugation_action, identity_action, composition_action, certificate] 欄序回答。

查看答案與解釋([[0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 26, 27], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 26, 27, 28, 29], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 26, 27, 28, 29, 30, 31], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 26, 27, 28, 29, 30, 31, 32, 33], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 44, 45, 46, 47, 48, 49, 50, 51, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 46, 47, 48, 49, 50, 51, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 48, 49, 50, 51, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 50, 51, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 26, 27], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 26, 27, 28, 29], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 26, 27, 28, 29, 30, 31], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 26, 27, 28, 29, 30, 31, 32, 33], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 44, 45, 46, 47, 48, 49, 50, 51, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 46, 47, 48, 49, 50, 51, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 48, 49, 50, 51, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 50, 51, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49], [0, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 26, 51, 50, 49, 48, 47, 46, 45, 44, 43, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27], [0, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 28, 27, 26, 51, 50, 49, 48, 47, 46, 45, 44, 43, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29], [0, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 30, 29, 28, 27, 26, 51, 50, 49, 48, 47, 46, 45, 44, 43, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31], [0, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 32, 31, 30, 29, 28, 27, 26, 51, 50, 49, 48, 47, 46, 45, 44, 43, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33], [0, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 34, 33, 32, 31, 30, 29, 28, 27, 26, 51, 50, 49, 48, 47, 46, 45, 44, 43, 42, 41, 40, 39, 38, 37, 36, 35], [0, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 26, 51, 50, 49, 48, 47, 46, 45, 44, 43, 42, 41, 40, 39, 38, 37], [0, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 26, 51, 50, 49, 48, 47, 46, 45, 44, 43, 42, 41, 40, 39], [0, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 26, 51, 50, 49, 48, 47, 46, 45, 44, 43, 42, 41], [0, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 26, 51, 50, 49, 48, 47, 46, 45, 44, 43], [0, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 44, 43, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 26, 51, 50, 49, 48, 47, 46, 45], [0, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 46, 45, 44, 43, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 26, 51, 50, 49, 48, 47], [0, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 48, 47, 46, 45, 44, 43, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 26, 51, 50, 49], [0, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 50, 49, 48, 47, 46, 45, 44, 43, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 26, 51], [0, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 26, 51, 50, 49, 48, 47, 46, 45, 44, 43, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27], [0, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 28, 27, 26, 51, 50, 49, 48, 47, 46, 45, 44, 43, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29], [0, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 30, 29, 28, 27, 26, 51, 50, 49, 48, 47, 46, 45, 44, 43, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31], [0, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 32, 31, 30, 29, 28, 27, 26, 51, 50, 49, 48, 47, 46, 45, 44, 43, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33], [0, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 34, 33, 32, 31, 30, 29, 28, 27, 26, 51, 50, 49, 48, 47, 46, 45, 44, 43, 42, 41, 40, 39, 38, 37, 36, 35], [0, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 26, 51, 50, 49, 48, 47, 46, 45, 44, 43, 42, 41, 40, 39, 38, 37], [0, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 26, 51, 50, 49, 48, 47, 46, 45, 44, 43, 42, 41, 40, 39], [0, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 26, 51, 50, 49, 48, 47, 46, 45, 44, 43, 42, 41], [0, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 26, 51, 50, 49, 48, 47, 46, 45, 44, 43], [0, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 44, 43, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 26, 51, 50, 49, 48, 47, 46, 45], [0, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 46, 45, 44, 43, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 26, 51, 50, 49, 48, 47], [0, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 48, 47, 46, 45, 44, 43, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 26, 51, 50, 49], [0, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 50, 49, 48, 47, 46, 45, 44, 43, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 26, 51]], 是, 是, g_dot_x_equals_g_x_g_inverse_is_a_complete_left_action)

Wave6第八層核對=([[0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 26, 27], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 26, 27, 28, 29], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 26, 27, 28, 29, 30, 31], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 26, 27, 28, 29, 30, 31, 32, 33], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 44, 45, 46, 47, 48, 49, 50, 51, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 46, 47, 48, 49, 50, 51, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 48, 49, 50, 51, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 50, 51, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 26, 27], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 26, 27, 28, 29], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 26, 27, 28, 29, 30, 31], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 26, 27, 28, 29, 30, 31, 32, 33], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 44, 45, 46, 47, 48, 49, 50, 51, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 46, 47, 48, 49, 50, 51, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 48, 49, 50, 51, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 50, 51, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49], [0, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 26, 51, 50, 49, 48, 47, 46, 45, 44, 43, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27], [0, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 28, 27, 26, 51, 50, 49, 48, 47, 46, 45, 44, 43, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29], [0, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 30, 29, 28, 27, 26, 51, 50, 49, 48, 47, 46, 45, 44, 43, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31], [0, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 32, 31, 30, 29, 28, 27, 26, 51, 50, 49, 48, 47, 46, 45, 44, 43, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33], [0, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 34, 33, 32, 31, 30, 29, 28, 27, 26, 51, 50, 49, 48, 47, 46, 45, 44, 43, 42, 41, 40, 39, 38, 37, 36, 35], [0, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 26, 51, 50, 49, 48, 47, 46, 45, 44, 43, 42, 41, 40, 39, 38, 37], [0, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 26, 51, 50, 49, 48, 47, 46, 45, 44, 43, 42, 41, 40, 39], [0, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 26, 51, 50, 49, 48, 47, 46, 45, 44, 43, 42, 41], [0, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 26, 51, 50, 49, 48, 47, 46, 45, 44, 43], [0, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 44, 43, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 26, 51, 50, 49, 48, 47, 46, 45], [0, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 46, 45, 44, 43, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 26, 51, 50, 49, 48, 47], [0, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 48, 47, 46, 45, 44, 43, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 26, 51, 50, 49], [0, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 50, 49, 48, 47, 46, 45, 44, 43, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 26, 51], [0, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 26, 51, 50, 49, 48, 47, 46, 45, 44, 43, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27], [0, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 28, 27, 26, 51, 50, 49, 48, 47, 46, 45, 44, 43, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29], [0, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 30, 29, 28, 27, 26, 51, 50, 49, 48, 47, 46, 45, 44, 43, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31], [0, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 32, 31, 30, 29, 28, 27, 26, 51, 50, 49, 48, 47, 46, 45, 44, 43, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33], [0, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 34, 33, 32, 31, 30, 29, 28, 27, 26, 51, 50, 49, 48, 47, 46, 45, 44, 43, 42, 41, 40, 39, 38, 37, 36, 35], [0, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 26, 51, 50, 49, 48, 47, 46, 45, 44, 43, 42, 41, 40, 39, 38, 37], [0, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 26, 51, 50, 49, 48, 47, 46, 45, 44, 43, 42, 41, 40, 39], [0, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 26, 51, 50, 49, 48, 47, 46, 45, 44, 43, 42, 41], [0, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 26, 51, 50, 49, 48, 47, 46, 45, 44, 43], [0, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 44, 43, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 26, 51, 50, 49, 48, 47, 46, 45], [0, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 46, 45, 44, 43, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 26, 51, 50, 49, 48, 47], [0, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 48, 47, 46, 45, 44, 43, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 26, 51, 50, 49], [0, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 50, 49, 48, 47, 46, 45, 44, 43, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 26, 51]], 是, 是, g_dot_x_equals_g_x_g_inverse_is_a_complete_left_action)；依完整明示資料獨立重算；共軛類是element orbit並形成完整partition；singleton以forall g commute核對；共軛類不是coset或conjugate subgroup；不使用centralizer、class-size公式或類方程。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r03-finite-group-conjugacy-class-0024/)

有限群共軛類 · qf-mod45-conjugacy-action-table · candidate





## 25. 有限群共軛類

由完整Cayley table導出全部conjugation action與orbits。操作=conjugacy-action-table；資料={"group_table":[[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,0,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,27],[2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,0,1,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,27,28],[3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,0,1,2,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,27,28,29],[4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,0,1,2,3,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,27,28,29,30],[5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,0,1,2,3,4,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,27,28,29,30,31],[6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,0,1,2,3,4,5,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,27,28,29,30,31,32],[7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,0,1,2,3,4,5,6,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,27,28,29,30,31,32,33],[8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,0,1,2,3,4,5,6,7,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,27,28,29,30,31,32,33,34],[9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,0,1,2,3,4,5,6,7,8,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,27,28,29,30,31,32,33,34,35],[10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,0,1,2,3,4,5,6,7,8,9,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,27,28,29,30,31,32,33,34,35,36],[11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,0,1,2,3,4,5,6,7,8,9,10,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,27,28,29,30,31,32,33,34,35,36,37],[12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,0,1,2,3,4,5,6,7,8,9,10,11,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,27,28,29,30,31,32,33,34,35,36,37,38],[13,14,15,16,17,18,19,20,21,22,23,24,25,26,0,1,2,3,4,5,6,7,8,9,10,11,12,40,41,42,43,44,45,46,47,48,49,50,51,52,53,27,28,29,30,31,32,33,34,35,36,37,38,39],[14,15,16,17,18,19,20,21,22,23,24,25,26,0,1,2,3,4,5,6,7,8,9,10,11,12,13,41,42,43,44,45,46,47,48,49,50,51,52,53,27,28,29,30,31,32,33,34,35,36,37,38,39,40],[15,16,17,18,19,20,21,22,23,24,25,26,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,42,43,44,45,46,47,48,49,50,51,52,53,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41],[16,17,18,19,20,21,22,23,24,25,26,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,43,44,45,46,47,48,49,50,51,52,53,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42],[17,18,19,20,21,22,23,24,25,26,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,44,45,46,47,48,49,50,51,52,53,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],[18,19,20,21,22,23,24,25,26,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,45,46,47,48,49,50,51,52,53,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44],[19,20,21,22,23,24,25,26,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,46,47,48,49,50,51,52,53,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45],[20,21,22,23,24,25,26,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,47,48,49,50,51,52,53,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46],[21,22,23,24,25,26,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,48,49,50,51,52,53,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47],[22,23,24,25,26,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,49,50,51,52,53,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48],[23,24,25,26,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,50,51,52,53,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49],[24,25,26,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,51,52,53,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50],[25,26,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,52,53,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51],[26,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,53,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52],[27,53,52,51,50,49,48,47,46,45,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,0,26,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1],[28,27,53,52,51,50,49,48,47,46,45,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,1,0,26,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2],[29,28,27,53,52,51,50,49,48,47,46,45,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,2,1,0,26,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3],[30,29,28,27,53,52,51,50,49,48,47,46,45,44,43,42,41,40,39,38,37,36,35,34,33,32,31,3,2,1,0,26,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4],[31,30,29,28,27,53,52,51,50,49,48,47,46,45,44,43,42,41,40,39,38,37,36,35,34,33,32,4,3,2,1,0,26,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5],[32,31,30,29,28,27,53,52,51,50,49,48,47,46,45,44,43,42,41,40,39,38,37,36,35,34,33,5,4,3,2,1,0,26,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6],[33,32,31,30,29,28,27,53,52,51,50,49,48,47,46,45,44,43,42,41,40,39,38,37,36,35,34,6,5,4,3,2,1,0,26,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7],[34,33,32,31,30,29,28,27,53,52,51,50,49,48,47,46,45,44,43,42,41,40,39,38,37,36,35,7,6,5,4,3,2,1,0,26,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8],[35,34,33,32,31,30,29,28,27,53,52,51,50,49,48,47,46,45,44,43,42,41,40,39,38,37,36,8,7,6,5,4,3,2,1,0,26,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9],[36,35,34,33,32,31,30,29,28,27,53,52,51,50,49,48,47,46,45,44,43,42,41,40,39,38,37,9,8,7,6,5,4,3,2,1,0,26,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10],[37,36,35,34,33,32,31,30,29,28,27,53,52,51,50,49,48,47,46,45,44,43,42,41,40,39,38,10,9,8,7,6,5,4,3,2,1,0,26,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11],[38,37,36,35,34,33,32,31,30,29,28,27,53,52,51,50,49,48,47,46,45,44,43,42,41,40,39,11,10,9,8,7,6,5,4,3,2,1,0,26,25,24,23,22,21,20,19,18,17,16,15,14,13,12],[39,38,37,36,35,34,33,32,31,30,29,28,27,53,52,51,50,49,48,47,46,45,44,43,42,41,40,12,11,10,9,8,7,6,5,4,3,2,1,0,26,25,24,23,22,21,20,19,18,17,16,15,14,13],[40,39,38,37,36,35,34,33,32,31,30,29,28,27,53,52,51,50,49,48,47,46,45,44,43,42,41,13,12,11,10,9,8,7,6,5,4,3,2,1,0,26,25,24,23,22,21,20,19,18,17,16,15,14],[41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,53,52,51,50,49,48,47,46,45,44,43,42,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0,26,25,24,23,22,21,20,19,18,17,16,15],[42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,53,52,51,50,49,48,47,46,45,44,43,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0,26,25,24,23,22,21,20,19,18,17,16],[43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,53,52,51,50,49,48,47,46,45,44,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0,26,25,24,23,22,21,20,19,18,17],[44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,53,52,51,50,49,48,47,46,45,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0,26,25,24,23,22,21,20,19,18],[45,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,53,52,51,50,49,48,47,46,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0,26,25,24,23,22,21,20,19],[46,45,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,53,52,51,50,49,48,47,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0,26,25,24,23,22,21,20],[47,46,45,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,53,52,51,50,49,48,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0,26,25,24,23,22,21],[48,47,46,45,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,53,52,51,50,49,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0,26,25,24,23,22],[49,48,47,46,45,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,53,52,51,50,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0,26,25,24,23],[50,49,48,47,46,45,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,53,52,51,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0,26,25,24],[51,50,49,48,47,46,45,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,53,52,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0,26,25],[52,51,50,49,48,47,46,45,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,53,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0,26],[53,52,51,50,49,48,47,46,45,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0]],"identity":0}。請依 [conjugation_action, identity_action, composition_action, certificate] 欄序回答。

查看答案與解釋([[0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 27, 28], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 27, 28, 29, 30], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 27, 28, 29, 30, 31, 32], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 27, 28, 29, 30, 31, 32, 33, 34], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 45, 46, 47, 48, 49, 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45], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 48, 49, 50, 51, 52, 53, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 50, 51, 52, 53, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 52, 53, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51], [0, 26, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 27, 53, 52, 51, 50, 49, 48, 47, 46, 45, 44, 43, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28], [0, 26, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 29, 28, 27, 53, 52, 51, 50, 49, 48, 47, 46, 45, 44, 43, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30], [0, 26, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 31, 30, 29, 28, 27, 53, 52, 51, 50, 49, 48, 47, 46, 45, 44, 43, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32], [0, 26, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 33, 32, 31, 30, 29, 28, 27, 53, 52, 51, 50, 49, 48, 47, 46, 45, 44, 43, 42, 41, 40, 39, 38, 37, 36, 35, 34], [0, 26, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 35, 34, 33, 32, 31, 30, 29, 28, 27, 53, 52, 51, 50, 49, 48, 47, 46, 45, 44, 43, 42, 41, 40, 39, 38, 37, 36], [0, 26, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 53, 52, 51, 50, 49, 48, 47, 46, 45, 44, 43, 42, 41, 40, 39, 38], [0, 26, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 53, 52, 51, 50, 49, 48, 47, 46, 45, 44, 43, 42, 41, 40], [0, 26, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 53, 52, 51, 50, 49, 48, 47, 46, 45, 44, 43, 42], [0, 26, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 43, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 53, 52, 51, 50, 49, 48, 47, 46, 45, 44], [0, 26, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 45, 44, 43, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 53, 52, 51, 50, 49, 48, 47, 46], [0, 26, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 47, 46, 45, 44, 43, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 53, 52, 51, 50, 49, 48], [0, 26, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 49, 48, 47, 46, 45, 44, 43, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 53, 52, 51, 50], [0, 26, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 51, 50, 49, 48, 47, 46, 45, 44, 43, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 53, 52], [0, 26, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 53, 52, 51, 50, 49, 48, 47, 46, 45, 44, 43, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27], [0, 26, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 28, 27, 53, 52, 51, 50, 49, 48, 47, 46, 45, 44, 43, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29], [0, 26, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 30, 29, 28, 27, 53, 52, 51, 50, 49, 48, 47, 46, 45, 44, 43, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31], [0, 26, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 32, 31, 30, 29, 28, 27, 53, 52, 51, 50, 49, 48, 47, 46, 45, 44, 43, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33], [0, 26, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 34, 33, 32, 31, 30, 29, 28, 27, 53, 52, 51, 50, 49, 48, 47, 46, 45, 44, 43, 42, 41, 40, 39, 38, 37, 36, 35], [0, 26, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 53, 52, 51, 50, 49, 48, 47, 46, 45, 44, 43, 42, 41, 40, 39, 38, 37], [0, 26, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 53, 52, 51, 50, 49, 48, 47, 46, 45, 44, 43, 42, 41, 40, 39], [0, 26, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 53, 52, 51, 50, 49, 48, 47, 46, 45, 44, 43, 42, 41], [0, 26, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 53, 52, 51, 50, 49, 48, 47, 46, 45, 44, 43], [0, 26, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 44, 43, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 53, 52, 51, 50, 49, 48, 47, 46, 45], [0, 26, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 46, 45, 44, 43, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 53, 52, 51, 50, 49, 48, 47], [0, 26, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 48, 47, 46, 45, 44, 43, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 53, 52, 51, 50, 49], [0, 26, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 50, 49, 48, 47, 46, 45, 44, 43, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 53, 52, 51], [0, 26, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 52, 51, 50, 49, 48, 47, 46, 45, 44, 43, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 53]], 是, 是, g_dot_x_equals_g_x_g_inverse_is_a_complete_left_action)；依完整明示資料獨立重算；共軛類是element orbit並形成完整partition；singleton以forall g commute核對；共軛類不是coset或conjugate subgroup；不使用centralizer、class-size公式或類方程。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r03-finite-group-conjugacy-class-0025/)

有限群共軛類 · qf-mod45-conjugacy-action-table · candidate





## 26. 有限群共軛類

由完整Cayley table導出全部conjugation action與orbits。操作=conjugacy-orbit-class；資料={"group_table":[[0,1,2,3,4,5],[1,2,0,4,5,3],[2,0,1,5,3,4],[3,5,4,0,2,1],[4,3,5,1,0,2],[5,4,3,2,1,0]],"identity":0,"element":3}。請依 [element, action_image_rows, conjugacy_class, certificate] 欄序回答。

查看答案與解釋(3, [[0, 3], [1, 5], [2, 4], [3, 3], [4, 5], [5, 4]], [3, 4, 5], conjugacy_class_is_the_complete_conjugation_orbit_not_a_coset)

Wave6第八層核對=(3, [[0, 3], [1, 5], [2, 4], [3, 3], [4, 5], [5, 4]], [3, 4, 5], conjugacy_class_is_the_complete_conjugation_orbit_not_a_coset)；依完整明示資料獨立重算；共軛類是element orbit並形成完整partition；singleton以forall g commute核對；共軛類不是coset或conjugate subgroup；不使用centralizer、class-size公式或類方程。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r03-finite-group-conjugacy-class-0026/)

有限群共軛類 · qf-mod45-conjugacy-orbit-class · candidate





## 27. 有限群共軛類

由完整Cayley table導出全部conjugation action與orbits。操作=conjugacy-orbit-class；資料={"group_table":[[0,1,2,3,4,5,6,7],[1,2,3,0,5,6,7,4],[2,3,0,1,6,7,4,5],[3,0,1,2,7,4,5,6],[4,7,6,5,0,3,2,1],[5,4,7,6,1,0,3,2],[6,5,4,7,2,1,0,3],[7,6,5,4,3,2,1,0]],"identity":0,"element":1}。請依 [element, action_image_rows, conjugacy_class, certificate] 欄序回答。

查看答案與解釋(1, [[0, 1], [1, 1], [2, 1], [3, 1], [4, 3], [5, 3], [6, 3], [7, 3]], [1, 3], conjugacy_class_is_the_complete_conjugation_orbit_not_a_coset)

Wave6第八層核對=(1, [[0, 1], [1, 1], [2, 1], [3, 1], [4, 3], [5, 3], [6, 3], [7, 3]], [1, 3], conjugacy_class_is_the_complete_conjugation_orbit_not_a_coset)；依完整明示資料獨立重算；共軛類是element orbit並形成完整partition；singleton以forall g commute核對；共軛類不是coset或conjugate subgroup；不使用centralizer、class-size公式或類方程。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r03-finite-group-conjugacy-class-0027/)

有限群共軛類 · qf-mod45-conjugacy-orbit-class · candidate





## 28. 有限群共軛類

由完整Cayley table導出全部conjugation action與orbits。操作=conjugacy-orbit-class；資料={"group_table":[[0,1,2,3,4,5,6,7,8,9],[1,2,3,4,0,6,7,8,9,5],[2,3,4,0,1,7,8,9,5,6],[3,4,0,1,2,8,9,5,6,7],[4,0,1,2,3,9,5,6,7,8],[5,9,8,7,6,0,4,3,2,1],[6,5,9,8,7,1,0,4,3,2],[7,6,5,9,8,2,1,0,4,3],[8,7,6,5,9,3,2,1,0,4],[9,8,7,6,5,4,3,2,1,0]],"identity":0,"element":5}。請依 [element, action_image_rows, conjugacy_class, certificate] 欄序回答。

查看答案與解釋(5, [[0, 5], [1, 7], [2, 9], [3, 6], [4, 8], [5, 5], [6, 7], [7, 9], [8, 6], [9, 8]], [5, 6, 7, 8, 9], conjugacy_class_is_the_complete_conjugation_orbit_not_a_coset)

Wave6第八層核對=(5, [[0, 5], [1, 7], [2, 9], [3, 6], [4, 8], [5, 5], [6, 7], [7, 9], [8, 6], [9, 8]], [5, 6, 7, 8, 9], conjugacy_class_is_the_complete_conjugation_orbit_not_a_coset)；依完整明示資料獨立重算；共軛類是element orbit並形成完整partition；singleton以forall g commute核對；共軛類不是coset或conjugate subgroup；不使用centralizer、class-size公式或類方程。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r03-finite-group-conjugacy-class-0028/)

有限群共軛類 · qf-mod45-conjugacy-orbit-class · candidate





## 29. 有限群共軛類

由完整Cayley table導出全部conjugation action與orbits。操作=conjugacy-orbit-class；資料={"group_table":[[0,1,2,3,4,5,6,7,8,9,10,11],[1,2,3,4,5,0,7,8,9,10,11,6],[2,3,4,5,0,1,8,9,10,11,6,7],[3,4,5,0,1,2,9,10,11,6,7,8],[4,5,0,1,2,3,10,11,6,7,8,9],[5,0,1,2,3,4,11,6,7,8,9,10],[6,11,10,9,8,7,0,5,4,3,2,1],[7,6,11,10,9,8,1,0,5,4,3,2],[8,7,6,11,10,9,2,1,0,5,4,3],[9,8,7,6,11,10,3,2,1,0,5,4],[10,9,8,7,6,11,4,3,2,1,0,5],[11,10,9,8,7,6,5,4,3,2,1,0]],"identity":0,"element":1}。請依 [element, action_image_rows, conjugacy_class, certificate] 欄序回答。

查看答案與解釋(1, [[0, 1], [1, 1], [2, 1], [3, 1], [4, 1], [5, 1], [6, 5], [7, 5], [8, 5], [9, 5], [10, 5], [11, 5]], [1, 5], conjugacy_class_is_the_complete_conjugation_orbit_not_a_coset)

Wave6第八層核對=(1, [[0, 1], [1, 1], [2, 1], [3, 1], [4, 1], [5, 1], [6, 5], [7, 5], [8, 5], [9, 5], [10, 5], [11, 5]], [1, 5], conjugacy_class_is_the_complete_conjugation_orbit_not_a_coset)；依完整明示資料獨立重算；共軛類是element orbit並形成完整partition；singleton以forall g commute核對；共軛類不是coset或conjugate subgroup；不使用centralizer、class-size公式或類方程。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r03-finite-group-conjugacy-class-0029/)

有限群共軛類 · qf-mod45-conjugacy-orbit-class · candidate





## 30. 有限群共軛類

由完整Cayley table導出全部conjugation action與orbits。操作=conjugacy-orbit-class；資料={"group_table":[[0,1,2,3,4,5,6,7,8,9,10,11,12,13],[1,2,3,4,5,6,0,8,9,10,11,12,13,7],[2,3,4,5,6,0,1,9,10,11,12,13,7,8],[3,4,5,6,0,1,2,10,11,12,13,7,8,9],[4,5,6,0,1,2,3,11,12,13,7,8,9,10],[5,6,0,1,2,3,4,12,13,7,8,9,10,11],[6,0,1,2,3,4,5,13,7,8,9,10,11,12],[7,13,12,11,10,9,8,0,6,5,4,3,2,1],[8,7,13,12,11,10,9,1,0,6,5,4,3,2],[9,8,7,13,12,11,10,2,1,0,6,5,4,3],[10,9,8,7,13,12,11,3,2,1,0,6,5,4],[11,10,9,8,7,13,12,4,3,2,1,0,6,5],[12,11,10,9,8,7,13,5,4,3,2,1,0,6],[13,12,11,10,9,8,7,6,5,4,3,2,1,0]],"identity":0,"element":7}。請依 [element, action_image_rows, conjugacy_class, certificate] 欄序回答。

查看答案與解釋(7, [[0, 7], [1, 9], [2, 11], [3, 13], [4, 8], [5, 10], [6, 12], [7, 7], [8, 9], [9, 11], [10, 13], [11, 8], [12, 10], [13, 12]], [7, 8, 9, 10, 11, 12, 13], conjugacy_class_is_the_complete_conjugation_orbit_not_a_coset)

Wave6第八層核對=(7, [[0, 7], [1, 9], [2, 11], [3, 13], [4, 8], [5, 10], [6, 12], [7, 7], [8, 9], [9, 11], [10, 13], [11, 8], [12, 10], [13, 12]], [7, 8, 9, 10, 11, 12, 13], conjugacy_class_is_the_complete_conjugation_orbit_not_a_coset)；依完整明示資料獨立重算；共軛類是element orbit並形成完整partition；singleton以forall g commute核對；共軛類不是coset或conjugate subgroup；不使用centralizer、class-size公式或類方程。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r03-finite-group-conjugacy-class-0030/)

有限群共軛類 · qf-mod45-conjugacy-orbit-class · candidate





## 31. 有限群共軛類

由完整Cayley table導出全部conjugation action與orbits。操作=conjugacy-orbit-class；資料={"group_table":[[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15],[1,2,3,4,5,6,7,0,9,10,11,12,13,14,15,8],[2,3,4,5,6,7,0,1,10,11,12,13,14,15,8,9],[3,4,5,6,7,0,1,2,11,12,13,14,15,8,9,10],[4,5,6,7,0,1,2,3,12,13,14,15,8,9,10,11],[5,6,7,0,1,2,3,4,13,14,15,8,9,10,11,12],[6,7,0,1,2,3,4,5,14,15,8,9,10,11,12,13],[7,0,1,2,3,4,5,6,15,8,9,10,11,12,13,14],[8,15,14,13,12,11,10,9,0,7,6,5,4,3,2,1],[9,8,15,14,13,12,11,10,1,0,7,6,5,4,3,2],[10,9,8,15,14,13,12,11,2,1,0,7,6,5,4,3],[11,10,9,8,15,14,13,12,3,2,1,0,7,6,5,4],[12,11,10,9,8,15,14,13,4,3,2,1,0,7,6,5],[13,12,11,10,9,8,15,14,5,4,3,2,1,0,7,6],[14,13,12,11,10,9,8,15,6,5,4,3,2,1,0,7],[15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0]],"identity":0,"element":1}。請依 [element, action_image_rows, conjugacy_class, certificate] 欄序回答。

查看答案與解釋(1, [[0, 1], [1, 1], [2, 1], [3, 1], [4, 1], [5, 1], [6, 1], [7, 1], [8, 7], [9, 7], [10, 7], [11, 7], [12, 7], [13, 7], [14, 7], [15, 7]], [1, 7], conjugacy_class_is_the_complete_conjugation_orbit_not_a_coset)

Wave6第八層核對=(1, [[0, 1], [1, 1], [2, 1], [3, 1], [4, 1], [5, 1], [6, 1], [7, 1], [8, 7], [9, 7], [10, 7], [11, 7], [12, 7], [13, 7], [14, 7], [15, 7]], [1, 7], conjugacy_class_is_the_complete_conjugation_orbit_not_a_coset)；依完整明示資料獨立重算；共軛類是element orbit並形成完整partition；singleton以forall g commute核對；共軛類不是coset或conjugate subgroup；不使用centralizer、class-size公式或類方程。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r03-finite-group-conjugacy-class-0031/)

有限群共軛類 · qf-mod45-conjugacy-orbit-class · candidate





## 32. 有限群共軛類

由完整Cayley table導出全部conjugation action與orbits。操作=conjugacy-orbit-class；資料={"group_table":[[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17],[1,2,3,4,5,6,7,8,0,10,11,12,13,14,15,16,17,9],[2,3,4,5,6,7,8,0,1,11,12,13,14,15,16,17,9,10],[3,4,5,6,7,8,0,1,2,12,13,14,15,16,17,9,10,11],[4,5,6,7,8,0,1,2,3,13,14,15,16,17,9,10,11,12],[5,6,7,8,0,1,2,3,4,14,15,16,17,9,10,11,12,13],[6,7,8,0,1,2,3,4,5,15,16,17,9,10,11,12,13,14],[7,8,0,1,2,3,4,5,6,16,17,9,10,11,12,13,14,15],[8,0,1,2,3,4,5,6,7,17,9,10,11,12,13,14,15,16],[9,17,16,15,14,13,12,11,10,0,8,7,6,5,4,3,2,1],[10,9,17,16,15,14,13,12,11,1,0,8,7,6,5,4,3,2],[11,10,9,17,16,15,14,13,12,2,1,0,8,7,6,5,4,3],[12,11,10,9,17,16,15,14,13,3,2,1,0,8,7,6,5,4],[13,12,11,10,9,17,16,15,14,4,3,2,1,0,8,7,6,5],[14,13,12,11,10,9,17,16,15,5,4,3,2,1,0,8,7,6],[15,14,13,12,11,10,9,17,16,6,5,4,3,2,1,0,8,7],[16,15,14,13,12,11,10,9,17,7,6,5,4,3,2,1,0,8],[17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0]],"identity":0,"element":9}。請依 [element, action_image_rows, conjugacy_class, certificate] 欄序回答。

查看答案與解釋(9, [[0, 9], [1, 11], [2, 13], [3, 15], [4, 17], [5, 10], [6, 12], [7, 14], [8, 16], [9, 9], [10, 11], [11, 13], [12, 15], [13, 17], [14, 10], [15, 12], [16, 14], [17, 16]], [9, 10, 11, 12, 13, 14, 15, 16, 17], conjugacy_class_is_the_complete_conjugation_orbit_not_a_coset)

Wave6第八層核對=(9, [[0, 9], [1, 11], [2, 13], [3, 15], [4, 17], [5, 10], [6, 12], [7, 14], [8, 16], [9, 9], [10, 11], [11, 13], [12, 15], [13, 17], [14, 10], [15, 12], [16, 14], [17, 16]], [9, 10, 11, 12, 13, 14, 15, 16, 17], conjugacy_class_is_the_complete_conjugation_orbit_not_a_coset)；依完整明示資料獨立重算；共軛類是element orbit並形成完整partition；singleton以forall g commute核對；共軛類不是coset或conjugate subgroup；不使用centralizer、class-size公式或類方程。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r03-finite-group-conjugacy-class-0032/)

有限群共軛類 · qf-mod45-conjugacy-orbit-class · candidate





## 33. 有限群共軛類

由完整Cayley table導出全部conjugation action與orbits。操作=conjugacy-orbit-class；資料={"group_table":[[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19],[1,2,3,4,5,6,7,8,9,0,11,12,13,14,15,16,17,18,19,10],[2,3,4,5,6,7,8,9,0,1,12,13,14,15,16,17,18,19,10,11],[3,4,5,6,7,8,9,0,1,2,13,14,15,16,17,18,19,10,11,12],[4,5,6,7,8,9,0,1,2,3,14,15,16,17,18,19,10,11,12,13],[5,6,7,8,9,0,1,2,3,4,15,16,17,18,19,10,11,12,13,14],[6,7,8,9,0,1,2,3,4,5,16,17,18,19,10,11,12,13,14,15],[7,8,9,0,1,2,3,4,5,6,17,18,19,10,11,12,13,14,15,16],[8,9,0,1,2,3,4,5,6,7,18,19,10,11,12,13,14,15,16,17],[9,0,1,2,3,4,5,6,7,8,19,10,11,12,13,14,15,16,17,18],[10,19,18,17,16,15,14,13,12,11,0,9,8,7,6,5,4,3,2,1],[11,10,19,18,17,16,15,14,13,12,1,0,9,8,7,6,5,4,3,2],[12,11,10,19,18,17,16,15,14,13,2,1,0,9,8,7,6,5,4,3],[13,12,11,10,19,18,17,16,15,14,3,2,1,0,9,8,7,6,5,4],[14,13,12,11,10,19,18,17,16,15,4,3,2,1,0,9,8,7,6,5],[15,14,13,12,11,10,19,18,17,16,5,4,3,2,1,0,9,8,7,6],[16,15,14,13,12,11,10,19,18,17,6,5,4,3,2,1,0,9,8,7],[17,16,15,14,13,12,11,10,19,18,7,6,5,4,3,2,1,0,9,8],[18,17,16,15,14,13,12,11,10,19,8,7,6,5,4,3,2,1,0,9],[19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0]],"identity":0,"element":1}。請依 [element, action_image_rows, conjugacy_class, certificate] 欄序回答。

查看答案與解釋(1, [[0, 1], [1, 1], [2, 1], [3, 1], [4, 1], [5, 1], [6, 1], [7, 1], [8, 1], [9, 1], [10, 9], [11, 9], [12, 9], [13, 9], [14, 9], [15, 9], [16, 9], [17, 9], [18, 9], [19, 9]], [1, 9], conjugacy_class_is_the_complete_conjugation_orbit_not_a_coset)

Wave6第八層核對=(1, [[0, 1], [1, 1], [2, 1], [3, 1], [4, 1], [5, 1], [6, 1], [7, 1], [8, 1], [9, 1], [10, 9], [11, 9], [12, 9], [13, 9], [14, 9], [15, 9], [16, 9], [17, 9], [18, 9], [19, 9]], [1, 9], conjugacy_class_is_the_complete_conjugation_orbit_not_a_coset)；依完整明示資料獨立重算；共軛類是element orbit並形成完整partition；singleton以forall g commute核對；共軛類不是coset或conjugate subgroup；不使用centralizer、class-size公式或類方程。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r03-finite-group-conjugacy-class-0033/)

有限群共軛類 · qf-mod45-conjugacy-orbit-class · candidate





## 34. 有限群共軛類

由完整Cayley table導出全部conjugation action與orbits。操作=conjugacy-orbit-class；資料={"group_table":[[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21],[1,2,3,4,5,6,7,8,9,10,0,12,13,14,15,16,17,18,19,20,21,11],[2,3,4,5,6,7,8,9,10,0,1,13,14,15,16,17,18,19,20,21,11,12],[3,4,5,6,7,8,9,10,0,1,2,14,15,16,17,18,19,20,21,11,12,13],[4,5,6,7,8,9,10,0,1,2,3,15,16,17,18,19,20,21,11,12,13,14],[5,6,7,8,9,10,0,1,2,3,4,16,17,18,19,20,21,11,12,13,14,15],[6,7,8,9,10,0,1,2,3,4,5,17,18,19,20,21,11,12,13,14,15,16],[7,8,9,10,0,1,2,3,4,5,6,18,19,20,21,11,12,13,14,15,16,17],[8,9,10,0,1,2,3,4,5,6,7,19,20,21,11,12,13,14,15,16,17,18],[9,10,0,1,2,3,4,5,6,7,8,20,21,11,12,13,14,15,16,17,18,19],[10,0,1,2,3,4,5,6,7,8,9,21,11,12,13,14,15,16,17,18,19,20],[11,21,20,19,18,17,16,15,14,13,12,0,10,9,8,7,6,5,4,3,2,1],[12,11,21,20,19,18,17,16,15,14,13,1,0,10,9,8,7,6,5,4,3,2],[13,12,11,21,20,19,18,17,16,15,14,2,1,0,10,9,8,7,6,5,4,3],[14,13,12,11,21,20,19,18,17,16,15,3,2,1,0,10,9,8,7,6,5,4],[15,14,13,12,11,21,20,19,18,17,16,4,3,2,1,0,10,9,8,7,6,5],[16,15,14,13,12,11,21,20,19,18,17,5,4,3,2,1,0,10,9,8,7,6],[17,16,15,14,13,12,11,21,20,19,18,6,5,4,3,2,1,0,10,9,8,7],[18,17,16,15,14,13,12,11,21,20,19,7,6,5,4,3,2,1,0,10,9,8],[19,18,17,16,15,14,13,12,11,21,20,8,7,6,5,4,3,2,1,0,10,9],[20,19,18,17,16,15,14,13,12,11,21,9,8,7,6,5,4,3,2,1,0,10],[21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0]],"identity":0,"element":11}。請依 [element, action_image_rows, conjugacy_class, certificate] 欄序回答。

查看答案與解釋(11, [[0, 11], [1, 13], [2, 15], [3, 17], [4, 19], [5, 21], [6, 12], [7, 14], [8, 16], [9, 18], [10, 20], [11, 11], [12, 13], [13, 15], [14, 17], [15, 19], [16, 21], [17, 12], [18, 14], [19, 16], [20, 18], [21, 20]], [11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21], conjugacy_class_is_the_complete_conjugation_orbit_not_a_coset)

Wave6第八層核對=(11, [[0, 11], [1, 13], [2, 15], [3, 17], [4, 19], [5, 21], [6, 12], [7, 14], [8, 16], [9, 18], [10, 20], [11, 11], [12, 13], [13, 15], [14, 17], [15, 19], [16, 21], [17, 12], [18, 14], [19, 16], [20, 18], [21, 20]], [11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21], conjugacy_class_is_the_complete_conjugation_orbit_not_a_coset)；依完整明示資料獨立重算；共軛類是element orbit並形成完整partition；singleton以forall g commute核對；共軛類不是coset或conjugate subgroup；不使用centralizer、class-size公式或類方程。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r03-finite-group-conjugacy-class-0034/)

有限群共軛類 · qf-mod45-conjugacy-orbit-class · candidate





## 35. 有限群共軛類

由完整Cayley table導出全部conjugation action與orbits。操作=conjugacy-orbit-class；資料={"group_table":[[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23],[1,2,3,4,5,6,7,8,9,10,11,0,13,14,15,16,17,18,19,20,21,22,23,12],[2,3,4,5,6,7,8,9,10,11,0,1,14,15,16,17,18,19,20,21,22,23,12,13],[3,4,5,6,7,8,9,10,11,0,1,2,15,16,17,18,19,20,21,22,23,12,13,14],[4,5,6,7,8,9,10,11,0,1,2,3,16,17,18,19,20,21,22,23,12,13,14,15],[5,6,7,8,9,10,11,0,1,2,3,4,17,18,19,20,21,22,23,12,13,14,15,16],[6,7,8,9,10,11,0,1,2,3,4,5,18,19,20,21,22,23,12,13,14,15,16,17],[7,8,9,10,11,0,1,2,3,4,5,6,19,20,21,22,23,12,13,14,15,16,17,18],[8,9,10,11,0,1,2,3,4,5,6,7,20,21,22,23,12,13,14,15,16,17,18,19],[9,10,11,0,1,2,3,4,5,6,7,8,21,22,23,12,13,14,15,16,17,18,19,20],[10,11,0,1,2,3,4,5,6,7,8,9,22,23,12,13,14,15,16,17,18,19,20,21],[11,0,1,2,3,4,5,6,7,8,9,10,23,12,13,14,15,16,17,18,19,20,21,22],[12,23,22,21,20,19,18,17,16,15,14,13,0,11,10,9,8,7,6,5,4,3,2,1],[13,12,23,22,21,20,19,18,17,16,15,14,1,0,11,10,9,8,7,6,5,4,3,2],[14,13,12,23,22,21,20,19,18,17,16,15,2,1,0,11,10,9,8,7,6,5,4,3],[15,14,13,12,23,22,21,20,19,18,17,16,3,2,1,0,11,10,9,8,7,6,5,4],[16,15,14,13,12,23,22,21,20,19,18,17,4,3,2,1,0,11,10,9,8,7,6,5],[17,16,15,14,13,12,23,22,21,20,19,18,5,4,3,2,1,0,11,10,9,8,7,6],[18,17,16,15,14,13,12,23,22,21,20,19,6,5,4,3,2,1,0,11,10,9,8,7],[19,18,17,16,15,14,13,12,23,22,21,20,7,6,5,4,3,2,1,0,11,10,9,8],[20,19,18,17,16,15,14,13,12,23,22,21,8,7,6,5,4,3,2,1,0,11,10,9],[21,20,19,18,17,16,15,14,13,12,23,22,9,8,7,6,5,4,3,2,1,0,11,10],[22,21,20,19,18,17,16,15,14,13,12,23,10,9,8,7,6,5,4,3,2,1,0,11],[23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0]],"identity":0,"element":1}。請依 [element, action_image_rows, conjugacy_class, certificate] 欄序回答。

查看答案與解釋(1, [[0, 1], [1, 1], [2, 1], [3, 1], [4, 1], [5, 1], [6, 1], [7, 1], [8, 1], [9, 1], [10, 1], [11, 1], [12, 11], [13, 11], [14, 11], [15, 11], [16, 11], [17, 11], [18, 11], [19, 11], [20, 11], [21, 11], [22, 11], [23, 11]], [1, 11], conjugacy_class_is_the_complete_conjugation_orbit_not_a_coset)

Wave6第八層核對=(1, [[0, 1], [1, 1], [2, 1], [3, 1], [4, 1], [5, 1], [6, 1], [7, 1], [8, 1], [9, 1], [10, 1], [11, 1], [12, 11], [13, 11], [14, 11], [15, 11], [16, 11], [17, 11], [18, 11], [19, 11], [20, 11], [21, 11], [22, 11], [23, 11]], [1, 11], conjugacy_class_is_the_complete_conjugation_orbit_not_a_coset)；依完整明示資料獨立重算；共軛類是element orbit並形成完整partition；singleton以forall g commute核對；共軛類不是coset或conjugate subgroup；不使用centralizer、class-size公式或類方程。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r03-finite-group-conjugacy-class-0035/)

有限群共軛類 · qf-mod45-conjugacy-orbit-class · candidate





## 36. 有限群共軛類

由完整Cayley table導出全部conjugation action與orbits。操作=conjugacy-orbit-class；資料={"group_table":[[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25],[1,2,3,4,5,6,7,8,9,10,11,12,0,14,15,16,17,18,19,20,21,22,23,24,25,13],[2,3,4,5,6,7,8,9,10,11,12,0,1,15,16,17,18,19,20,21,22,23,24,25,13,14],[3,4,5,6,7,8,9,10,11,12,0,1,2,16,17,18,19,20,21,22,23,24,25,13,14,15],[4,5,6,7,8,9,10,11,12,0,1,2,3,17,18,19,20,21,22,23,24,25,13,14,15,16],[5,6,7,8,9,10,11,12,0,1,2,3,4,18,19,20,21,22,23,24,25,13,14,15,16,17],[6,7,8,9,10,11,12,0,1,2,3,4,5,19,20,21,22,23,24,25,13,14,15,16,17,18],[7,8,9,10,11,12,0,1,2,3,4,5,6,20,21,22,23,24,25,13,14,15,16,17,18,19],[8,9,10,11,12,0,1,2,3,4,5,6,7,21,22,23,24,25,13,14,15,16,17,18,19,20],[9,10,11,12,0,1,2,3,4,5,6,7,8,22,23,24,25,13,14,15,16,17,18,19,20,21],[10,11,12,0,1,2,3,4,5,6,7,8,9,23,24,25,13,14,15,16,17,18,19,20,21,22],[11,12,0,1,2,3,4,5,6,7,8,9,10,24,25,13,14,15,16,17,18,19,20,21,22,23],[12,0,1,2,3,4,5,6,7,8,9,10,11,25,13,14,15,16,17,18,19,20,21,22,23,24],[13,25,24,23,22,21,20,19,18,17,16,15,14,0,12,11,10,9,8,7,6,5,4,3,2,1],[14,13,25,24,23,22,21,20,19,18,17,16,15,1,0,12,11,10,9,8,7,6,5,4,3,2],[15,14,13,25,24,23,22,21,20,19,18,17,16,2,1,0,12,11,10,9,8,7,6,5,4,3],[16,15,14,13,25,24,23,22,21,20,19,18,17,3,2,1,0,12,11,10,9,8,7,6,5,4],[17,16,15,14,13,25,24,23,22,21,20,19,18,4,3,2,1,0,12,11,10,9,8,7,6,5],[18,17,16,15,14,13,25,24,23,22,21,20,19,5,4,3,2,1,0,12,11,10,9,8,7,6],[19,18,17,16,15,14,13,25,24,23,22,21,20,6,5,4,3,2,1,0,12,11,10,9,8,7],[20,19,18,17,16,15,14,13,25,24,23,22,21,7,6,5,4,3,2,1,0,12,11,10,9,8],[21,20,19,18,17,16,15,14,13,25,24,23,22,8,7,6,5,4,3,2,1,0,12,11,10,9],[22,21,20,19,18,17,16,15,14,13,25,24,23,9,8,7,6,5,4,3,2,1,0,12,11,10],[23,22,21,20,19,18,17,16,15,14,13,25,24,10,9,8,7,6,5,4,3,2,1,0,12,11],[24,23,22,21,20,19,18,17,16,15,14,13,25,11,10,9,8,7,6,5,4,3,2,1,0,12],[25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0]],"identity":0,"element":13}。請依 [element, action_image_rows, conjugacy_class, certificate] 欄序回答。

查看答案與解釋(13, [[0, 13], [1, 15], [2, 17], [3, 19], [4, 21], [5, 23], [6, 25], [7, 14], [8, 16], [9, 18], [10, 20], [11, 22], [12, 24], [13, 13], [14, 15], [15, 17], [16, 19], [17, 21], [18, 23], [19, 25], [20, 14], [21, 16], [22, 18], [23, 20], [24, 22], [25, 24]], [13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25], conjugacy_class_is_the_complete_conjugation_orbit_not_a_coset)

Wave6第八層核對=(13, [[0, 13], [1, 15], [2, 17], [3, 19], [4, 21], [5, 23], [6, 25], [7, 14], [8, 16], [9, 18], [10, 20], [11, 22], [12, 24], [13, 13], [14, 15], [15, 17], [16, 19], [17, 21], [18, 23], [19, 25], [20, 14], [21, 16], [22, 18], [23, 20], [24, 22], [25, 24]], [13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25], conjugacy_class_is_the_complete_conjugation_orbit_not_a_coset)；依完整明示資料獨立重算；共軛類是element orbit並形成完整partition；singleton以forall g commute核對；共軛類不是coset或conjugate subgroup；不使用centralizer、class-size公式或類方程。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r03-finite-group-conjugacy-class-0036/)

有限群共軛類 · qf-mod45-conjugacy-orbit-class · candidate





## 37. 有限群共軛類

由完整Cayley table導出全部conjugation action與orbits。操作=conjugacy-orbit-class；資料={"group_table":[[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27],[1,2,3,4,5,6,7,8,9,10,11,12,13,0,15,16,17,18,19,20,21,22,23,24,25,26,27,14],[2,3,4,5,6,7,8,9,10,11,12,13,0,1,16,17,18,19,20,21,22,23,24,25,26,27,14,15],[3,4,5,6,7,8,9,10,11,12,13,0,1,2,17,18,19,20,21,22,23,24,25,26,27,14,15,16],[4,5,6,7,8,9,10,11,12,13,0,1,2,3,18,19,20,21,22,23,24,25,26,27,14,15,16,17],[5,6,7,8,9,10,11,12,13,0,1,2,3,4,19,20,21,22,23,24,25,26,27,14,15,16,17,18],[6,7,8,9,10,11,12,13,0,1,2,3,4,5,20,21,22,23,24,25,26,27,14,15,16,17,18,19],[7,8,9,10,11,12,13,0,1,2,3,4,5,6,21,22,23,24,25,26,27,14,15,16,17,18,19,20],[8,9,10,11,12,13,0,1,2,3,4,5,6,7,22,23,24,25,26,27,14,15,16,17,18,19,20,21],[9,10,11,12,13,0,1,2,3,4,5,6,7,8,23,24,25,26,27,14,15,16,17,18,19,20,21,22],[10,11,12,13,0,1,2,3,4,5,6,7,8,9,24,25,26,27,14,15,16,17,18,19,20,21,22,23],[11,12,13,0,1,2,3,4,5,6,7,8,9,10,25,26,27,14,15,16,17,18,19,20,21,22,23,24],[12,13,0,1,2,3,4,5,6,7,8,9,10,11,26,27,14,15,16,17,18,19,20,21,22,23,24,25],[13,0,1,2,3,4,5,6,7,8,9,10,11,12,27,14,15,16,17,18,19,20,21,22,23,24,25,26],[14,27,26,25,24,23,22,21,20,19,18,17,16,15,0,13,12,11,10,9,8,7,6,5,4,3,2,1],[15,14,27,26,25,24,23,22,21,20,19,18,17,16,1,0,13,12,11,10,9,8,7,6,5,4,3,2],[16,15,14,27,26,25,24,23,22,21,20,19,18,17,2,1,0,13,12,11,10,9,8,7,6,5,4,3],[17,16,15,14,27,26,25,24,23,22,21,20,19,18,3,2,1,0,13,12,11,10,9,8,7,6,5,4],[18,17,16,15,14,27,26,25,24,23,22,21,20,19,4,3,2,1,0,13,12,11,10,9,8,7,6,5],[19,18,17,16,15,14,27,26,25,24,23,22,21,20,5,4,3,2,1,0,13,12,11,10,9,8,7,6],[20,19,18,17,16,15,14,27,26,25,24,23,22,21,6,5,4,3,2,1,0,13,12,11,10,9,8,7],[21,20,19,18,17,16,15,14,27,26,25,24,23,22,7,6,5,4,3,2,1,0,13,12,11,10,9,8],[22,21,20,19,18,17,16,15,14,27,26,25,24,23,8,7,6,5,4,3,2,1,0,13,12,11,10,9],[23,22,21,20,19,18,17,16,15,14,27,26,25,24,9,8,7,6,5,4,3,2,1,0,13,12,11,10],[24,23,22,21,20,19,18,17,16,15,14,27,26,25,10,9,8,7,6,5,4,3,2,1,0,13,12,11],[25,24,23,22,21,20,19,18,17,16,15,14,27,26,11,10,9,8,7,6,5,4,3,2,1,0,13,12],[26,25,24,23,22,21,20,19,18,17,16,15,14,27,12,11,10,9,8,7,6,5,4,3,2,1,0,13],[27,26,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0]],"identity":0,"element":1}。請依 [element, action_image_rows, conjugacy_class, certificate] 欄序回答。

查看答案與解釋(1, [[0, 1], [1, 1], [2, 1], [3, 1], [4, 1], [5, 1], [6, 1], [7, 1], [8, 1], [9, 1], [10, 1], [11, 1], [12, 1], [13, 1], [14, 13], [15, 13], [16, 13], [17, 13], [18, 13], [19, 13], [20, 13], [21, 13], [22, 13], [23, 13], [24, 13], [25, 13], [26, 13], [27, 13]], [1, 13], conjugacy_class_is_the_complete_conjugation_orbit_not_a_coset)

Wave6第八層核對=(1, [[0, 1], [1, 1], [2, 1], [3, 1], [4, 1], [5, 1], [6, 1], [7, 1], [8, 1], [9, 1], [10, 1], [11, 1], [12, 1], [13, 1], [14, 13], [15, 13], [16, 13], [17, 13], [18, 13], [19, 13], [20, 13], [21, 13], [22, 13], [23, 13], [24, 13], [25, 13], [26, 13], [27, 13]], [1, 13], conjugacy_class_is_the_complete_conjugation_orbit_not_a_coset)；依完整明示資料獨立重算；共軛類是element orbit並形成完整partition；singleton以forall g commute核對；共軛類不是coset或conjugate subgroup；不使用centralizer、class-size公式或類方程。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r03-finite-group-conjugacy-class-0037/)

有限群共軛類 · qf-mod45-conjugacy-orbit-class · candidate





## 38. 有限群共軛類

由完整Cayley table導出全部conjugation action與orbits。操作=conjugacy-orbit-class；資料={"group_table":[[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,0,16,17,18,19,20,21,22,23,24,25,26,27,28,29,15],[2,3,4,5,6,7,8,9,10,11,12,13,14,0,1,17,18,19,20,21,22,23,24,25,26,27,28,29,15,16],[3,4,5,6,7,8,9,10,11,12,13,14,0,1,2,18,19,20,21,22,23,24,25,26,27,28,29,15,16,17],[4,5,6,7,8,9,10,11,12,13,14,0,1,2,3,19,20,21,22,23,24,25,26,27,28,29,15,16,17,18],[5,6,7,8,9,10,11,12,13,14,0,1,2,3,4,20,21,22,23,24,25,26,27,28,29,15,16,17,18,19],[6,7,8,9,10,11,12,13,14,0,1,2,3,4,5,21,22,23,24,25,26,27,28,29,15,16,17,18,19,20],[7,8,9,10,11,12,13,14,0,1,2,3,4,5,6,22,23,24,25,26,27,28,29,15,16,17,18,19,20,21],[8,9,10,11,12,13,14,0,1,2,3,4,5,6,7,23,24,25,26,27,28,29,15,16,17,18,19,20,21,22],[9,10,11,12,13,14,0,1,2,3,4,5,6,7,8,24,25,26,27,28,29,15,16,17,18,19,20,21,22,23],[10,11,12,13,14,0,1,2,3,4,5,6,7,8,9,25,26,27,28,29,15,16,17,18,19,20,21,22,23,24],[11,12,13,14,0,1,2,3,4,5,6,7,8,9,10,26,27,28,29,15,16,17,18,19,20,21,22,23,24,25],[12,13,14,0,1,2,3,4,5,6,7,8,9,10,11,27,28,29,15,16,17,18,19,20,21,22,23,24,25,26],[13,14,0,1,2,3,4,5,6,7,8,9,10,11,12,28,29,15,16,17,18,19,20,21,22,23,24,25,26,27],[14,0,1,2,3,4,5,6,7,8,9,10,11,12,13,29,15,16,17,18,19,20,21,22,23,24,25,26,27,28],[15,29,28,27,26,25,24,23,22,21,20,19,18,17,16,0,14,13,12,11,10,9,8,7,6,5,4,3,2,1],[16,15,29,28,27,26,25,24,23,22,21,20,19,18,17,1,0,14,13,12,11,10,9,8,7,6,5,4,3,2],[17,16,15,29,28,27,26,25,24,23,22,21,20,19,18,2,1,0,14,13,12,11,10,9,8,7,6,5,4,3],[18,17,16,15,29,28,27,26,25,24,23,22,21,20,19,3,2,1,0,14,13,12,11,10,9,8,7,6,5,4],[19,18,17,16,15,29,28,27,26,25,24,23,22,21,20,4,3,2,1,0,14,13,12,11,10,9,8,7,6,5],[20,19,18,17,16,15,29,28,27,26,25,24,23,22,21,5,4,3,2,1,0,14,13,12,11,10,9,8,7,6],[21,20,19,18,17,16,15,29,28,27,26,25,24,23,22,6,5,4,3,2,1,0,14,13,12,11,10,9,8,7],[22,21,20,19,18,17,16,15,29,28,27,26,25,24,23,7,6,5,4,3,2,1,0,14,13,12,11,10,9,8],[23,22,21,20,19,18,17,16,15,29,28,27,26,25,24,8,7,6,5,4,3,2,1,0,14,13,12,11,10,9],[24,23,22,21,20,19,18,17,16,15,29,28,27,26,25,9,8,7,6,5,4,3,2,1,0,14,13,12,11,10],[25,24,23,22,21,20,19,18,17,16,15,29,28,27,26,10,9,8,7,6,5,4,3,2,1,0,14,13,12,11],[26,25,24,23,22,21,20,19,18,17,16,15,29,28,27,11,10,9,8,7,6,5,4,3,2,1,0,14,13,12],[27,26,25,24,23,22,21,20,19,18,17,16,15,29,28,12,11,10,9,8,7,6,5,4,3,2,1,0,14,13],[28,27,26,25,24,23,22,21,20,19,18,17,16,15,29,13,12,11,10,9,8,7,6,5,4,3,2,1,0,14],[29,28,27,26,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0]],"identity":0,"element":15}。請依 [element, action_image_rows, conjugacy_class, certificate] 欄序回答。

查看答案與解釋(15, [[0, 15], [1, 17], [2, 19], [3, 21], [4, 23], [5, 25], [6, 27], [7, 29], [8, 16], [9, 18], [10, 20], [11, 22], [12, 24], [13, 26], [14, 28], [15, 15], [16, 17], [17, 19], [18, 21], [19, 23], [20, 25], [21, 27], [22, 29], [23, 16], [24, 18], [25, 20], [26, 22], [27, 24], [28, 26], [29, 28]], [15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29], conjugacy_class_is_the_complete_conjugation_orbit_not_a_coset)

Wave6第八層核對=(15, [[0, 15], [1, 17], [2, 19], [3, 21], [4, 23], [5, 25], [6, 27], [7, 29], [8, 16], [9, 18], [10, 20], [11, 22], [12, 24], [13, 26], [14, 28], [15, 15], [16, 17], [17, 19], [18, 21], [19, 23], [20, 25], [21, 27], [22, 29], [23, 16], [24, 18], [25, 20], [26, 22], [27, 24], [28, 26], [29, 28]], [15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29], conjugacy_class_is_the_complete_conjugation_orbit_not_a_coset)；依完整明示資料獨立重算；共軛類是element orbit並形成完整partition；singleton以forall g commute核對；共軛類不是coset或conjugate subgroup；不使用centralizer、class-size公式或類方程。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r03-finite-group-conjugacy-class-0038/)

有限群共軛類 · qf-mod45-conjugacy-orbit-class · candidate





## 39. 有限群共軛類

由完整Cayley table導出全部conjugation action與orbits。操作=conjugacy-orbit-class；資料={"group_table":[[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,0,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,16],[2,3,4,5,6,7,8,9,10,11,12,13,14,15,0,1,18,19,20,21,22,23,24,25,26,27,28,29,30,31,16,17],[3,4,5,6,7,8,9,10,11,12,13,14,15,0,1,2,19,20,21,22,23,24,25,26,27,28,29,30,31,16,17,18],[4,5,6,7,8,9,10,11,12,13,14,15,0,1,2,3,20,21,22,23,24,25,26,27,28,29,30,31,16,17,18,19],[5,6,7,8,9,10,11,12,13,14,15,0,1,2,3,4,21,22,23,24,25,26,27,28,29,30,31,16,17,18,19,20],[6,7,8,9,10,11,12,13,14,15,0,1,2,3,4,5,22,23,24,25,26,27,28,29,30,31,16,17,18,19,20,21],[7,8,9,10,11,12,13,14,15,0,1,2,3,4,5,6,23,24,25,26,27,28,29,30,31,16,17,18,19,20,21,22],[8,9,10,11,12,13,14,15,0,1,2,3,4,5,6,7,24,25,26,27,28,29,30,31,16,17,18,19,20,21,22,23],[9,10,11,12,13,14,15,0,1,2,3,4,5,6,7,8,25,26,27,28,29,30,31,16,17,18,19,20,21,22,23,24],[10,11,12,13,14,15,0,1,2,3,4,5,6,7,8,9,26,27,28,29,30,31,16,17,18,19,20,21,22,23,24,25],[11,12,13,14,15,0,1,2,3,4,5,6,7,8,9,10,27,28,29,30,31,16,17,18,19,20,21,22,23,24,25,26],[12,13,14,15,0,1,2,3,4,5,6,7,8,9,10,11,28,29,30,31,16,17,18,19,20,21,22,23,24,25,26,27],[13,14,15,0,1,2,3,4,5,6,7,8,9,10,11,12,29,30,31,16,17,18,19,20,21,22,23,24,25,26,27,28],[14,15,0,1,2,3,4,5,6,7,8,9,10,11,12,13,30,31,16,17,18,19,20,21,22,23,24,25,26,27,28,29],[15,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,31,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30],[16,31,30,29,28,27,26,25,24,23,22,21,20,19,18,17,0,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1],[17,16,31,30,29,28,27,26,25,24,23,22,21,20,19,18,1,0,15,14,13,12,11,10,9,8,7,6,5,4,3,2],[18,17,16,31,30,29,28,27,26,25,24,23,22,21,20,19,2,1,0,15,14,13,12,11,10,9,8,7,6,5,4,3],[19,18,17,16,31,30,29,28,27,26,25,24,23,22,21,20,3,2,1,0,15,14,13,12,11,10,9,8,7,6,5,4],[20,19,18,17,16,31,30,29,28,27,26,25,24,23,22,21,4,3,2,1,0,15,14,13,12,11,10,9,8,7,6,5],[21,20,19,18,17,16,31,30,29,28,27,26,25,24,23,22,5,4,3,2,1,0,15,14,13,12,11,10,9,8,7,6],[22,21,20,19,18,17,16,31,30,29,28,27,26,25,24,23,6,5,4,3,2,1,0,15,14,13,12,11,10,9,8,7],[23,22,21,20,19,18,17,16,31,30,29,28,27,26,25,24,7,6,5,4,3,2,1,0,15,14,13,12,11,10,9,8],[24,23,22,21,20,19,18,17,16,31,30,29,28,27,26,25,8,7,6,5,4,3,2,1,0,15,14,13,12,11,10,9],[25,24,23,22,21,20,19,18,17,16,31,30,29,28,27,26,9,8,7,6,5,4,3,2,1,0,15,14,13,12,11,10],[26,25,24,23,22,21,20,19,18,17,16,31,30,29,28,27,10,9,8,7,6,5,4,3,2,1,0,15,14,13,12,11],[27,26,25,24,23,22,21,20,19,18,17,16,31,30,29,28,11,10,9,8,7,6,5,4,3,2,1,0,15,14,13,12],[28,27,26,25,24,23,22,21,20,19,18,17,16,31,30,29,12,11,10,9,8,7,6,5,4,3,2,1,0,15,14,13],[29,28,27,26,25,24,23,22,21,20,19,18,17,16,31,30,13,12,11,10,9,8,7,6,5,4,3,2,1,0,15,14],[30,29,28,27,26,25,24,23,22,21,20,19,18,17,16,31,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0,15],[31,30,29,28,27,26,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0]],"identity":0,"element":1}。請依 [element, action_image_rows, conjugacy_class, certificate] 欄序回答。

查看答案與解釋(1, [[0, 1], [1, 1], [2, 1], [3, 1], [4, 1], [5, 1], [6, 1], [7, 1], [8, 1], [9, 1], [10, 1], [11, 1], [12, 1], [13, 1], [14, 1], [15, 1], [16, 15], [17, 15], [18, 15], [19, 15], [20, 15], [21, 15], [22, 15], [23, 15], [24, 15], [25, 15], [26, 15], [27, 15], [28, 15], [29, 15], [30, 15], [31, 15]], [1, 15], conjugacy_class_is_the_complete_conjugation_orbit_not_a_coset)

Wave6第八層核對=(1, [[0, 1], [1, 1], [2, 1], [3, 1], [4, 1], [5, 1], [6, 1], [7, 1], [8, 1], [9, 1], [10, 1], [11, 1], [12, 1], [13, 1], [14, 1], [15, 1], [16, 15], [17, 15], [18, 15], [19, 15], [20, 15], [21, 15], [22, 15], [23, 15], [24, 15], [25, 15], [26, 15], [27, 15], [28, 15], [29, 15], [30, 15], [31, 15]], [1, 15], conjugacy_class_is_the_complete_conjugation_orbit_not_a_coset)；依完整明示資料獨立重算；共軛類是element orbit並形成完整partition；singleton以forall g commute核對；共軛類不是coset或conjugate subgroup；不使用centralizer、class-size公式或類方程。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r03-finite-group-conjugacy-class-0039/)

有限群共軛類 · qf-mod45-conjugacy-orbit-class · candidate





## 40. 有限群共軛類

由完整Cayley table導出全部conjugation action與orbits。操作=conjugacy-orbit-class；資料={"group_table":[[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,0,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,17],[2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,0,1,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,17,18],[3,4,5,6,7,8,9,10,11,12,13,14,15,16,0,1,2,20,21,22,23,24,25,26,27,28,29,30,31,32,33,17,18,19],[4,5,6,7,8,9,10,11,12,13,14,15,16,0,1,2,3,21,22,23,24,25,26,27,28,29,30,31,32,33,17,18,19,20],[5,6,7,8,9,10,11,12,13,14,15,16,0,1,2,3,4,22,23,24,25,26,27,28,29,30,31,32,33,17,18,19,20,21],[6,7,8,9,10,11,12,13,14,15,16,0,1,2,3,4,5,23,24,25,26,27,28,29,30,31,32,33,17,18,19,20,21,22],[7,8,9,10,11,12,13,14,15,16,0,1,2,3,4,5,6,24,25,26,27,28,29,30,31,32,33,17,18,19,20,21,22,23],[8,9,10,11,12,13,14,15,16,0,1,2,3,4,5,6,7,25,26,27,28,29,30,31,32,33,17,18,19,20,21,22,23,24],[9,10,11,12,13,14,15,16,0,1,2,3,4,5,6,7,8,26,27,28,29,30,31,32,33,17,18,19,20,21,22,23,24,25],[10,11,12,13,14,15,16,0,1,2,3,4,5,6,7,8,9,27,28,29,30,31,32,33,17,18,19,20,21,22,23,24,25,26],[11,12,13,14,15,16,0,1,2,3,4,5,6,7,8,9,10,28,29,30,31,32,33,17,18,19,20,21,22,23,24,25,26,27],[12,13,14,15,16,0,1,2,3,4,5,6,7,8,9,10,11,29,30,31,32,33,17,18,19,20,21,22,23,24,25,26,27,28],[13,14,15,16,0,1,2,3,4,5,6,7,8,9,10,11,12,30,31,32,33,17,18,19,20,21,22,23,24,25,26,27,28,29],[14,15,16,0,1,2,3,4,5,6,7,8,9,10,11,12,13,31,32,33,17,18,19,20,21,22,23,24,25,26,27,28,29,30],[15,16,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,32,33,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31],[16,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,33,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32],[17,33,32,31,30,29,28,27,26,25,24,23,22,21,20,19,18,0,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1],[18,17,33,32,31,30,29,28,27,26,25,24,23,22,21,20,19,1,0,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2],[19,18,17,33,32,31,30,29,28,27,26,25,24,23,22,21,20,2,1,0,16,15,14,13,12,11,10,9,8,7,6,5,4,3],[20,19,18,17,33,32,31,30,29,28,27,26,25,24,23,22,21,3,2,1,0,16,15,14,13,12,11,10,9,8,7,6,5,4],[21,20,19,18,17,33,32,31,30,29,28,27,26,25,24,23,22,4,3,2,1,0,16,15,14,13,12,11,10,9,8,7,6,5],[22,21,20,19,18,17,33,32,31,30,29,28,27,26,25,24,23,5,4,3,2,1,0,16,15,14,13,12,11,10,9,8,7,6],[23,22,21,20,19,18,17,33,32,31,30,29,28,27,26,25,24,6,5,4,3,2,1,0,16,15,14,13,12,11,10,9,8,7],[24,23,22,21,20,19,18,17,33,32,31,30,29,28,27,26,25,7,6,5,4,3,2,1,0,16,15,14,13,12,11,10,9,8],[25,24,23,22,21,20,19,18,17,33,32,31,30,29,28,27,26,8,7,6,5,4,3,2,1,0,16,15,14,13,12,11,10,9],[26,25,24,23,22,21,20,19,18,17,33,32,31,30,29,28,27,9,8,7,6,5,4,3,2,1,0,16,15,14,13,12,11,10],[27,26,25,24,23,22,21,20,19,18,17,33,32,31,30,29,28,10,9,8,7,6,5,4,3,2,1,0,16,15,14,13,12,11],[28,27,26,25,24,23,22,21,20,19,18,17,33,32,31,30,29,11,10,9,8,7,6,5,4,3,2,1,0,16,15,14,13,12],[29,28,27,26,25,24,23,22,21,20,19,18,17,33,32,31,30,12,11,10,9,8,7,6,5,4,3,2,1,0,16,15,14,13],[30,29,28,27,26,25,24,23,22,21,20,19,18,17,33,32,31,13,12,11,10,9,8,7,6,5,4,3,2,1,0,16,15,14],[31,30,29,28,27,26,25,24,23,22,21,20,19,18,17,33,32,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0,16,15],[32,31,30,29,28,27,26,25,24,23,22,21,20,19,18,17,33,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0,16],[33,32,31,30,29,28,27,26,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0]],"identity":0,"element":17}。請依 [element, action_image_rows, conjugacy_class, certificate] 欄序回答。

查看答案與解釋(17, [[0, 17], [1, 19], [2, 21], [3, 23], [4, 25], [5, 27], [6, 29], [7, 31], [8, 33], [9, 18], [10, 20], [11, 22], [12, 24], [13, 26], [14, 28], [15, 30], [16, 32], [17, 17], [18, 19], [19, 21], [20, 23], [21, 25], [22, 27], [23, 29], [24, 31], [25, 33], [26, 18], [27, 20], [28, 22], [29, 24], [30, 26], [31, 28], [32, 30], [33, 32]], [17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33], conjugacy_class_is_the_complete_conjugation_orbit_not_a_coset)

Wave6第八層核對=(17, [[0, 17], [1, 19], [2, 21], [3, 23], [4, 25], [5, 27], [6, 29], [7, 31], [8, 33], [9, 18], [10, 20], [11, 22], [12, 24], [13, 26], [14, 28], [15, 30], [16, 32], [17, 17], [18, 19], [19, 21], [20, 23], [21, 25], [22, 27], [23, 29], [24, 31], [25, 33], [26, 18], [27, 20], [28, 22], [29, 24], [30, 26], [31, 28], [32, 30], [33, 32]], [17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33], conjugacy_class_is_the_complete_conjugation_orbit_not_a_coset)；依完整明示資料獨立重算；共軛類是element orbit並形成完整partition；singleton以forall g commute核對；共軛類不是coset或conjugate subgroup；不使用centralizer、class-size公式或類方程。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r03-finite-group-conjugacy-class-0040/)

有限群共軛類 · qf-mod45-conjugacy-orbit-class · candidate





## 41. 有限群共軛類

由完整Cayley table導出全部conjugation action與orbits。操作=conjugacy-orbit-class；資料={"group_table":[[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,0,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,18],[2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,0,1,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,18,19],[3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,0,1,2,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,18,19,20],[4,5,6,7,8,9,10,11,12,13,14,15,16,17,0,1,2,3,22,23,24,25,26,27,28,29,30,31,32,33,34,35,18,19,20,21],[5,6,7,8,9,10,11,12,13,14,15,16,17,0,1,2,3,4,23,24,25,26,27,28,29,30,31,32,33,34,35,18,19,20,21,22],[6,7,8,9,10,11,12,13,14,15,16,17,0,1,2,3,4,5,24,25,26,27,28,29,30,31,32,33,34,35,18,19,20,21,22,23],[7,8,9,10,11,12,13,14,15,16,17,0,1,2,3,4,5,6,25,26,27,28,29,30,31,32,33,34,35,18,19,20,21,22,23,24],[8,9,10,11,12,13,14,15,16,17,0,1,2,3,4,5,6,7,26,27,28,29,30,31,32,33,34,35,18,19,20,21,22,23,24,25],[9,10,11,12,13,14,15,16,17,0,1,2,3,4,5,6,7,8,27,28,29,30,31,32,33,34,35,18,19,20,21,22,23,24,25,26],[10,11,12,13,14,15,16,17,0,1,2,3,4,5,6,7,8,9,28,29,30,31,32,33,34,35,18,19,20,21,22,23,24,25,26,27],[11,12,13,14,15,16,17,0,1,2,3,4,5,6,7,8,9,10,29,30,31,32,33,34,35,18,19,20,21,22,23,24,25,26,27,28],[12,13,14,15,16,17,0,1,2,3,4,5,6,7,8,9,10,11,30,31,32,33,34,35,18,19,20,21,22,23,24,25,26,27,28,29],[13,14,15,16,17,0,1,2,3,4,5,6,7,8,9,10,11,12,31,32,33,34,35,18,19,20,21,22,23,24,25,26,27,28,29,30],[14,15,16,17,0,1,2,3,4,5,6,7,8,9,10,11,12,13,32,33,34,35,18,19,20,21,22,23,24,25,26,27,28,29,30,31],[15,16,17,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,33,34,35,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32],[16,17,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,34,35,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33],[17,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,35,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34],[18,35,34,33,32,31,30,29,28,27,26,25,24,23,22,21,20,19,0,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1],[19,18,35,34,33,32,31,30,29,28,27,26,25,24,23,22,21,20,1,0,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2],[20,19,18,35,34,33,32,31,30,29,28,27,26,25,24,23,22,21,2,1,0,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3],[21,20,19,18,35,34,33,32,31,30,29,28,27,26,25,24,23,22,3,2,1,0,17,16,15,14,13,12,11,10,9,8,7,6,5,4],[22,21,20,19,18,35,34,33,32,31,30,29,28,27,26,25,24,23,4,3,2,1,0,17,16,15,14,13,12,11,10,9,8,7,6,5],[23,22,21,20,19,18,35,34,33,32,31,30,29,28,27,26,25,24,5,4,3,2,1,0,17,16,15,14,13,12,11,10,9,8,7,6],[24,23,22,21,20,19,18,35,34,33,32,31,30,29,28,27,26,25,6,5,4,3,2,1,0,17,16,15,14,13,12,11,10,9,8,7],[25,24,23,22,21,20,19,18,35,34,33,32,31,30,29,28,27,26,7,6,5,4,3,2,1,0,17,16,15,14,13,12,11,10,9,8],[26,25,24,23,22,21,20,19,18,35,34,33,32,31,30,29,28,27,8,7,6,5,4,3,2,1,0,17,16,15,14,13,12,11,10,9],[27,26,25,24,23,22,21,20,19,18,35,34,33,32,31,30,29,28,9,8,7,6,5,4,3,2,1,0,17,16,15,14,13,12,11,10],[28,27,26,25,24,23,22,21,20,19,18,35,34,33,32,31,30,29,10,9,8,7,6,5,4,3,2,1,0,17,16,15,14,13,12,11],[29,28,27,26,25,24,23,22,21,20,19,18,35,34,33,32,31,30,11,10,9,8,7,6,5,4,3,2,1,0,17,16,15,14,13,12],[30,29,28,27,26,25,24,23,22,21,20,19,18,35,34,33,32,31,12,11,10,9,8,7,6,5,4,3,2,1,0,17,16,15,14,13],[31,30,29,28,27,26,25,24,23,22,21,20,19,18,35,34,33,32,13,12,11,10,9,8,7,6,5,4,3,2,1,0,17,16,15,14],[32,31,30,29,28,27,26,25,24,23,22,21,20,19,18,35,34,33,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0,17,16,15],[33,32,31,30,29,28,27,26,25,24,23,22,21,20,19,18,35,34,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0,17,16],[34,33,32,31,30,29,28,27,26,25,24,23,22,21,20,19,18,35,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0,17],[35,34,33,32,31,30,29,28,27,26,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0]],"identity":0,"element":1}。請依 [element, action_image_rows, conjugacy_class, certificate] 欄序回答。

查看答案與解釋(1, [[0, 1], [1, 1], [2, 1], [3, 1], [4, 1], [5, 1], [6, 1], [7, 1], [8, 1], [9, 1], [10, 1], [11, 1], [12, 1], [13, 1], [14, 1], [15, 1], [16, 1], [17, 1], [18, 17], [19, 17], [20, 17], [21, 17], [22, 17], [23, 17], [24, 17], [25, 17], [26, 17], [27, 17], [28, 17], [29, 17], [30, 17], [31, 17], [32, 17], [33, 17], [34, 17], [35, 17]], [1, 17], conjugacy_class_is_the_complete_conjugation_orbit_not_a_coset)

Wave6第八層核對=(1, [[0, 1], [1, 1], [2, 1], [3, 1], [4, 1], [5, 1], [6, 1], [7, 1], [8, 1], [9, 1], [10, 1], [11, 1], [12, 1], [13, 1], [14, 1], [15, 1], [16, 1], [17, 1], [18, 17], [19, 17], [20, 17], [21, 17], [22, 17], [23, 17], [24, 17], [25, 17], [26, 17], [27, 17], [28, 17], [29, 17], [30, 17], [31, 17], [32, 17], [33, 17], [34, 17], [35, 17]], [1, 17], conjugacy_class_is_the_complete_conjugation_orbit_not_a_coset)；依完整明示資料獨立重算；共軛類是element orbit並形成完整partition；singleton以forall g commute核對；共軛類不是coset或conjugate subgroup；不使用centralizer、class-size公式或類方程。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r03-finite-group-conjugacy-class-0041/)

有限群共軛類 · qf-mod45-conjugacy-orbit-class · candidate





## 42. 有限群共軛類

由完整Cayley table導出全部conjugation action與orbits。操作=conjugacy-orbit-class；資料={"group_table":[[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,0,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,19],[2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,0,1,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,19,20],[3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,0,1,2,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,19,20,21],[4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,0,1,2,3,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,19,20,21,22],[5,6,7,8,9,10,11,12,13,14,15,16,17,18,0,1,2,3,4,24,25,26,27,28,29,30,31,32,33,34,35,36,37,19,20,21,22,23],[6,7,8,9,10,11,12,13,14,15,16,17,18,0,1,2,3,4,5,25,26,27,28,29,30,31,32,33,34,35,36,37,19,20,21,22,23,24],[7,8,9,10,11,12,13,14,15,16,17,18,0,1,2,3,4,5,6,26,27,28,29,30,31,32,33,34,35,36,37,19,20,21,22,23,24,25],[8,9,10,11,12,13,14,15,16,17,18,0,1,2,3,4,5,6,7,27,28,29,30,31,32,33,34,35,36,37,19,20,21,22,23,24,25,26],[9,10,11,12,13,14,15,16,17,18,0,1,2,3,4,5,6,7,8,28,29,30,31,32,33,34,35,36,37,19,20,21,22,23,24,25,26,27],[10,11,12,13,14,15,16,17,18,0,1,2,3,4,5,6,7,8,9,29,30,31,32,33,34,35,36,37,19,20,21,22,23,24,25,26,27,28],[11,12,13,14,15,16,17,18,0,1,2,3,4,5,6,7,8,9,10,30,31,32,33,34,35,36,37,19,20,21,22,23,24,25,26,27,28,29],[12,13,14,15,16,17,18,0,1,2,3,4,5,6,7,8,9,10,11,31,32,33,34,35,36,37,19,20,21,22,23,24,25,26,27,28,29,30],[13,14,15,16,17,18,0,1,2,3,4,5,6,7,8,9,10,11,12,32,33,34,35,36,37,19,20,21,22,23,24,25,26,27,28,29,30,31],[14,15,16,17,18,0,1,2,3,4,5,6,7,8,9,10,11,12,13,33,34,35,36,37,19,20,21,22,23,24,25,26,27,28,29,30,31,32],[15,16,17,18,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,34,35,36,37,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33],[16,17,18,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,35,36,37,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34],[17,18,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,36,37,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35],[18,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,37,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36],[19,37,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,21,20,0,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1],[20,19,37,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,21,1,0,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2],[21,20,19,37,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,2,1,0,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3],[22,21,20,19,37,36,35,34,33,32,31,30,29,28,27,26,25,24,23,3,2,1,0,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4],[23,22,21,20,19,37,36,35,34,33,32,31,30,29,28,27,26,25,24,4,3,2,1,0,18,17,16,15,14,13,12,11,10,9,8,7,6,5],[24,23,22,21,20,19,37,36,35,34,33,32,31,30,29,28,27,26,25,5,4,3,2,1,0,18,17,16,15,14,13,12,11,10,9,8,7,6],[25,24,23,22,21,20,19,37,36,35,34,33,32,31,30,29,28,27,26,6,5,4,3,2,1,0,18,17,16,15,14,13,12,11,10,9,8,7],[26,25,24,23,22,21,20,19,37,36,35,34,33,32,31,30,29,28,27,7,6,5,4,3,2,1,0,18,17,16,15,14,13,12,11,10,9,8],[27,26,25,24,23,22,21,20,19,37,36,35,34,33,32,31,30,29,28,8,7,6,5,4,3,2,1,0,18,17,16,15,14,13,12,11,10,9],[28,27,26,25,24,23,22,21,20,19,37,36,35,34,33,32,31,30,29,9,8,7,6,5,4,3,2,1,0,18,17,16,15,14,13,12,11,10],[29,28,27,26,25,24,23,22,21,20,19,37,36,35,34,33,32,31,30,10,9,8,7,6,5,4,3,2,1,0,18,17,16,15,14,13,12,11],[30,29,28,27,26,25,24,23,22,21,20,19,37,36,35,34,33,32,31,11,10,9,8,7,6,5,4,3,2,1,0,18,17,16,15,14,13,12],[31,30,29,28,27,26,25,24,23,22,21,20,19,37,36,35,34,33,32,12,11,10,9,8,7,6,5,4,3,2,1,0,18,17,16,15,14,13],[32,31,30,29,28,27,26,25,24,23,22,21,20,19,37,36,35,34,33,13,12,11,10,9,8,7,6,5,4,3,2,1,0,18,17,16,15,14],[33,32,31,30,29,28,27,26,25,24,23,22,21,20,19,37,36,35,34,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0,18,17,16,15],[34,33,32,31,30,29,28,27,26,25,24,23,22,21,20,19,37,36,35,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0,18,17,16],[35,34,33,32,31,30,29,28,27,26,25,24,23,22,21,20,19,37,36,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0,18,17],[36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,21,20,19,37,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0,18],[37,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0]],"identity":0,"element":19}。請依 [element, action_image_rows, conjugacy_class, certificate] 欄序回答。

查看答案與解釋(19, [[0, 19], [1, 21], [2, 23], [3, 25], [4, 27], [5, 29], [6, 31], [7, 33], [8, 35], [9, 37], [10, 20], [11, 22], [12, 24], [13, 26], [14, 28], [15, 30], [16, 32], [17, 34], [18, 36], [19, 19], [20, 21], [21, 23], [22, 25], [23, 27], [24, 29], [25, 31], [26, 33], [27, 35], [28, 37], [29, 20], [30, 22], [31, 24], [32, 26], [33, 28], [34, 30], [35, 32], [36, 34], [37, 36]], [19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37], conjugacy_class_is_the_complete_conjugation_orbit_not_a_coset)

Wave6第八層核對=(19, [[0, 19], [1, 21], [2, 23], [3, 25], [4, 27], [5, 29], [6, 31], [7, 33], [8, 35], [9, 37], [10, 20], [11, 22], [12, 24], [13, 26], [14, 28], [15, 30], [16, 32], [17, 34], [18, 36], [19, 19], [20, 21], [21, 23], [22, 25], [23, 27], [24, 29], [25, 31], [26, 33], [27, 35], [28, 37], [29, 20], [30, 22], [31, 24], [32, 26], [33, 28], [34, 30], [35, 32], [36, 34], [37, 36]], [19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37], conjugacy_class_is_the_complete_conjugation_orbit_not_a_coset)；依完整明示資料獨立重算；共軛類是element orbit並形成完整partition；singleton以forall g commute核對；共軛類不是coset或conjugate subgroup；不使用centralizer、class-size公式或類方程。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r03-finite-group-conjugacy-class-0042/)

有限群共軛類 · qf-mod45-conjugacy-orbit-class · candidate





## 43. 有限群共軛類

由完整Cayley table導出全部conjugation action與orbits。操作=conjugacy-orbit-class；資料={"group_table":[[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,0,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,20],[2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,0,1,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,20,21],[3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,0,1,2,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,20,21,22],[4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,0,1,2,3,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,20,21,22,23],[5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,0,1,2,3,4,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,20,21,22,23,24],[6,7,8,9,10,11,12,13,14,15,16,17,18,19,0,1,2,3,4,5,26,27,28,29,30,31,32,33,34,35,36,37,38,39,20,21,22,23,24,25],[7,8,9,10,11,12,13,14,15,16,17,18,19,0,1,2,3,4,5,6,27,28,29,30,31,32,33,34,35,36,37,38,39,20,21,22,23,24,25,26],[8,9,10,11,12,13,14,15,16,17,18,19,0,1,2,3,4,5,6,7,28,29,30,31,32,33,34,35,36,37,38,39,20,21,22,23,24,25,26,27],[9,10,11,12,13,14,15,16,17,18,19,0,1,2,3,4,5,6,7,8,29,30,31,32,33,34,35,36,37,38,39,20,21,22,23,24,25,26,27,28],[10,11,12,13,14,15,16,17,18,19,0,1,2,3,4,5,6,7,8,9,30,31,32,33,34,35,36,37,38,39,20,21,22,23,24,25,26,27,28,29],[11,12,13,14,15,16,17,18,19,0,1,2,3,4,5,6,7,8,9,10,31,32,33,34,35,36,37,38,39,20,21,22,23,24,25,26,27,28,29,30],[12,13,14,15,16,17,18,19,0,1,2,3,4,5,6,7,8,9,10,11,32,33,34,35,36,37,38,39,20,21,22,23,24,25,26,27,28,29,30,31],[13,14,15,16,17,18,19,0,1,2,3,4,5,6,7,8,9,10,11,12,33,34,35,36,37,38,39,20,21,22,23,24,25,26,27,28,29,30,31,32],[14,15,16,17,18,19,0,1,2,3,4,5,6,7,8,9,10,11,12,13,34,35,36,37,38,39,20,21,22,23,24,25,26,27,28,29,30,31,32,33],[15,16,17,18,19,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,35,36,37,38,39,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34],[16,17,18,19,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,36,37,38,39,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35],[17,18,19,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,37,38,39,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36],[18,19,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,38,39,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37],[19,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,39,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38],[20,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,21,0,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1],[21,20,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,1,0,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2],[22,21,20,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,23,2,1,0,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3],[23,22,21,20,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,3,2,1,0,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4],[24,23,22,21,20,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,4,3,2,1,0,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5],[25,24,23,22,21,20,39,38,37,36,35,34,33,32,31,30,29,28,27,26,5,4,3,2,1,0,19,18,17,16,15,14,13,12,11,10,9,8,7,6],[26,25,24,23,22,21,20,39,38,37,36,35,34,33,32,31,30,29,28,27,6,5,4,3,2,1,0,19,18,17,16,15,14,13,12,11,10,9,8,7],[27,26,25,24,23,22,21,20,39,38,37,36,35,34,33,32,31,30,29,28,7,6,5,4,3,2,1,0,19,18,17,16,15,14,13,12,11,10,9,8],[28,27,26,25,24,23,22,21,20,39,38,37,36,35,34,33,32,31,30,29,8,7,6,5,4,3,2,1,0,19,18,17,16,15,14,13,12,11,10,9],[29,28,27,26,25,24,23,22,21,20,39,38,37,36,35,34,33,32,31,30,9,8,7,6,5,4,3,2,1,0,19,18,17,16,15,14,13,12,11,10],[30,29,28,27,26,25,24,23,22,21,20,39,38,37,36,35,34,33,32,31,10,9,8,7,6,5,4,3,2,1,0,19,18,17,16,15,14,13,12,11],[31,30,29,28,27,26,25,24,23,22,21,20,39,38,37,36,35,34,33,32,11,10,9,8,7,6,5,4,3,2,1,0,19,18,17,16,15,14,13,12],[32,31,30,29,28,27,26,25,24,23,22,21,20,39,38,37,36,35,34,33,12,11,10,9,8,7,6,5,4,3,2,1,0,19,18,17,16,15,14,13],[33,32,31,30,29,28,27,26,25,24,23,22,21,20,39,38,37,36,35,34,13,12,11,10,9,8,7,6,5,4,3,2,1,0,19,18,17,16,15,14],[34,33,32,31,30,29,28,27,26,25,24,23,22,21,20,39,38,37,36,35,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0,19,18,17,16,15],[35,34,33,32,31,30,29,28,27,26,25,24,23,22,21,20,39,38,37,36,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0,19,18,17,16],[36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,21,20,39,38,37,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0,19,18,17],[37,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,21,20,39,38,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0,19,18],[38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,21,20,39,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0,19],[39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0]],"identity":0,"element":1}。請依 [element, action_image_rows, conjugacy_class, certificate] 欄序回答。

查看答案與解釋(1, [[0, 1], [1, 1], [2, 1], [3, 1], [4, 1], [5, 1], [6, 1], [7, 1], [8, 1], [9, 1], [10, 1], [11, 1], [12, 1], [13, 1], [14, 1], [15, 1], [16, 1], [17, 1], [18, 1], [19, 1], [20, 19], [21, 19], [22, 19], [23, 19], [24, 19], [25, 19], [26, 19], [27, 19], [28, 19], [29, 19], [30, 19], [31, 19], [32, 19], [33, 19], [34, 19], [35, 19], [36, 19], [37, 19], [38, 19], [39, 19]], [1, 19], conjugacy_class_is_the_complete_conjugation_orbit_not_a_coset)

Wave6第八層核對=(1, [[0, 1], [1, 1], [2, 1], [3, 1], [4, 1], [5, 1], [6, 1], [7, 1], [8, 1], [9, 1], [10, 1], [11, 1], [12, 1], [13, 1], [14, 1], [15, 1], [16, 1], [17, 1], [18, 1], [19, 1], [20, 19], [21, 19], [22, 19], [23, 19], [24, 19], [25, 19], [26, 19], [27, 19], [28, 19], [29, 19], [30, 19], [31, 19], [32, 19], [33, 19], [34, 19], [35, 19], [36, 19], [37, 19], [38, 19], [39, 19]], [1, 19], conjugacy_class_is_the_complete_conjugation_orbit_not_a_coset)；依完整明示資料獨立重算；共軛類是element orbit並形成完整partition；singleton以forall g commute核對；共軛類不是coset或conjugate subgroup；不使用centralizer、class-size公式或類方程。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r03-finite-group-conjugacy-class-0043/)

有限群共軛類 · qf-mod45-conjugacy-orbit-class · candidate





## 44. 有限群共軛類

由完整Cayley table導出全部conjugation action與orbits。操作=conjugacy-orbit-class；資料={"group_table":[[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,0,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,21],[2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,0,1,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,21,22],[3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,0,1,2,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,21,22,23],[4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,0,1,2,3,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,21,22,23,24],[5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,0,1,2,3,4,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,21,22,23,24,25],[6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,0,1,2,3,4,5,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,21,22,23,24,25,26],[7,8,9,10,11,12,13,14,15,16,17,18,19,20,0,1,2,3,4,5,6,28,29,30,31,32,33,34,35,36,37,38,39,40,41,21,22,23,24,25,26,27],[8,9,10,11,12,13,14,15,16,17,18,19,20,0,1,2,3,4,5,6,7,29,30,31,32,33,34,35,36,37,38,39,40,41,21,22,23,24,25,26,27,28],[9,10,11,12,13,14,15,16,17,18,19,20,0,1,2,3,4,5,6,7,8,30,31,32,33,34,35,36,37,38,39,40,41,21,22,23,24,25,26,27,28,29],[10,11,12,13,14,15,16,17,18,19,20,0,1,2,3,4,5,6,7,8,9,31,32,33,34,35,36,37,38,39,40,41,21,22,23,24,25,26,27,28,29,30],[11,12,13,14,15,16,17,18,19,20,0,1,2,3,4,5,6,7,8,9,10,32,33,34,35,36,37,38,39,40,41,21,22,23,24,25,26,27,28,29,30,31],[12,13,14,15,16,17,18,19,20,0,1,2,3,4,5,6,7,8,9,10,11,33,34,35,36,37,38,39,40,41,21,22,23,24,25,26,27,28,29,30,31,32],[13,14,15,16,17,18,19,20,0,1,2,3,4,5,6,7,8,9,10,11,12,34,35,36,37,38,39,40,41,21,22,23,24,25,26,27,28,29,30,31,32,33],[14,15,16,17,18,19,20,0,1,2,3,4,5,6,7,8,9,10,11,12,13,35,36,37,38,39,40,41,21,22,23,24,25,26,27,28,29,30,31,32,33,34],[15,16,17,18,19,20,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,36,37,38,39,40,41,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35],[16,17,18,19,20,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,37,38,39,40,41,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36],[17,18,19,20,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,38,39,40,41,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37],[18,19,20,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,39,40,41,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38],[19,20,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,40,41,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39],[20,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,41,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40],[21,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,0,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1],[22,21,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,23,1,0,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2],[23,22,21,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,2,1,0,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3],[24,23,22,21,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,3,2,1,0,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4],[25,24,23,22,21,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,4,3,2,1,0,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5],[26,25,24,23,22,21,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,5,4,3,2,1,0,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6],[27,26,25,24,23,22,21,41,40,39,38,37,36,35,34,33,32,31,30,29,28,6,5,4,3,2,1,0,20,19,18,17,16,15,14,13,12,11,10,9,8,7],[28,27,26,25,24,23,22,21,41,40,39,38,37,36,35,34,33,32,31,30,29,7,6,5,4,3,2,1,0,20,19,18,17,16,15,14,13,12,11,10,9,8],[29,28,27,26,25,24,23,22,21,41,40,39,38,37,36,35,34,33,32,31,30,8,7,6,5,4,3,2,1,0,20,19,18,17,16,15,14,13,12,11,10,9],[30,29,28,27,26,25,24,23,22,21,41,40,39,38,37,36,35,34,33,32,31,9,8,7,6,5,4,3,2,1,0,20,19,18,17,16,15,14,13,12,11,10],[31,30,29,28,27,26,25,24,23,22,21,41,40,39,38,37,36,35,34,33,32,10,9,8,7,6,5,4,3,2,1,0,20,19,18,17,16,15,14,13,12,11],[32,31,30,29,28,27,26,25,24,23,22,21,41,40,39,38,37,36,35,34,33,11,10,9,8,7,6,5,4,3,2,1,0,20,19,18,17,16,15,14,13,12],[33,32,31,30,29,28,27,26,25,24,23,22,21,41,40,39,38,37,36,35,34,12,11,10,9,8,7,6,5,4,3,2,1,0,20,19,18,17,16,15,14,13],[34,33,32,31,30,29,28,27,26,25,24,23,22,21,41,40,39,38,37,36,35,13,12,11,10,9,8,7,6,5,4,3,2,1,0,20,19,18,17,16,15,14],[35,34,33,32,31,30,29,28,27,26,25,24,23,22,21,41,40,39,38,37,36,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0,20,19,18,17,16,15],[36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,21,41,40,39,38,37,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0,20,19,18,17,16],[37,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,21,41,40,39,38,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0,20,19,18,17],[38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,21,41,40,39,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0,20,19,18],[39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,21,41,40,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0,20,19],[40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,21,41,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0,20],[41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0]],"identity":0,"element":21}。請依 [element, action_image_rows, conjugacy_class, certificate] 欄序回答。

查看答案與解釋(21, [[0, 21], [1, 23], [2, 25], [3, 27], [4, 29], [5, 31], [6, 33], [7, 35], [8, 37], [9, 39], [10, 41], [11, 22], [12, 24], [13, 26], [14, 28], [15, 30], [16, 32], [17, 34], [18, 36], [19, 38], [20, 40], [21, 21], [22, 23], [23, 25], [24, 27], [25, 29], [26, 31], [27, 33], [28, 35], [29, 37], [30, 39], [31, 41], [32, 22], [33, 24], [34, 26], [35, 28], [36, 30], [37, 32], [38, 34], [39, 36], [40, 38], [41, 40]], [21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41], conjugacy_class_is_the_complete_conjugation_orbit_not_a_coset)

Wave6第八層核對=(21, [[0, 21], [1, 23], [2, 25], [3, 27], [4, 29], [5, 31], [6, 33], [7, 35], [8, 37], [9, 39], [10, 41], [11, 22], [12, 24], [13, 26], [14, 28], [15, 30], [16, 32], [17, 34], [18, 36], [19, 38], [20, 40], [21, 21], [22, 23], [23, 25], [24, 27], [25, 29], [26, 31], [27, 33], [28, 35], [29, 37], [30, 39], [31, 41], [32, 22], [33, 24], [34, 26], [35, 28], [36, 30], [37, 32], [38, 34], [39, 36], [40, 38], [41, 40]], [21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41], conjugacy_class_is_the_complete_conjugation_orbit_not_a_coset)；依完整明示資料獨立重算；共軛類是element orbit並形成完整partition；singleton以forall g commute核對；共軛類不是coset或conjugate subgroup；不使用centralizer、class-size公式或類方程。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r03-finite-group-conjugacy-class-0044/)

有限群共軛類 · qf-mod45-conjugacy-orbit-class · candidate





## 45. 有限群共軛類

由完整Cayley table導出全部conjugation action與orbits。操作=conjugacy-orbit-class；資料={"group_table":[[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,0,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,22],[2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,0,1,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,22,23],[3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,0,1,2,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,22,23,24],[4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,0,1,2,3,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,22,23,24,25],[5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,0,1,2,3,4,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,22,23,24,25,26],[6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,0,1,2,3,4,5,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,22,23,24,25,26,27],[7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,0,1,2,3,4,5,6,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,22,23,24,25,26,27,28],[8,9,10,11,12,13,14,15,16,17,18,19,20,21,0,1,2,3,4,5,6,7,30,31,32,33,34,35,36,37,38,39,40,41,42,43,22,23,24,25,26,27,28,29],[9,10,11,12,13,14,15,16,17,18,19,20,21,0,1,2,3,4,5,6,7,8,31,32,33,34,35,36,37,38,39,40,41,42,43,22,23,24,25,26,27,28,29,30],[10,11,12,13,14,15,16,17,18,19,20,21,0,1,2,3,4,5,6,7,8,9,32,33,34,35,36,37,38,39,40,41,42,43,22,23,24,25,26,27,28,29,30,31],[11,12,13,14,15,16,17,18,19,20,21,0,1,2,3,4,5,6,7,8,9,10,33,34,35,36,37,38,39,40,41,42,43,22,23,24,25,26,27,28,29,30,31,32],[12,13,14,15,16,17,18,19,20,21,0,1,2,3,4,5,6,7,8,9,10,11,34,35,36,37,38,39,40,41,42,43,22,23,24,25,26,27,28,29,30,31,32,33],[13,14,15,16,17,18,19,20,21,0,1,2,3,4,5,6,7,8,9,10,11,12,35,36,37,38,39,40,41,42,43,22,23,24,25,26,27,28,29,30,31,32,33,34],[14,15,16,17,18,19,20,21,0,1,2,3,4,5,6,7,8,9,10,11,12,13,36,37,38,39,40,41,42,43,22,23,24,25,26,27,28,29,30,31,32,33,34,35],[15,16,17,18,19,20,21,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,37,38,39,40,41,42,43,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36],[16,17,18,19,20,21,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,38,39,40,41,42,43,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37],[17,18,19,20,21,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,39,40,41,42,43,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38],[18,19,20,21,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,40,41,42,43,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39],[19,20,21,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,41,42,43,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40],[20,21,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,42,43,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41],[21,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,43,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42],[22,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,23,0,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1],[23,22,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,1,0,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2],[24,23,22,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,2,1,0,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3],[25,24,23,22,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,3,2,1,0,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4],[26,25,24,23,22,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,4,3,2,1,0,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5],[27,26,25,24,23,22,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,5,4,3,2,1,0,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6],[28,27,26,25,24,23,22,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,6,5,4,3,2,1,0,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7],[29,28,27,26,25,24,23,22,43,42,41,40,39,38,37,36,35,34,33,32,31,30,7,6,5,4,3,2,1,0,21,20,19,18,17,16,15,14,13,12,11,10,9,8],[30,29,28,27,26,25,24,23,22,43,42,41,40,39,38,37,36,35,34,33,32,31,8,7,6,5,4,3,2,1,0,21,20,19,18,17,16,15,14,13,12,11,10,9],[31,30,29,28,27,26,25,24,23,22,43,42,41,40,39,38,37,36,35,34,33,32,9,8,7,6,5,4,3,2,1,0,21,20,19,18,17,16,15,14,13,12,11,10],[32,31,30,29,28,27,26,25,24,23,22,43,42,41,40,39,38,37,36,35,34,33,10,9,8,7,6,5,4,3,2,1,0,21,20,19,18,17,16,15,14,13,12,11],[33,32,31,30,29,28,27,26,25,24,23,22,43,42,41,40,39,38,37,36,35,34,11,10,9,8,7,6,5,4,3,2,1,0,21,20,19,18,17,16,15,14,13,12],[34,33,32,31,30,29,28,27,26,25,24,23,22,43,42,41,40,39,38,37,36,35,12,11,10,9,8,7,6,5,4,3,2,1,0,21,20,19,18,17,16,15,14,13],[35,34,33,32,31,30,29,28,27,26,25,24,23,22,43,42,41,40,39,38,37,36,13,12,11,10,9,8,7,6,5,4,3,2,1,0,21,20,19,18,17,16,15,14],[36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,43,42,41,40,39,38,37,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0,21,20,19,18,17,16,15],[37,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,43,42,41,40,39,38,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0,21,20,19,18,17,16],[38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,43,42,41,40,39,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0,21,20,19,18,17],[39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,43,42,41,40,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0,21,20,19,18],[40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,43,42,41,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0,21,20,19],[41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,43,42,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0,21,20],[42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,43,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0,21],[43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0]],"identity":0,"element":1}。請依 [element, action_image_rows, conjugacy_class, certificate] 欄序回答。

查看答案與解釋(1, [[0, 1], [1, 1], [2, 1], [3, 1], [4, 1], [5, 1], [6, 1], [7, 1], [8, 1], [9, 1], [10, 1], [11, 1], [12, 1], [13, 1], [14, 1], [15, 1], [16, 1], [17, 1], [18, 1], [19, 1], [20, 1], [21, 1], [22, 21], [23, 21], [24, 21], [25, 21], [26, 21], [27, 21], [28, 21], [29, 21], [30, 21], [31, 21], [32, 21], [33, 21], [34, 21], [35, 21], [36, 21], [37, 21], [38, 21], [39, 21], [40, 21], [41, 21], [42, 21], [43, 21]], [1, 21], conjugacy_class_is_the_complete_conjugation_orbit_not_a_coset)

Wave6第八層核對=(1, [[0, 1], [1, 1], [2, 1], [3, 1], [4, 1], [5, 1], [6, 1], [7, 1], [8, 1], [9, 1], [10, 1], [11, 1], [12, 1], [13, 1], [14, 1], [15, 1], [16, 1], [17, 1], [18, 1], [19, 1], [20, 1], [21, 1], [22, 21], [23, 21], [24, 21], [25, 21], [26, 21], [27, 21], [28, 21], [29, 21], [30, 21], [31, 21], [32, 21], [33, 21], [34, 21], [35, 21], [36, 21], [37, 21], [38, 21], [39, 21], [40, 21], [41, 21], [42, 21], [43, 21]], [1, 21], conjugacy_class_is_the_complete_conjugation_orbit_not_a_coset)；依完整明示資料獨立重算；共軛類是element orbit並形成完整partition；singleton以forall g commute核對；共軛類不是coset或conjugate subgroup；不使用centralizer、class-size公式或類方程。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r03-finite-group-conjugacy-class-0045/)

有限群共軛類 · qf-mod45-conjugacy-orbit-class · candidate





## 46. 有限群共軛類

由完整Cayley table導出全部conjugation action與orbits。操作=conjugacy-orbit-class；資料={"group_table":[[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,0,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,23],[2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,0,1,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,23,24],[3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,0,1,2,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,23,24,25],[4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,0,1,2,3,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,23,24,25,26],[5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,0,1,2,3,4,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,23,24,25,26,27],[6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,0,1,2,3,4,5,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,23,24,25,26,27,28],[7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,0,1,2,3,4,5,6,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,23,24,25,26,27,28,29],[8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,0,1,2,3,4,5,6,7,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,23,24,25,26,27,28,29,30],[9,10,11,12,13,14,15,16,17,18,19,20,21,22,0,1,2,3,4,5,6,7,8,32,33,34,35,36,37,38,39,40,41,42,43,44,45,23,24,25,26,27,28,29,30,31],[10,11,12,13,14,15,16,17,18,19,20,21,22,0,1,2,3,4,5,6,7,8,9,33,34,35,36,37,38,39,40,41,42,43,44,45,23,24,25,26,27,28,29,30,31,32],[11,12,13,14,15,16,17,18,19,20,21,22,0,1,2,3,4,5,6,7,8,9,10,34,35,36,37,38,39,40,41,42,43,44,45,23,24,25,26,27,28,29,30,31,32,33],[12,13,14,15,16,17,18,19,20,21,22,0,1,2,3,4,5,6,7,8,9,10,11,35,36,37,38,39,40,41,42,43,44,45,23,24,25,26,27,28,29,30,31,32,33,34],[13,14,15,16,17,18,19,20,21,22,0,1,2,3,4,5,6,7,8,9,10,11,12,36,37,38,39,40,41,42,43,44,45,23,24,25,26,27,28,29,30,31,32,33,34,35],[14,15,16,17,18,19,20,21,22,0,1,2,3,4,5,6,7,8,9,10,11,12,13,37,38,39,40,41,42,43,44,45,23,24,25,26,27,28,29,30,31,32,33,34,35,36],[15,16,17,18,19,20,21,22,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,38,39,40,41,42,43,44,45,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37],[16,17,18,19,20,21,22,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,39,40,41,42,43,44,45,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38],[17,18,19,20,21,22,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,40,41,42,43,44,45,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39],[18,19,20,21,22,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,41,42,43,44,45,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40],[19,20,21,22,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,42,43,44,45,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41],[20,21,22,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,43,44,45,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42],[21,22,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,44,45,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],[22,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,45,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44],[23,45,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,0,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1],[24,23,45,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,1,0,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2],[25,24,23,45,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,2,1,0,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3],[26,25,24,23,45,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,3,2,1,0,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4],[27,26,25,24,23,45,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,4,3,2,1,0,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5],[28,27,26,25,24,23,45,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,5,4,3,2,1,0,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6],[29,28,27,26,25,24,23,45,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,6,5,4,3,2,1,0,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7],[30,29,28,27,26,25,24,23,45,44,43,42,41,40,39,38,37,36,35,34,33,32,31,7,6,5,4,3,2,1,0,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8],[31,30,29,28,27,26,25,24,23,45,44,43,42,41,40,39,38,37,36,35,34,33,32,8,7,6,5,4,3,2,1,0,22,21,20,19,18,17,16,15,14,13,12,11,10,9],[32,31,30,29,28,27,26,25,24,23,45,44,43,42,41,40,39,38,37,36,35,34,33,9,8,7,6,5,4,3,2,1,0,22,21,20,19,18,17,16,15,14,13,12,11,10],[33,32,31,30,29,28,27,26,25,24,23,45,44,43,42,41,40,39,38,37,36,35,34,10,9,8,7,6,5,4,3,2,1,0,22,21,20,19,18,17,16,15,14,13,12,11],[34,33,32,31,30,29,28,27,26,25,24,23,45,44,43,42,41,40,39,38,37,36,35,11,10,9,8,7,6,5,4,3,2,1,0,22,21,20,19,18,17,16,15,14,13,12],[35,34,33,32,31,30,29,28,27,26,25,24,23,45,44,43,42,41,40,39,38,37,36,12,11,10,9,8,7,6,5,4,3,2,1,0,22,21,20,19,18,17,16,15,14,13],[36,35,34,33,32,31,30,29,28,27,26,25,24,23,45,44,43,42,41,40,39,38,37,13,12,11,10,9,8,7,6,5,4,3,2,1,0,22,21,20,19,18,17,16,15,14],[37,36,35,34,33,32,31,30,29,28,27,26,25,24,23,45,44,43,42,41,40,39,38,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0,22,21,20,19,18,17,16,15],[38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,23,45,44,43,42,41,40,39,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0,22,21,20,19,18,17,16],[39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,23,45,44,43,42,41,40,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0,22,21,20,19,18,17],[40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,23,45,44,43,42,41,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0,22,21,20,19,18],[41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,23,45,44,43,42,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0,22,21,20,19],[42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,23,45,44,43,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0,22,21,20],[43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,23,45,44,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0,22,21],[44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,23,45,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0,22],[45,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0]],"identity":0,"element":23}。請依 [element, action_image_rows, conjugacy_class, certificate] 欄序回答。

查看答案與解釋(23, [[0, 23], [1, 25], [2, 27], [3, 29], [4, 31], [5, 33], [6, 35], [7, 37], [8, 39], [9, 41], [10, 43], [11, 45], [12, 24], [13, 26], [14, 28], [15, 30], [16, 32], [17, 34], [18, 36], [19, 38], [20, 40], [21, 42], [22, 44], [23, 23], [24, 25], [25, 27], [26, 29], [27, 31], [28, 33], [29, 35], [30, 37], [31, 39], [32, 41], [33, 43], [34, 45], [35, 24], [36, 26], [37, 28], [38, 30], [39, 32], [40, 34], [41, 36], [42, 38], [43, 40], [44, 42], [45, 44]], [23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45], conjugacy_class_is_the_complete_conjugation_orbit_not_a_coset)

Wave6第八層核對=(23, [[0, 23], [1, 25], [2, 27], [3, 29], [4, 31], [5, 33], [6, 35], [7, 37], [8, 39], [9, 41], [10, 43], [11, 45], [12, 24], [13, 26], [14, 28], [15, 30], [16, 32], [17, 34], [18, 36], [19, 38], [20, 40], [21, 42], [22, 44], [23, 23], [24, 25], [25, 27], [26, 29], [27, 31], [28, 33], [29, 35], [30, 37], [31, 39], [32, 41], [33, 43], [34, 45], [35, 24], [36, 26], [37, 28], [38, 30], [39, 32], [40, 34], [41, 36], [42, 38], [43, 40], [44, 42], [45, 44]], [23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45], conjugacy_class_is_the_complete_conjugation_orbit_not_a_coset)；依完整明示資料獨立重算；共軛類是element orbit並形成完整partition；singleton以forall g commute核對；共軛類不是coset或conjugate subgroup；不使用centralizer、class-size公式或類方程。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r03-finite-group-conjugacy-class-0046/)

有限群共軛類 · qf-mod45-conjugacy-orbit-class · candidate





## 47. 有限群共軛類

由完整Cayley table導出全部conjugation action與orbits。操作=conjugacy-orbit-class；資料={"group_table":[[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,0,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,24],[2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,0,1,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,24,25],[3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,0,1,2,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,24,25,26],[4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,0,1,2,3,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,24,25,26,27],[5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,0,1,2,3,4,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,24,25,26,27,28],[6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,0,1,2,3,4,5,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,24,25,26,27,28,29],[7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,0,1,2,3,4,5,6,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,24,25,26,27,28,29,30],[8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,0,1,2,3,4,5,6,7,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,24,25,26,27,28,29,30,31],[9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,0,1,2,3,4,5,6,7,8,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,24,25,26,27,28,29,30,31,32],[10,11,12,13,14,15,16,17,18,19,20,21,22,23,0,1,2,3,4,5,6,7,8,9,34,35,36,37,38,39,40,41,42,43,44,45,46,47,24,25,26,27,28,29,30,31,32,33],[11,12,13,14,15,16,17,18,19,20,21,22,23,0,1,2,3,4,5,6,7,8,9,10,35,36,37,38,39,40,41,42,43,44,45,46,47,24,25,26,27,28,29,30,31,32,33,34],[12,13,14,15,16,17,18,19,20,21,22,23,0,1,2,3,4,5,6,7,8,9,10,11,36,37,38,39,40,41,42,43,44,45,46,47,24,25,26,27,28,29,30,31,32,33,34,35],[13,14,15,16,17,18,19,20,21,22,23,0,1,2,3,4,5,6,7,8,9,10,11,12,37,38,39,40,41,42,43,44,45,46,47,24,25,26,27,28,29,30,31,32,33,34,35,36],[14,15,16,17,18,19,20,21,22,23,0,1,2,3,4,5,6,7,8,9,10,11,12,13,38,39,40,41,42,43,44,45,46,47,24,25,26,27,28,29,30,31,32,33,34,35,36,37],[15,16,17,18,19,20,21,22,23,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,39,40,41,42,43,44,45,46,47,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38],[16,17,18,19,20,21,22,23,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,40,41,42,43,44,45,46,47,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39],[17,18,19,20,21,22,23,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,41,42,43,44,45,46,47,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40],[18,19,20,21,22,23,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,42,43,44,45,46,47,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41],[19,20,21,22,23,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,43,44,45,46,47,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42],[20,21,22,23,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,44,45,46,47,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],[21,22,23,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,45,46,47,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44],[22,23,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,46,47,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45],[23,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,47,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46],[24,47,46,45,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,0,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1],[25,24,47,46,45,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,1,0,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2],[26,25,24,47,46,45,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,2,1,0,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3],[27,26,25,24,47,46,45,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,3,2,1,0,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4],[28,27,26,25,24,47,46,45,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,4,3,2,1,0,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5],[29,28,27,26,25,24,47,46,45,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,5,4,3,2,1,0,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6],[30,29,28,27,26,25,24,47,46,45,44,43,42,41,40,39,38,37,36,35,34,33,32,31,6,5,4,3,2,1,0,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7],[31,30,29,28,27,26,25,24,47,46,45,44,43,42,41,40,39,38,37,36,35,34,33,32,7,6,5,4,3,2,1,0,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8],[32,31,30,29,28,27,26,25,24,47,46,45,44,43,42,41,40,39,38,37,36,35,34,33,8,7,6,5,4,3,2,1,0,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9],[33,32,31,30,29,28,27,26,25,24,47,46,45,44,43,42,41,40,39,38,37,36,35,34,9,8,7,6,5,4,3,2,1,0,23,22,21,20,19,18,17,16,15,14,13,12,11,10],[34,33,32,31,30,29,28,27,26,25,24,47,46,45,44,43,42,41,40,39,38,37,36,35,10,9,8,7,6,5,4,3,2,1,0,23,22,21,20,19,18,17,16,15,14,13,12,11],[35,34,33,32,31,30,29,28,27,26,25,24,47,46,45,44,43,42,41,40,39,38,37,36,11,10,9,8,7,6,5,4,3,2,1,0,23,22,21,20,19,18,17,16,15,14,13,12],[36,35,34,33,32,31,30,29,28,27,26,25,24,47,46,45,44,43,42,41,40,39,38,37,12,11,10,9,8,7,6,5,4,3,2,1,0,23,22,21,20,19,18,17,16,15,14,13],[37,36,35,34,33,32,31,30,29,28,27,26,25,24,47,46,45,44,43,42,41,40,39,38,13,12,11,10,9,8,7,6,5,4,3,2,1,0,23,22,21,20,19,18,17,16,15,14],[38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,47,46,45,44,43,42,41,40,39,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0,23,22,21,20,19,18,17,16,15],[39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,47,46,45,44,43,42,41,40,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0,23,22,21,20,19,18,17,16],[40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,47,46,45,44,43,42,41,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0,23,22,21,20,19,18,17],[41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,47,46,45,44,43,42,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0,23,22,21,20,19,18],[42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,47,46,45,44,43,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0,23,22,21,20,19],[43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,47,46,45,44,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0,23,22,21,20],[44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,47,46,45,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0,23,22,21],[45,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,47,46,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0,23,22],[46,45,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,47,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0,23],[47,46,45,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0]],"identity":0,"element":1}。請依 [element, action_image_rows, conjugacy_class, certificate] 欄序回答。

查看答案與解釋(1, [[0, 1], [1, 1], [2, 1], [3, 1], [4, 1], [5, 1], [6, 1], [7, 1], [8, 1], [9, 1], [10, 1], [11, 1], [12, 1], [13, 1], [14, 1], [15, 1], [16, 1], [17, 1], [18, 1], [19, 1], [20, 1], [21, 1], [22, 1], [23, 1], [24, 23], [25, 23], [26, 23], [27, 23], [28, 23], [29, 23], [30, 23], [31, 23], [32, 23], [33, 23], [34, 23], [35, 23], [36, 23], [37, 23], [38, 23], [39, 23], [40, 23], [41, 23], [42, 23], [43, 23], [44, 23], [45, 23], [46, 23], [47, 23]], [1, 23], conjugacy_class_is_the_complete_conjugation_orbit_not_a_coset)

Wave6第八層核對=(1, [[0, 1], [1, 1], [2, 1], [3, 1], [4, 1], [5, 1], [6, 1], [7, 1], [8, 1], [9, 1], [10, 1], [11, 1], [12, 1], [13, 1], [14, 1], [15, 1], [16, 1], [17, 1], [18, 1], [19, 1], [20, 1], [21, 1], [22, 1], [23, 1], [24, 23], [25, 23], [26, 23], [27, 23], [28, 23], [29, 23], [30, 23], [31, 23], [32, 23], [33, 23], [34, 23], [35, 23], [36, 23], [37, 23], [38, 23], [39, 23], [40, 23], [41, 23], [42, 23], [43, 23], [44, 23], [45, 23], [46, 23], [47, 23]], [1, 23], conjugacy_class_is_the_complete_conjugation_orbit_not_a_coset)；依完整明示資料獨立重算；共軛類是element orbit並形成完整partition；singleton以forall g commute核對；共軛類不是coset或conjugate subgroup；不使用centralizer、class-size公式或類方程。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r03-finite-group-conjugacy-class-0047/)

有限群共軛類 · qf-mod45-conjugacy-orbit-class · candidate





## 48. 有限群共軛類

由完整Cayley table導出全部conjugation action與orbits。操作=conjugacy-orbit-class；資料={"group_table":[[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,0,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,25],[2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,0,1,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,25,26],[3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,0,1,2,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,25,26,27],[4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,0,1,2,3,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,25,26,27,28],[5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,0,1,2,3,4,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,25,26,27,28,29],[6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,0,1,2,3,4,5,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,25,26,27,28,29,30],[7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,0,1,2,3,4,5,6,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,25,26,27,28,29,30,31],[8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,0,1,2,3,4,5,6,7,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,25,26,27,28,29,30,31,32],[9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,0,1,2,3,4,5,6,7,8,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,25,26,27,28,29,30,31,32,33],[10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,0,1,2,3,4,5,6,7,8,9,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,25,26,27,28,29,30,31,32,33,34],[11,12,13,14,15,16,17,18,19,20,21,22,23,24,0,1,2,3,4,5,6,7,8,9,10,36,37,38,39,40,41,42,43,44,45,46,47,48,49,25,26,27,28,29,30,31,32,33,34,35],[12,13,14,15,16,17,18,19,20,21,22,23,24,0,1,2,3,4,5,6,7,8,9,10,11,37,38,39,40,41,42,43,44,45,46,47,48,49,25,26,27,28,29,30,31,32,33,34,35,36],[13,14,15,16,17,18,19,20,21,22,23,24,0,1,2,3,4,5,6,7,8,9,10,11,12,38,39,40,41,42,43,44,45,46,47,48,49,25,26,27,28,29,30,31,32,33,34,35,36,37],[14,15,16,17,18,19,20,21,22,23,24,0,1,2,3,4,5,6,7,8,9,10,11,12,13,39,40,41,42,43,44,45,46,47,48,49,25,26,27,28,29,30,31,32,33,34,35,36,37,38],[15,16,17,18,19,20,21,22,23,24,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,40,41,42,43,44,45,46,47,48,49,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39],[16,17,18,19,20,21,22,23,24,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,41,42,43,44,45,46,47,48,49,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40],[17,18,19,20,21,22,23,24,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,42,43,44,45,46,47,48,49,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41],[18,19,20,21,22,23,24,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,43,44,45,46,47,48,49,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42],[19,20,21,22,23,24,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,44,45,46,47,48,49,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],[20,21,22,23,24,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,45,46,47,48,49,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44],[21,22,23,24,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,46,47,48,49,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45],[22,23,24,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,47,48,49,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46],[23,24,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,48,49,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47],[24,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,49,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48],[25,49,48,47,46,45,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,0,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1],[26,25,49,48,47,46,45,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,1,0,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2],[27,26,25,49,48,47,46,45,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,2,1,0,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3],[28,27,26,25,49,48,47,46,45,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,3,2,1,0,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4],[29,28,27,26,25,49,48,47,46,45,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,4,3,2,1,0,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5],[30,29,28,27,26,25,49,48,47,46,45,44,43,42,41,40,39,38,37,36,35,34,33,32,31,5,4,3,2,1,0,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6],[31,30,29,28,27,26,25,49,48,47,46,45,44,43,42,41,40,39,38,37,36,35,34,33,32,6,5,4,3,2,1,0,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7],[32,31,30,29,28,27,26,25,49,48,47,46,45,44,43,42,41,40,39,38,37,36,35,34,33,7,6,5,4,3,2,1,0,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8],[33,32,31,30,29,28,27,26,25,49,48,47,46,45,44,43,42,41,40,39,38,37,36,35,34,8,7,6,5,4,3,2,1,0,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9],[34,33,32,31,30,29,28,27,26,25,49,48,47,46,45,44,43,42,41,40,39,38,37,36,35,9,8,7,6,5,4,3,2,1,0,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10],[35,34,33,32,31,30,29,28,27,26,25,49,48,47,46,45,44,43,42,41,40,39,38,37,36,10,9,8,7,6,5,4,3,2,1,0,24,23,22,21,20,19,18,17,16,15,14,13,12,11],[36,35,34,33,32,31,30,29,28,27,26,25,49,48,47,46,45,44,43,42,41,40,39,38,37,11,10,9,8,7,6,5,4,3,2,1,0,24,23,22,21,20,19,18,17,16,15,14,13,12],[37,36,35,34,33,32,31,30,29,28,27,26,25,49,48,47,46,45,44,43,42,41,40,39,38,12,11,10,9,8,7,6,5,4,3,2,1,0,24,23,22,21,20,19,18,17,16,15,14,13],[38,37,36,35,34,33,32,31,30,29,28,27,26,25,49,48,47,46,45,44,43,42,41,40,39,13,12,11,10,9,8,7,6,5,4,3,2,1,0,24,23,22,21,20,19,18,17,16,15,14],[39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,49,48,47,46,45,44,43,42,41,40,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0,24,23,22,21,20,19,18,17,16,15],[40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,49,48,47,46,45,44,43,42,41,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0,24,23,22,21,20,19,18,17,16],[41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,49,48,47,46,45,44,43,42,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0,24,23,22,21,20,19,18,17],[42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,49,48,47,46,45,44,43,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0,24,23,22,21,20,19,18],[43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,49,48,47,46,45,44,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0,24,23,22,21,20,19],[44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,49,48,47,46,45,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0,24,23,22,21,20],[45,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,49,48,47,46,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0,24,23,22,21],[46,45,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,49,48,47,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0,24,23,22],[47,46,45,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,49,48,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0,24,23],[48,47,46,45,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,49,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0,24],[49,48,47,46,45,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0]],"identity":0,"element":25}。請依 [element, action_image_rows, conjugacy_class, certificate] 欄序回答。

查看答案與解釋(25, [[0, 25], [1, 27], [2, 29], [3, 31], [4, 33], [5, 35], [6, 37], [7, 39], [8, 41], [9, 43], [10, 45], [11, 47], [12, 49], [13, 26], [14, 28], [15, 30], [16, 32], [17, 34], [18, 36], [19, 38], [20, 40], [21, 42], [22, 44], [23, 46], [24, 48], [25, 25], [26, 27], [27, 29], [28, 31], [29, 33], [30, 35], [31, 37], [32, 39], [33, 41], [34, 43], [35, 45], [36, 47], [37, 49], [38, 26], [39, 28], [40, 30], [41, 32], [42, 34], [43, 36], [44, 38], [45, 40], [46, 42], [47, 44], [48, 46], [49, 48]], [25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49], conjugacy_class_is_the_complete_conjugation_orbit_not_a_coset)

Wave6第八層核對=(25, [[0, 25], [1, 27], [2, 29], [3, 31], [4, 33], [5, 35], [6, 37], [7, 39], [8, 41], [9, 43], [10, 45], [11, 47], [12, 49], [13, 26], [14, 28], [15, 30], [16, 32], [17, 34], [18, 36], [19, 38], [20, 40], [21, 42], [22, 44], [23, 46], [24, 48], [25, 25], [26, 27], [27, 29], [28, 31], [29, 33], [30, 35], [31, 37], [32, 39], [33, 41], [34, 43], [35, 45], [36, 47], [37, 49], [38, 26], [39, 28], [40, 30], [41, 32], [42, 34], [43, 36], [44, 38], [45, 40], [46, 42], [47, 44], [48, 46], [49, 48]], [25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49], conjugacy_class_is_the_complete_conjugation_orbit_not_a_coset)；依完整明示資料獨立重算；共軛類是element orbit並形成完整partition；singleton以forall g commute核對；共軛類不是coset或conjugate subgroup；不使用centralizer、class-size公式或類方程。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r03-finite-group-conjugacy-class-0048/)

有限群共軛類 · qf-mod45-conjugacy-orbit-class · candidate





## 49. 有限群共軛類

由完整Cayley table導出全部conjugation action與orbits。操作=conjugacy-orbit-class；資料={"group_table":[[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,0,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,26],[2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,0,1,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,26,27],[3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,0,1,2,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,26,27,28],[4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,0,1,2,3,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,26,27,28,29],[5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,0,1,2,3,4,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,26,27,28,29,30],[6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,0,1,2,3,4,5,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,26,27,28,29,30,31],[7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,0,1,2,3,4,5,6,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,26,27,28,29,30,31,32],[8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,0,1,2,3,4,5,6,7,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,26,27,28,29,30,31,32,33],[9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,0,1,2,3,4,5,6,7,8,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,26,27,28,29,30,31,32,33,34],[10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,0,1,2,3,4,5,6,7,8,9,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,26,27,28,29,30,31,32,33,34,35],[11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,0,1,2,3,4,5,6,7,8,9,10,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,26,27,28,29,30,31,32,33,34,35,36],[12,13,14,15,16,17,18,19,20,21,22,23,24,25,0,1,2,3,4,5,6,7,8,9,10,11,38,39,40,41,42,43,44,45,46,47,48,49,50,51,26,27,28,29,30,31,32,33,34,35,36,37],[13,14,15,16,17,18,19,20,21,22,23,24,25,0,1,2,3,4,5,6,7,8,9,10,11,12,39,40,41,42,43,44,45,46,47,48,49,50,51,26,27,28,29,30,31,32,33,34,35,36,37,38],[14,15,16,17,18,19,20,21,22,23,24,25,0,1,2,3,4,5,6,7,8,9,10,11,12,13,40,41,42,43,44,45,46,47,48,49,50,51,26,27,28,29,30,31,32,33,34,35,36,37,38,39],[15,16,17,18,19,20,21,22,23,24,25,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,41,42,43,44,45,46,47,48,49,50,51,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40],[16,17,18,19,20,21,22,23,24,25,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,42,43,44,45,46,47,48,49,50,51,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41],[17,18,19,20,21,22,23,24,25,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,43,44,45,46,47,48,49,50,51,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42],[18,19,20,21,22,23,24,25,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,44,45,46,47,48,49,50,51,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],[19,20,21,22,23,24,25,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,45,46,47,48,49,50,51,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44],[20,21,22,23,24,25,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,46,47,48,49,50,51,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45],[21,22,23,24,25,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,47,48,49,50,51,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46],[22,23,24,25,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,48,49,50,51,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47],[23,24,25,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,49,50,51,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48],[24,25,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,50,51,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49],[25,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,51,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50],[26,51,50,49,48,47,46,45,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,0,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1],[27,26,51,50,49,48,47,46,45,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,1,0,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2],[28,27,26,51,50,49,48,47,46,45,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,2,1,0,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3],[29,28,27,26,51,50,49,48,47,46,45,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,3,2,1,0,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4],[30,29,28,27,26,51,50,49,48,47,46,45,44,43,42,41,40,39,38,37,36,35,34,33,32,31,4,3,2,1,0,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5],[31,30,29,28,27,26,51,50,49,48,47,46,45,44,43,42,41,40,39,38,37,36,35,34,33,32,5,4,3,2,1,0,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6],[32,31,30,29,28,27,26,51,50,49,48,47,46,45,44,43,42,41,40,39,38,37,36,35,34,33,6,5,4,3,2,1,0,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7],[33,32,31,30,29,28,27,26,51,50,49,48,47,46,45,44,43,42,41,40,39,38,37,36,35,34,7,6,5,4,3,2,1,0,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8],[34,33,32,31,30,29,28,27,26,51,50,49,48,47,46,45,44,43,42,41,40,39,38,37,36,35,8,7,6,5,4,3,2,1,0,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9],[35,34,33,32,31,30,29,28,27,26,51,50,49,48,47,46,45,44,43,42,41,40,39,38,37,36,9,8,7,6,5,4,3,2,1,0,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10],[36,35,34,33,32,31,30,29,28,27,26,51,50,49,48,47,46,45,44,43,42,41,40,39,38,37,10,9,8,7,6,5,4,3,2,1,0,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11],[37,36,35,34,33,32,31,30,29,28,27,26,51,50,49,48,47,46,45,44,43,42,41,40,39,38,11,10,9,8,7,6,5,4,3,2,1,0,25,24,23,22,21,20,19,18,17,16,15,14,13,12],[38,37,36,35,34,33,32,31,30,29,28,27,26,51,50,49,48,47,46,45,44,43,42,41,40,39,12,11,10,9,8,7,6,5,4,3,2,1,0,25,24,23,22,21,20,19,18,17,16,15,14,13],[39,38,37,36,35,34,33,32,31,30,29,28,27,26,51,50,49,48,47,46,45,44,43,42,41,40,13,12,11,10,9,8,7,6,5,4,3,2,1,0,25,24,23,22,21,20,19,18,17,16,15,14],[40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,51,50,49,48,47,46,45,44,43,42,41,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0,25,24,23,22,21,20,19,18,17,16,15],[41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,51,50,49,48,47,46,45,44,43,42,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0,25,24,23,22,21,20,19,18,17,16],[42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,51,50,49,48,47,46,45,44,43,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0,25,24,23,22,21,20,19,18,17],[43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,51,50,49,48,47,46,45,44,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0,25,24,23,22,21,20,19,18],[44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,51,50,49,48,47,46,45,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0,25,24,23,22,21,20,19],[45,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,51,50,49,48,47,46,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0,25,24,23,22,21,20],[46,45,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,51,50,49,48,47,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0,25,24,23,22,21],[47,46,45,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,51,50,49,48,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0,25,24,23,22],[48,47,46,45,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,51,50,49,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0,25,24,23],[49,48,47,46,45,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,51,50,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0,25,24],[50,49,48,47,46,45,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,51,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0,25],[51,50,49,48,47,46,45,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0]],"identity":0,"element":1}。請依 [element, action_image_rows, conjugacy_class, certificate] 欄序回答。

查看答案與解釋(1, [[0, 1], [1, 1], [2, 1], [3, 1], [4, 1], [5, 1], [6, 1], [7, 1], [8, 1], [9, 1], [10, 1], [11, 1], [12, 1], [13, 1], [14, 1], [15, 1], [16, 1], [17, 1], [18, 1], [19, 1], [20, 1], [21, 1], [22, 1], [23, 1], [24, 1], [25, 1], [26, 25], [27, 25], [28, 25], [29, 25], [30, 25], [31, 25], [32, 25], [33, 25], [34, 25], [35, 25], [36, 25], [37, 25], [38, 25], [39, 25], [40, 25], [41, 25], [42, 25], [43, 25], [44, 25], [45, 25], [46, 25], [47, 25], [48, 25], [49, 25], [50, 25], [51, 25]], [1, 25], conjugacy_class_is_the_complete_conjugation_orbit_not_a_coset)

Wave6第八層核對=(1, [[0, 1], [1, 1], [2, 1], [3, 1], [4, 1], [5, 1], [6, 1], [7, 1], [8, 1], [9, 1], [10, 1], [11, 1], [12, 1], [13, 1], [14, 1], [15, 1], [16, 1], [17, 1], [18, 1], [19, 1], [20, 1], [21, 1], [22, 1], [23, 1], [24, 1], [25, 1], [26, 25], [27, 25], [28, 25], [29, 25], [30, 25], [31, 25], [32, 25], [33, 25], [34, 25], [35, 25], [36, 25], [37, 25], [38, 25], [39, 25], [40, 25], [41, 25], [42, 25], [43, 25], [44, 25], [45, 25], [46, 25], [47, 25], [48, 25], [49, 25], [50, 25], [51, 25]], [1, 25], conjugacy_class_is_the_complete_conjugation_orbit_not_a_coset)；依完整明示資料獨立重算；共軛類是element orbit並形成完整partition；singleton以forall g commute核對；共軛類不是coset或conjugate subgroup；不使用centralizer、class-size公式或類方程。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r03-finite-group-conjugacy-class-0049/)

有限群共軛類 · qf-mod45-conjugacy-orbit-class · candidate





## 50. 有限群共軛類

由完整Cayley table導出全部conjugation action與orbits。操作=conjugacy-orbit-class；資料={"group_table":[[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,0,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,27],[2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,0,1,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,27,28],[3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,0,1,2,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,27,28,29],[4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,0,1,2,3,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,27,28,29,30],[5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,0,1,2,3,4,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,27,28,29,30,31],[6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,0,1,2,3,4,5,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,27,28,29,30,31,32],[7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,0,1,2,3,4,5,6,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,27,28,29,30,31,32,33],[8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,0,1,2,3,4,5,6,7,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,27,28,29,30,31,32,33,34],[9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,0,1,2,3,4,5,6,7,8,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,27,28,29,30,31,32,33,34,35],[10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,0,1,2,3,4,5,6,7,8,9,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,27,28,29,30,31,32,33,34,35,36],[11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,0,1,2,3,4,5,6,7,8,9,10,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,27,28,29,30,31,32,33,34,35,36,37],[12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,0,1,2,3,4,5,6,7,8,9,10,11,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,27,28,29,30,31,32,33,34,35,36,37,38],[13,14,15,16,17,18,19,20,21,22,23,24,25,26,0,1,2,3,4,5,6,7,8,9,10,11,12,40,41,42,43,44,45,46,47,48,49,50,51,52,53,27,28,29,30,31,32,33,34,35,36,37,38,39],[14,15,16,17,18,19,20,21,22,23,24,25,26,0,1,2,3,4,5,6,7,8,9,10,11,12,13,41,42,43,44,45,46,47,48,49,50,51,52,53,27,28,29,30,31,32,33,34,35,36,37,38,39,40],[15,16,17,18,19,20,21,22,23,24,25,26,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,42,43,44,45,46,47,48,49,50,51,52,53,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41],[16,17,18,19,20,21,22,23,24,25,26,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,43,44,45,46,47,48,49,50,51,52,53,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42],[17,18,19,20,21,22,23,24,25,26,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,44,45,46,47,48,49,50,51,52,53,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],[18,19,20,21,22,23,24,25,26,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,45,46,47,48,49,50,51,52,53,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44],[19,20,21,22,23,24,25,26,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,46,47,48,49,50,51,52,53,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45],[20,21,22,23,24,25,26,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,47,48,49,50,51,52,53,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46],[21,22,23,24,25,26,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,48,49,50,51,52,53,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47],[22,23,24,25,26,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,49,50,51,52,53,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48],[23,24,25,26,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,50,51,52,53,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49],[24,25,26,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,51,52,53,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50],[25,26,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,52,53,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51],[26,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,53,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52],[27,53,52,51,50,49,48,47,46,45,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,0,26,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1],[28,27,53,52,51,50,49,48,47,46,45,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,1,0,26,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2],[29,28,27,53,52,51,50,49,48,47,46,45,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,2,1,0,26,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3],[30,29,28,27,53,52,51,50,49,48,47,46,45,44,43,42,41,40,39,38,37,36,35,34,33,32,31,3,2,1,0,26,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4],[31,30,29,28,27,53,52,51,50,49,48,47,46,45,44,43,42,41,40,39,38,37,36,35,34,33,32,4,3,2,1,0,26,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5],[32,31,30,29,28,27,53,52,51,50,49,48,47,46,45,44,43,42,41,40,39,38,37,36,35,34,33,5,4,3,2,1,0,26,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6],[33,32,31,30,29,28,27,53,52,51,50,49,48,47,46,45,44,43,42,41,40,39,38,37,36,35,34,6,5,4,3,2,1,0,26,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7],[34,33,32,31,30,29,28,27,53,52,51,50,49,48,47,46,45,44,43,42,41,40,39,38,37,36,35,7,6,5,4,3,2,1,0,26,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8],[35,34,33,32,31,30,29,28,27,53,52,51,50,49,48,47,46,45,44,43,42,41,40,39,38,37,36,8,7,6,5,4,3,2,1,0,26,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9],[36,35,34,33,32,31,30,29,28,27,53,52,51,50,49,48,47,46,45,44,43,42,41,40,39,38,37,9,8,7,6,5,4,3,2,1,0,26,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10],[37,36,35,34,33,32,31,30,29,28,27,53,52,51,50,49,48,47,46,45,44,43,42,41,40,39,38,10,9,8,7,6,5,4,3,2,1,0,26,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11],[38,37,36,35,34,33,32,31,30,29,28,27,53,52,51,50,49,48,47,46,45,44,43,42,41,40,39,11,10,9,8,7,6,5,4,3,2,1,0,26,25,24,23,22,21,20,19,18,17,16,15,14,13,12],[39,38,37,36,35,34,33,32,31,30,29,28,27,53,52,51,50,49,48,47,46,45,44,43,42,41,40,12,11,10,9,8,7,6,5,4,3,2,1,0,26,25,24,23,22,21,20,19,18,17,16,15,14,13],[40,39,38,37,36,35,34,33,32,31,30,29,28,27,53,52,51,50,49,48,47,46,45,44,43,42,41,13,12,11,10,9,8,7,6,5,4,3,2,1,0,26,25,24,23,22,21,20,19,18,17,16,15,14],[41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,53,52,51,50,49,48,47,46,45,44,43,42,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0,26,25,24,23,22,21,20,19,18,17,16,15],[42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,53,52,51,50,49,48,47,46,45,44,43,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0,26,25,24,23,22,21,20,19,18,17,16],[43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,53,52,51,50,49,48,47,46,45,44,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0,26,25,24,23,22,21,20,19,18,17],[44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,53,52,51,50,49,48,47,46,45,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0,26,25,24,23,22,21,20,19,18],[45,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,53,52,51,50,49,48,47,46,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0,26,25,24,23,22,21,20,19],[46,45,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,53,52,51,50,49,48,47,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0,26,25,24,23,22,21,20],[47,46,45,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,53,52,51,50,49,48,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0,26,25,24,23,22,21],[48,47,46,45,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,53,52,51,50,49,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0,26,25,24,23,22],[49,48,47,46,45,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,53,52,51,50,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0,26,25,24,23],[50,49,48,47,46,45,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,53,52,51,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0,26,25,24],[51,50,49,48,47,46,45,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,53,52,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0,26,25],[52,51,50,49,48,47,46,45,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,53,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0,26],[53,52,51,50,49,48,47,46,45,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0]],"identity":0,"element":27}。請依 [element, action_image_rows, conjugacy_class, certificate] 欄序回答。

查看答案與解釋(27, [[0, 27], [1, 29], [2, 31], [3, 33], [4, 35], [5, 37], [6, 39], [7, 41], [8, 43], [9, 45], [10, 47], [11, 49], [12, 51], [13, 53], [14, 28], [15, 30], [16, 32], [17, 34], [18, 36], [19, 38], [20, 40], [21, 42], [22, 44], [23, 46], [24, 48], [25, 50], [26, 52], [27, 27], [28, 29], [29, 31], [30, 33], [31, 35], [32, 37], [33, 39], [34, 41], [35, 43], [36, 45], [37, 47], [38, 49], [39, 51], [40, 53], [41, 28], [42, 30], [43, 32], [44, 34], [45, 36], [46, 38], [47, 40], [48, 42], [49, 44], [50, 46], [51, 48], [52, 50], [53, 52]], [27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53], conjugacy_class_is_the_complete_conjugation_orbit_not_a_coset)

Wave6第八層核對=(27, [[0, 27], [1, 29], [2, 31], [3, 33], [4, 35], [5, 37], [6, 39], [7, 41], [8, 43], [9, 45], [10, 47], [11, 49], [12, 51], [13, 53], [14, 28], [15, 30], [16, 32], [17, 34], [18, 36], [19, 38], [20, 40], [21, 42], [22, 44], [23, 46], [24, 48], [25, 50], [26, 52], [27, 27], [28, 29], [29, 31], [30, 33], [31, 35], [32, 37], [33, 39], [34, 41], [35, 43], [36, 45], [37, 47], [38, 49], [39, 51], [40, 53], [41, 28], [42, 30], [43, 32], [44, 34], [45, 36], [46, 38], [47, 40], [48, 42], [49, 44], [50, 46], [51, 48], [52, 50], [53, 52]], [27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53], conjugacy_class_is_the_complete_conjugation_orbit_not_a_coset)；依完整明示資料獨立重算；共軛類是element orbit並形成完整partition；singleton以forall g commute核對；共軛類不是coset或conjugate subgroup；不使用centralizer、class-size公式或類方程。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r03-finite-group-conjugacy-class-0050/)

有限群共軛類 · qf-mod45-conjugacy-orbit-class · candidate





## 51. 有限群共軛類

由完整Cayley table導出全部conjugation action與orbits。操作=conjugacy-partition-audit；資料={"group_table":[[0,1,2,3,4,5],[1,2,0,4,5,3],[2,0,1,5,3,4],[3,5,4,0,2,1],[4,3,5,1,0,2],[5,4,3,2,1,0]],"identity":0}。請依 [classes, partition_certificate, covered_element_count, group_order, certificate] 欄序回答。

查看答案與解釋([[0], [1, 2], [3, 4, 5]], 是, 6, 6, all_conjugacy_classes_are_equal_or_disjoint_and_cover_G)

Wave6第八層核對=([[0], [1, 2], [3, 4, 5]], 是, 6, 6, all_conjugacy_classes_are_equal_or_disjoint_and_cover_G)；依完整明示資料獨立重算；共軛類是element orbit並形成完整partition；singleton以forall g commute核對；共軛類不是coset或conjugate subgroup；不使用centralizer、class-size公式或類方程。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r03-finite-group-conjugacy-class-0051/)

有限群共軛類 · qf-mod45-conjugacy-partition-audit · candidate





## 52. 有限群共軛類

由完整Cayley table導出全部conjugation action與orbits。操作=conjugacy-partition-audit；資料={"group_table":[[0,1,2,3,4,5,6,7],[1,2,3,0,5,6,7,4],[2,3,0,1,6,7,4,5],[3,0,1,2,7,4,5,6],[4,7,6,5,0,3,2,1],[5,4,7,6,1,0,3,2],[6,5,4,7,2,1,0,3],[7,6,5,4,3,2,1,0]],"identity":0}。請依 [classes, partition_certificate, covered_element_count, group_order, certificate] 欄序回答。

查看答案與解釋([[0], [1, 3], [2], [4, 6], [5, 7]], 是, 8, 8, all_conjugacy_classes_are_equal_or_disjoint_and_cover_G)

Wave6第八層核對=([[0], [1, 3], [2], [4, 6], [5, 7]], 是, 8, 8, all_conjugacy_classes_are_equal_or_disjoint_and_cover_G)；依完整明示資料獨立重算；共軛類是element orbit並形成完整partition；singleton以forall g commute核對；共軛類不是coset或conjugate subgroup；不使用centralizer、class-size公式或類方程。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r03-finite-group-conjugacy-class-0052/)

有限群共軛類 · qf-mod45-conjugacy-partition-audit · candidate





## 53. 有限群共軛類

由完整Cayley table導出全部conjugation action與orbits。操作=conjugacy-partition-audit；資料={"group_table":[[0,1,2,3,4,5,6,7,8,9],[1,2,3,4,0,6,7,8,9,5],[2,3,4,0,1,7,8,9,5,6],[3,4,0,1,2,8,9,5,6,7],[4,0,1,2,3,9,5,6,7,8],[5,9,8,7,6,0,4,3,2,1],[6,5,9,8,7,1,0,4,3,2],[7,6,5,9,8,2,1,0,4,3],[8,7,6,5,9,3,2,1,0,4],[9,8,7,6,5,4,3,2,1,0]],"identity":0}。請依 [classes, partition_certificate, covered_element_count, group_order, certificate] 欄序回答。

查看答案與解釋([[0], [1, 4], [2, 3], [5, 6, 7, 8, 9]], 是, 10, 10, all_conjugacy_classes_are_equal_or_disjoint_and_cover_G)

Wave6第八層核對=([[0], [1, 4], [2, 3], [5, 6, 7, 8, 9]], 是, 10, 10, all_conjugacy_classes_are_equal_or_disjoint_and_cover_G)；依完整明示資料獨立重算；共軛類是element orbit並形成完整partition；singleton以forall g commute核對；共軛類不是coset或conjugate subgroup；不使用centralizer、class-size公式或類方程。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r03-finite-group-conjugacy-class-0053/)

有限群共軛類 · qf-mod45-conjugacy-partition-audit · candidate





## 54. 有限群共軛類

由完整Cayley table導出全部conjugation action與orbits。操作=conjugacy-partition-audit；資料={"group_table":[[0,1,2,3,4,5,6,7,8,9,10,11],[1,2,3,4,5,0,7,8,9,10,11,6],[2,3,4,5,0,1,8,9,10,11,6,7],[3,4,5,0,1,2,9,10,11,6,7,8],[4,5,0,1,2,3,10,11,6,7,8,9],[5,0,1,2,3,4,11,6,7,8,9,10],[6,11,10,9,8,7,0,5,4,3,2,1],[7,6,11,10,9,8,1,0,5,4,3,2],[8,7,6,11,10,9,2,1,0,5,4,3],[9,8,7,6,11,10,3,2,1,0,5,4],[10,9,8,7,6,11,4,3,2,1,0,5],[11,10,9,8,7,6,5,4,3,2,1,0]],"identity":0}。請依 [classes, partition_certificate, covered_element_count, group_order, certificate] 欄序回答。

查看答案與解釋([[0], [1, 5], [2, 4], [3], [6, 8, 10], [7, 9, 11]], 是, 12, 12, all_conjugacy_classes_are_equal_or_disjoint_and_cover_G)

Wave6第八層核對=([[0], [1, 5], [2, 4], [3], [6, 8, 10], [7, 9, 11]], 是, 12, 12, all_conjugacy_classes_are_equal_or_disjoint_and_cover_G)；依完整明示資料獨立重算；共軛類是element orbit並形成完整partition；singleton以forall g commute核對；共軛類不是coset或conjugate subgroup；不使用centralizer、class-size公式或類方程。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r03-finite-group-conjugacy-class-0054/)

有限群共軛類 · qf-mod45-conjugacy-partition-audit · candidate





## 55. 有限群共軛類

由完整Cayley table導出全部conjugation action與orbits。操作=conjugacy-partition-audit；資料={"group_table":[[0,1,2,3,4,5,6,7,8,9,10,11,12,13],[1,2,3,4,5,6,0,8,9,10,11,12,13,7],[2,3,4,5,6,0,1,9,10,11,12,13,7,8],[3,4,5,6,0,1,2,10,11,12,13,7,8,9],[4,5,6,0,1,2,3,11,12,13,7,8,9,10],[5,6,0,1,2,3,4,12,13,7,8,9,10,11],[6,0,1,2,3,4,5,13,7,8,9,10,11,12],[7,13,12,11,10,9,8,0,6,5,4,3,2,1],[8,7,13,12,11,10,9,1,0,6,5,4,3,2],[9,8,7,13,12,11,10,2,1,0,6,5,4,3],[10,9,8,7,13,12,11,3,2,1,0,6,5,4],[11,10,9,8,7,13,12,4,3,2,1,0,6,5],[12,11,10,9,8,7,13,5,4,3,2,1,0,6],[13,12,11,10,9,8,7,6,5,4,3,2,1,0]],"identity":0}。請依 [classes, partition_certificate, covered_element_count, group_order, certificate] 欄序回答。

查看答案與解釋([[0], [1, 6], [2, 5], [3, 4], [7, 8, 9, 10, 11, 12, 13]], 是, 14, 14, all_conjugacy_classes_are_equal_or_disjoint_and_cover_G)

Wave6第八層核對=([[0], [1, 6], [2, 5], [3, 4], [7, 8, 9, 10, 11, 12, 13]], 是, 14, 14, all_conjugacy_classes_are_equal_or_disjoint_and_cover_G)；依完整明示資料獨立重算；共軛類是element orbit並形成完整partition；singleton以forall g commute核對；共軛類不是coset或conjugate subgroup；不使用centralizer、class-size公式或類方程。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r03-finite-group-conjugacy-class-0055/)

有限群共軛類 · qf-mod45-conjugacy-partition-audit · candidate





## 56. 有限群共軛類

由完整Cayley table導出全部conjugation action與orbits。操作=conjugacy-partition-audit；資料={"group_table":[[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15],[1,2,3,4,5,6,7,0,9,10,11,12,13,14,15,8],[2,3,4,5,6,7,0,1,10,11,12,13,14,15,8,9],[3,4,5,6,7,0,1,2,11,12,13,14,15,8,9,10],[4,5,6,7,0,1,2,3,12,13,14,15,8,9,10,11],[5,6,7,0,1,2,3,4,13,14,15,8,9,10,11,12],[6,7,0,1,2,3,4,5,14,15,8,9,10,11,12,13],[7,0,1,2,3,4,5,6,15,8,9,10,11,12,13,14],[8,15,14,13,12,11,10,9,0,7,6,5,4,3,2,1],[9,8,15,14,13,12,11,10,1,0,7,6,5,4,3,2],[10,9,8,15,14,13,12,11,2,1,0,7,6,5,4,3],[11,10,9,8,15,14,13,12,3,2,1,0,7,6,5,4],[12,11,10,9,8,15,14,13,4,3,2,1,0,7,6,5],[13,12,11,10,9,8,15,14,5,4,3,2,1,0,7,6],[14,13,12,11,10,9,8,15,6,5,4,3,2,1,0,7],[15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0]],"identity":0}。請依 [classes, partition_certificate, covered_element_count, group_order, certificate] 欄序回答。

查看答案與解釋([[0], [1, 7], [2, 6], [3, 5], [4], [8, 10, 12, 14], [9, 11, 13, 15]], 是, 16, 16, all_conjugacy_classes_are_equal_or_disjoint_and_cover_G)

Wave6第八層核對=([[0], [1, 7], [2, 6], [3, 5], [4], [8, 10, 12, 14], [9, 11, 13, 15]], 是, 16, 16, all_conjugacy_classes_are_equal_or_disjoint_and_cover_G)；依完整明示資料獨立重算；共軛類是element orbit並形成完整partition；singleton以forall g commute核對；共軛類不是coset或conjugate subgroup；不使用centralizer、class-size公式或類方程。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r03-finite-group-conjugacy-class-0056/)

有限群共軛類 · qf-mod45-conjugacy-partition-audit · candidate





## 57. 有限群共軛類

由完整Cayley table導出全部conjugation action與orbits。操作=conjugacy-partition-audit；資料={"group_table":[[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17],[1,2,3,4,5,6,7,8,0,10,11,12,13,14,15,16,17,9],[2,3,4,5,6,7,8,0,1,11,12,13,14,15,16,17,9,10],[3,4,5,6,7,8,0,1,2,12,13,14,15,16,17,9,10,11],[4,5,6,7,8,0,1,2,3,13,14,15,16,17,9,10,11,12],[5,6,7,8,0,1,2,3,4,14,15,16,17,9,10,11,12,13],[6,7,8,0,1,2,3,4,5,15,16,17,9,10,11,12,13,14],[7,8,0,1,2,3,4,5,6,16,17,9,10,11,12,13,14,15],[8,0,1,2,3,4,5,6,7,17,9,10,11,12,13,14,15,16],[9,17,16,15,14,13,12,11,10,0,8,7,6,5,4,3,2,1],[10,9,17,16,15,14,13,12,11,1,0,8,7,6,5,4,3,2],[11,10,9,17,16,15,14,13,12,2,1,0,8,7,6,5,4,3],[12,11,10,9,17,16,15,14,13,3,2,1,0,8,7,6,5,4],[13,12,11,10,9,17,16,15,14,4,3,2,1,0,8,7,6,5],[14,13,12,11,10,9,17,16,15,5,4,3,2,1,0,8,7,6],[15,14,13,12,11,10,9,17,16,6,5,4,3,2,1,0,8,7],[16,15,14,13,12,11,10,9,17,7,6,5,4,3,2,1,0,8],[17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0]],"identity":0}。請依 [classes, partition_certificate, covered_element_count, group_order, certificate] 欄序回答。

查看答案與解釋([[0], [1, 8], [2, 7], [3, 6], [4, 5], [9, 10, 11, 12, 13, 14, 15, 16, 17]], 是, 18, 18, all_conjugacy_classes_are_equal_or_disjoint_and_cover_G)

Wave6第八層核對=([[0], [1, 8], [2, 7], [3, 6], [4, 5], [9, 10, 11, 12, 13, 14, 15, 16, 17]], 是, 18, 18, all_conjugacy_classes_are_equal_or_disjoint_and_cover_G)；依完整明示資料獨立重算；共軛類是element orbit並形成完整partition；singleton以forall g commute核對；共軛類不是coset或conjugate subgroup；不使用centralizer、class-size公式或類方程。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r03-finite-group-conjugacy-class-0057/)

有限群共軛類 · qf-mod45-conjugacy-partition-audit · candidate





## 58. 有限群共軛類

由完整Cayley table導出全部conjugation action與orbits。操作=conjugacy-partition-audit；資料={"group_table":[[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19],[1,2,3,4,5,6,7,8,9,0,11,12,13,14,15,16,17,18,19,10],[2,3,4,5,6,7,8,9,0,1,12,13,14,15,16,17,18,19,10,11],[3,4,5,6,7,8,9,0,1,2,13,14,15,16,17,18,19,10,11,12],[4,5,6,7,8,9,0,1,2,3,14,15,16,17,18,19,10,11,12,13],[5,6,7,8,9,0,1,2,3,4,15,16,17,18,19,10,11,12,13,14],[6,7,8,9,0,1,2,3,4,5,16,17,18,19,10,11,12,13,14,15],[7,8,9,0,1,2,3,4,5,6,17,18,19,10,11,12,13,14,15,16],[8,9,0,1,2,3,4,5,6,7,18,19,10,11,12,13,14,15,16,17],[9,0,1,2,3,4,5,6,7,8,19,10,11,12,13,14,15,16,17,18],[10,19,18,17,16,15,14,13,12,11,0,9,8,7,6,5,4,3,2,1],[11,10,19,18,17,16,15,14,13,12,1,0,9,8,7,6,5,4,3,2],[12,11,10,19,18,17,16,15,14,13,2,1,0,9,8,7,6,5,4,3],[13,12,11,10,19,18,17,16,15,14,3,2,1,0,9,8,7,6,5,4],[14,13,12,11,10,19,18,17,16,15,4,3,2,1,0,9,8,7,6,5],[15,14,13,12,11,10,19,18,17,16,5,4,3,2,1,0,9,8,7,6],[16,15,14,13,12,11,10,19,18,17,6,5,4,3,2,1,0,9,8,7],[17,16,15,14,13,12,11,10,19,18,7,6,5,4,3,2,1,0,9,8],[18,17,16,15,14,13,12,11,10,19,8,7,6,5,4,3,2,1,0,9],[19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0]],"identity":0}。請依 [classes, partition_certificate, covered_element_count, group_order, certificate] 欄序回答。

查看答案與解釋([[0], [1, 9], [10, 12, 14, 16, 18], [11, 13, 15, 17, 19], [2, 8], [3, 7], [4, 6], [5]], 是, 20, 20, all_conjugacy_classes_are_equal_or_disjoint_and_cover_G)

Wave6第八層核對=([[0], [1, 9], [10, 12, 14, 16, 18], [11, 13, 15, 17, 19], [2, 8], [3, 7], [4, 6], [5]], 是, 20, 20, all_conjugacy_classes_are_equal_or_disjoint_and_cover_G)；依完整明示資料獨立重算；共軛類是element orbit並形成完整partition；singleton以forall g commute核對；共軛類不是coset或conjugate subgroup；不使用centralizer、class-size公式或類方程。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r03-finite-group-conjugacy-class-0058/)

有限群共軛類 · qf-mod45-conjugacy-partition-audit · candidate





## 59. 有限群共軛類

由完整Cayley table導出全部conjugation action與orbits。操作=conjugacy-partition-audit；資料={"group_table":[[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21],[1,2,3,4,5,6,7,8,9,10,0,12,13,14,15,16,17,18,19,20,21,11],[2,3,4,5,6,7,8,9,10,0,1,13,14,15,16,17,18,19,20,21,11,12],[3,4,5,6,7,8,9,10,0,1,2,14,15,16,17,18,19,20,21,11,12,13],[4,5,6,7,8,9,10,0,1,2,3,15,16,17,18,19,20,21,11,12,13,14],[5,6,7,8,9,10,0,1,2,3,4,16,17,18,19,20,21,11,12,13,14,15],[6,7,8,9,10,0,1,2,3,4,5,17,18,19,20,21,11,12,13,14,15,16],[7,8,9,10,0,1,2,3,4,5,6,18,19,20,21,11,12,13,14,15,16,17],[8,9,10,0,1,2,3,4,5,6,7,19,20,21,11,12,13,14,15,16,17,18],[9,10,0,1,2,3,4,5,6,7,8,20,21,11,12,13,14,15,16,17,18,19],[10,0,1,2,3,4,5,6,7,8,9,21,11,12,13,14,15,16,17,18,19,20],[11,21,20,19,18,17,16,15,14,13,12,0,10,9,8,7,6,5,4,3,2,1],[12,11,21,20,19,18,17,16,15,14,13,1,0,10,9,8,7,6,5,4,3,2],[13,12,11,21,20,19,18,17,16,15,14,2,1,0,10,9,8,7,6,5,4,3],[14,13,12,11,21,20,19,18,17,16,15,3,2,1,0,10,9,8,7,6,5,4],[15,14,13,12,11,21,20,19,18,17,16,4,3,2,1,0,10,9,8,7,6,5],[16,15,14,13,12,11,21,20,19,18,17,5,4,3,2,1,0,10,9,8,7,6],[17,16,15,14,13,12,11,21,20,19,18,6,5,4,3,2,1,0,10,9,8,7],[18,17,16,15,14,13,12,11,21,20,19,7,6,5,4,3,2,1,0,10,9,8],[19,18,17,16,15,14,13,12,11,21,20,8,7,6,5,4,3,2,1,0,10,9],[20,19,18,17,16,15,14,13,12,11,21,9,8,7,6,5,4,3,2,1,0,10],[21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0]],"identity":0}。請依 [classes, partition_certificate, covered_element_count, group_order, certificate] 欄序回答。

查看答案與解釋([[0], [1, 10], [11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21], [2, 9], [3, 8], [4, 7], [5, 6]], 是, 22, 22, all_conjugacy_classes_are_equal_or_disjoint_and_cover_G)

Wave6第八層核對=([[0], [1, 10], [11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21], [2, 9], [3, 8], [4, 7], [5, 6]], 是, 22, 22, all_conjugacy_classes_are_equal_or_disjoint_and_cover_G)；依完整明示資料獨立重算；共軛類是element orbit並形成完整partition；singleton以forall g commute核對；共軛類不是coset或conjugate subgroup；不使用centralizer、class-size公式或類方程。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r03-finite-group-conjugacy-class-0059/)

有限群共軛類 · qf-mod45-conjugacy-partition-audit · candidate





## 60. 有限群共軛類

由完整Cayley table導出全部conjugation action與orbits。操作=conjugacy-partition-audit；資料={"group_table":[[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23],[1,2,3,4,5,6,7,8,9,10,11,0,13,14,15,16,17,18,19,20,21,22,23,12],[2,3,4,5,6,7,8,9,10,11,0,1,14,15,16,17,18,19,20,21,22,23,12,13],[3,4,5,6,7,8,9,10,11,0,1,2,15,16,17,18,19,20,21,22,23,12,13,14],[4,5,6,7,8,9,10,11,0,1,2,3,16,17,18,19,20,21,22,23,12,13,14,15],[5,6,7,8,9,10,11,0,1,2,3,4,17,18,19,20,21,22,23,12,13,14,15,16],[6,7,8,9,10,11,0,1,2,3,4,5,18,19,20,21,22,23,12,13,14,15,16,17],[7,8,9,10,11,0,1,2,3,4,5,6,19,20,21,22,23,12,13,14,15,16,17,18],[8,9,10,11,0,1,2,3,4,5,6,7,20,21,22,23,12,13,14,15,16,17,18,19],[9,10,11,0,1,2,3,4,5,6,7,8,21,22,23,12,13,14,15,16,17,18,19,20],[10,11,0,1,2,3,4,5,6,7,8,9,22,23,12,13,14,15,16,17,18,19,20,21],[11,0,1,2,3,4,5,6,7,8,9,10,23,12,13,14,15,16,17,18,19,20,21,22],[12,23,22,21,20,19,18,17,16,15,14,13,0,11,10,9,8,7,6,5,4,3,2,1],[13,12,23,22,21,20,19,18,17,16,15,14,1,0,11,10,9,8,7,6,5,4,3,2],[14,13,12,23,22,21,20,19,18,17,16,15,2,1,0,11,10,9,8,7,6,5,4,3],[15,14,13,12,23,22,21,20,19,18,17,16,3,2,1,0,11,10,9,8,7,6,5,4],[16,15,14,13,12,23,22,21,20,19,18,17,4,3,2,1,0,11,10,9,8,7,6,5],[17,16,15,14,13,12,23,22,21,20,19,18,5,4,3,2,1,0,11,10,9,8,7,6],[18,17,16,15,14,13,12,23,22,21,20,19,6,5,4,3,2,1,0,11,10,9,8,7],[19,18,17,16,15,14,13,12,23,22,21,20,7,6,5,4,3,2,1,0,11,10,9,8],[20,19,18,17,16,15,14,13,12,23,22,21,8,7,6,5,4,3,2,1,0,11,10,9],[21,20,19,18,17,16,15,14,13,12,23,22,9,8,7,6,5,4,3,2,1,0,11,10],[22,21,20,19,18,17,16,15,14,13,12,23,10,9,8,7,6,5,4,3,2,1,0,11],[23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0]],"identity":0}。請依 [classes, partition_certificate, covered_element_count, group_order, certificate] 欄序回答。

查看答案與解釋([[0], [1, 11], [12, 14, 16, 18, 20, 22], [13, 15, 17, 19, 21, 23], [2, 10], [3, 9], [4, 8], [5, 7], [6]], 是, 24, 24, all_conjugacy_classes_are_equal_or_disjoint_and_cover_G)

Wave6第八層核對=([[0], [1, 11], [12, 14, 16, 18, 20, 22], [13, 15, 17, 19, 21, 23], [2, 10], [3, 9], [4, 8], [5, 7], [6]], 是, 24, 24, all_conjugacy_classes_are_equal_or_disjoint_and_cover_G)；依完整明示資料獨立重算；共軛類是element orbit並形成完整partition；singleton以forall g commute核對；共軛類不是coset或conjugate subgroup；不使用centralizer、class-size公式或類方程。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r03-finite-group-conjugacy-class-0060/)

有限群共軛類 · qf-mod45-conjugacy-partition-audit · candidate





## 61. 有限群共軛類

由完整Cayley table導出全部conjugation action與orbits。操作=conjugacy-partition-audit；資料={"group_table":[[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25],[1,2,3,4,5,6,7,8,9,10,11,12,0,14,15,16,17,18,19,20,21,22,23,24,25,13],[2,3,4,5,6,7,8,9,10,11,12,0,1,15,16,17,18,19,20,21,22,23,24,25,13,14],[3,4,5,6,7,8,9,10,11,12,0,1,2,16,17,18,19,20,21,22,23,24,25,13,14,15],[4,5,6,7,8,9,10,11,12,0,1,2,3,17,18,19,20,21,22,23,24,25,13,14,15,16],[5,6,7,8,9,10,11,12,0,1,2,3,4,18,19,20,21,22,23,24,25,13,14,15,16,17],[6,7,8,9,10,11,12,0,1,2,3,4,5,19,20,21,22,23,24,25,13,14,15,16,17,18],[7,8,9,10,11,12,0,1,2,3,4,5,6,20,21,22,23,24,25,13,14,15,16,17,18,19],[8,9,10,11,12,0,1,2,3,4,5,6,7,21,22,23,24,25,13,14,15,16,17,18,19,20],[9,10,11,12,0,1,2,3,4,5,6,7,8,22,23,24,25,13,14,15,16,17,18,19,20,21],[10,11,12,0,1,2,3,4,5,6,7,8,9,23,24,25,13,14,15,16,17,18,19,20,21,22],[11,12,0,1,2,3,4,5,6,7,8,9,10,24,25,13,14,15,16,17,18,19,20,21,22,23],[12,0,1,2,3,4,5,6,7,8,9,10,11,25,13,14,15,16,17,18,19,20,21,22,23,24],[13,25,24,23,22,21,20,19,18,17,16,15,14,0,12,11,10,9,8,7,6,5,4,3,2,1],[14,13,25,24,23,22,21,20,19,18,17,16,15,1,0,12,11,10,9,8,7,6,5,4,3,2],[15,14,13,25,24,23,22,21,20,19,18,17,16,2,1,0,12,11,10,9,8,7,6,5,4,3],[16,15,14,13,25,24,23,22,21,20,19,18,17,3,2,1,0,12,11,10,9,8,7,6,5,4],[17,16,15,14,13,25,24,23,22,21,20,19,18,4,3,2,1,0,12,11,10,9,8,7,6,5],[18,17,16,15,14,13,25,24,23,22,21,20,19,5,4,3,2,1,0,12,11,10,9,8,7,6],[19,18,17,16,15,14,13,25,24,23,22,21,20,6,5,4,3,2,1,0,12,11,10,9,8,7],[20,19,18,17,16,15,14,13,25,24,23,22,21,7,6,5,4,3,2,1,0,12,11,10,9,8],[21,20,19,18,17,16,15,14,13,25,24,23,22,8,7,6,5,4,3,2,1,0,12,11,10,9],[22,21,20,19,18,17,16,15,14,13,25,24,23,9,8,7,6,5,4,3,2,1,0,12,11,10],[23,22,21,20,19,18,17,16,15,14,13,25,24,10,9,8,7,6,5,4,3,2,1,0,12,11],[24,23,22,21,20,19,18,17,16,15,14,13,25,11,10,9,8,7,6,5,4,3,2,1,0,12],[25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0]],"identity":0}。請依 [classes, partition_certificate, covered_element_count, group_order, certificate] 欄序回答。

查看答案與解釋([[0], [1, 12], [13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25], [2, 11], [3, 10], [4, 9], [5, 8], [6, 7]], 是, 26, 26, all_conjugacy_classes_are_equal_or_disjoint_and_cover_G)

Wave6第八層核對=([[0], [1, 12], [13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25], [2, 11], [3, 10], [4, 9], [5, 8], [6, 7]], 是, 26, 26, all_conjugacy_classes_are_equal_or_disjoint_and_cover_G)；依完整明示資料獨立重算；共軛類是element orbit並形成完整partition；singleton以forall g commute核對；共軛類不是coset或conjugate subgroup；不使用centralizer、class-size公式或類方程。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r03-finite-group-conjugacy-class-0061/)

有限群共軛類 · qf-mod45-conjugacy-partition-audit · candidate





## 62. 有限群共軛類

由完整Cayley table導出全部conjugation action與orbits。操作=conjugacy-partition-audit；資料={"group_table":[[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27],[1,2,3,4,5,6,7,8,9,10,11,12,13,0,15,16,17,18,19,20,21,22,23,24,25,26,27,14],[2,3,4,5,6,7,8,9,10,11,12,13,0,1,16,17,18,19,20,21,22,23,24,25,26,27,14,15],[3,4,5,6,7,8,9,10,11,12,13,0,1,2,17,18,19,20,21,22,23,24,25,26,27,14,15,16],[4,5,6,7,8,9,10,11,12,13,0,1,2,3,18,19,20,21,22,23,24,25,26,27,14,15,16,17],[5,6,7,8,9,10,11,12,13,0,1,2,3,4,19,20,21,22,23,24,25,26,27,14,15,16,17,18],[6,7,8,9,10,11,12,13,0,1,2,3,4,5,20,21,22,23,24,25,26,27,14,15,16,17,18,19],[7,8,9,10,11,12,13,0,1,2,3,4,5,6,21,22,23,24,25,26,27,14,15,16,17,18,19,20],[8,9,10,11,12,13,0,1,2,3,4,5,6,7,22,23,24,25,26,27,14,15,16,17,18,19,20,21],[9,10,11,12,13,0,1,2,3,4,5,6,7,8,23,24,25,26,27,14,15,16,17,18,19,20,21,22],[10,11,12,13,0,1,2,3,4,5,6,7,8,9,24,25,26,27,14,15,16,17,18,19,20,21,22,23],[11,12,13,0,1,2,3,4,5,6,7,8,9,10,25,26,27,14,15,16,17,18,19,20,21,22,23,24],[12,13,0,1,2,3,4,5,6,7,8,9,10,11,26,27,14,15,16,17,18,19,20,21,22,23,24,25],[13,0,1,2,3,4,5,6,7,8,9,10,11,12,27,14,15,16,17,18,19,20,21,22,23,24,25,26],[14,27,26,25,24,23,22,21,20,19,18,17,16,15,0,13,12,11,10,9,8,7,6,5,4,3,2,1],[15,14,27,26,25,24,23,22,21,20,19,18,17,16,1,0,13,12,11,10,9,8,7,6,5,4,3,2],[16,15,14,27,26,25,24,23,22,21,20,19,18,17,2,1,0,13,12,11,10,9,8,7,6,5,4,3],[17,16,15,14,27,26,25,24,23,22,21,20,19,18,3,2,1,0,13,12,11,10,9,8,7,6,5,4],[18,17,16,15,14,27,26,25,24,23,22,21,20,19,4,3,2,1,0,13,12,11,10,9,8,7,6,5],[19,18,17,16,15,14,27,26,25,24,23,22,21,20,5,4,3,2,1,0,13,12,11,10,9,8,7,6],[20,19,18,17,16,15,14,27,26,25,24,23,22,21,6,5,4,3,2,1,0,13,12,11,10,9,8,7],[21,20,19,18,17,16,15,14,27,26,25,24,23,22,7,6,5,4,3,2,1,0,13,12,11,10,9,8],[22,21,20,19,18,17,16,15,14,27,26,25,24,23,8,7,6,5,4,3,2,1,0,13,12,11,10,9],[23,22,21,20,19,18,17,16,15,14,27,26,25,24,9,8,7,6,5,4,3,2,1,0,13,12,11,10],[24,23,22,21,20,19,18,17,16,15,14,27,26,25,10,9,8,7,6,5,4,3,2,1,0,13,12,11],[25,24,23,22,21,20,19,18,17,16,15,14,27,26,11,10,9,8,7,6,5,4,3,2,1,0,13,12],[26,25,24,23,22,21,20,19,18,17,16,15,14,27,12,11,10,9,8,7,6,5,4,3,2,1,0,13],[27,26,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0]],"identity":0}。請依 [classes, partition_certificate, covered_element_count, group_order, certificate] 欄序回答。

查看答案與解釋([[0], [1, 13], [14, 16, 18, 20, 22, 24, 26], [15, 17, 19, 21, 23, 25, 27], [2, 12], [3, 11], [4, 10], [5, 9], [6, 8], [7]], 是, 28, 28, all_conjugacy_classes_are_equal_or_disjoint_and_cover_G)

Wave6第八層核對=([[0], [1, 13], [14, 16, 18, 20, 22, 24, 26], [15, 17, 19, 21, 23, 25, 27], [2, 12], [3, 11], [4, 10], [5, 9], [6, 8], [7]], 是, 28, 28, all_conjugacy_classes_are_equal_or_disjoint_and_cover_G)；依完整明示資料獨立重算；共軛類是element orbit並形成完整partition；singleton以forall g commute核對；共軛類不是coset或conjugate subgroup；不使用centralizer、class-size公式或類方程。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r03-finite-group-conjugacy-class-0062/)

有限群共軛類 · qf-mod45-conjugacy-partition-audit · candidate





## 63. 有限群共軛類

由完整Cayley table導出全部conjugation action與orbits。操作=conjugacy-partition-audit；資料={"group_table":[[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,0,16,17,18,19,20,21,22,23,24,25,26,27,28,29,15],[2,3,4,5,6,7,8,9,10,11,12,13,14,0,1,17,18,19,20,21,22,23,24,25,26,27,28,29,15,16],[3,4,5,6,7,8,9,10,11,12,13,14,0,1,2,18,19,20,21,22,23,24,25,26,27,28,29,15,16,17],[4,5,6,7,8,9,10,11,12,13,14,0,1,2,3,19,20,21,22,23,24,25,26,27,28,29,15,16,17,18],[5,6,7,8,9,10,11,12,13,14,0,1,2,3,4,20,21,22,23,24,25,26,27,28,29,15,16,17,18,19],[6,7,8,9,10,11,12,13,14,0,1,2,3,4,5,21,22,23,24,25,26,27,28,29,15,16,17,18,19,20],[7,8,9,10,11,12,13,14,0,1,2,3,4,5,6,22,23,24,25,26,27,28,29,15,16,17,18,19,20,21],[8,9,10,11,12,13,14,0,1,2,3,4,5,6,7,23,24,25,26,27,28,29,15,16,17,18,19,20,21,22],[9,10,11,12,13,14,0,1,2,3,4,5,6,7,8,24,25,26,27,28,29,15,16,17,18,19,20,21,22,23],[10,11,12,13,14,0,1,2,3,4,5,6,7,8,9,25,26,27,28,29,15,16,17,18,19,20,21,22,23,24],[11,12,13,14,0,1,2,3,4,5,6,7,8,9,10,26,27,28,29,15,16,17,18,19,20,21,22,23,24,25],[12,13,14,0,1,2,3,4,5,6,7,8,9,10,11,27,28,29,15,16,17,18,19,20,21,22,23,24,25,26],[13,14,0,1,2,3,4,5,6,7,8,9,10,11,12,28,29,15,16,17,18,19,20,21,22,23,24,25,26,27],[14,0,1,2,3,4,5,6,7,8,9,10,11,12,13,29,15,16,17,18,19,20,21,22,23,24,25,26,27,28],[15,29,28,27,26,25,24,23,22,21,20,19,18,17,16,0,14,13,12,11,10,9,8,7,6,5,4,3,2,1],[16,15,29,28,27,26,25,24,23,22,21,20,19,18,17,1,0,14,13,12,11,10,9,8,7,6,5,4,3,2],[17,16,15,29,28,27,26,25,24,23,22,21,20,19,18,2,1,0,14,13,12,11,10,9,8,7,6,5,4,3],[18,17,16,15,29,28,27,26,25,24,23,22,21,20,19,3,2,1,0,14,13,12,11,10,9,8,7,6,5,4],[19,18,17,16,15,29,28,27,26,25,24,23,22,21,20,4,3,2,1,0,14,13,12,11,10,9,8,7,6,5],[20,19,18,17,16,15,29,28,27,26,25,24,23,22,21,5,4,3,2,1,0,14,13,12,11,10,9,8,7,6],[21,20,19,18,17,16,15,29,28,27,26,25,24,23,22,6,5,4,3,2,1,0,14,13,12,11,10,9,8,7],[22,21,20,19,18,17,16,15,29,28,27,26,25,24,23,7,6,5,4,3,2,1,0,14,13,12,11,10,9,8],[23,22,21,20,19,18,17,16,15,29,28,27,26,25,24,8,7,6,5,4,3,2,1,0,14,13,12,11,10,9],[24,23,22,21,20,19,18,17,16,15,29,28,27,26,25,9,8,7,6,5,4,3,2,1,0,14,13,12,11,10],[25,24,23,22,21,20,19,18,17,16,15,29,28,27,26,10,9,8,7,6,5,4,3,2,1,0,14,13,12,11],[26,25,24,23,22,21,20,19,18,17,16,15,29,28,27,11,10,9,8,7,6,5,4,3,2,1,0,14,13,12],[27,26,25,24,23,22,21,20,19,18,17,16,15,29,28,12,11,10,9,8,7,6,5,4,3,2,1,0,14,13],[28,27,26,25,24,23,22,21,20,19,18,17,16,15,29,13,12,11,10,9,8,7,6,5,4,3,2,1,0,14],[29,28,27,26,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0]],"identity":0}。請依 [classes, partition_certificate, covered_element_count, group_order, certificate] 欄序回答。

查看答案與解釋([[0], [1, 14], [15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29], [2, 13], [3, 12], [4, 11], [5, 10], [6, 9], [7, 8]], 是, 30, 30, all_conjugacy_classes_are_equal_or_disjoint_and_cover_G)

Wave6第八層核對=([[0], [1, 14], [15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29], [2, 13], [3, 12], [4, 11], [5, 10], [6, 9], [7, 8]], 是, 30, 30, all_conjugacy_classes_are_equal_or_disjoint_and_cover_G)；依完整明示資料獨立重算；共軛類是element orbit並形成完整partition；singleton以forall g commute核對；共軛類不是coset或conjugate subgroup；不使用centralizer、class-size公式或類方程。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r03-finite-group-conjugacy-class-0063/)

有限群共軛類 · qf-mod45-conjugacy-partition-audit · candidate





## 64. 有限群共軛類

由完整Cayley table導出全部conjugation action與orbits。操作=conjugacy-partition-audit；資料={"group_table":[[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,0,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,16],[2,3,4,5,6,7,8,9,10,11,12,13,14,15,0,1,18,19,20,21,22,23,24,25,26,27,28,29,30,31,16,17],[3,4,5,6,7,8,9,10,11,12,13,14,15,0,1,2,19,20,21,22,23,24,25,26,27,28,29,30,31,16,17,18],[4,5,6,7,8,9,10,11,12,13,14,15,0,1,2,3,20,21,22,23,24,25,26,27,28,29,30,31,16,17,18,19],[5,6,7,8,9,10,11,12,13,14,15,0,1,2,3,4,21,22,23,24,25,26,27,28,29,30,31,16,17,18,19,20],[6,7,8,9,10,11,12,13,14,15,0,1,2,3,4,5,22,23,24,25,26,27,28,29,30,31,16,17,18,19,20,21],[7,8,9,10,11,12,13,14,15,0,1,2,3,4,5,6,23,24,25,26,27,28,29,30,31,16,17,18,19,20,21,22],[8,9,10,11,12,13,14,15,0,1,2,3,4,5,6,7,24,25,26,27,28,29,30,31,16,17,18,19,20,21,22,23],[9,10,11,12,13,14,15,0,1,2,3,4,5,6,7,8,25,26,27,28,29,30,31,16,17,18,19,20,21,22,23,24],[10,11,12,13,14,15,0,1,2,3,4,5,6,7,8,9,26,27,28,29,30,31,16,17,18,19,20,21,22,23,24,25],[11,12,13,14,15,0,1,2,3,4,5,6,7,8,9,10,27,28,29,30,31,16,17,18,19,20,21,22,23,24,25,26],[12,13,14,15,0,1,2,3,4,5,6,7,8,9,10,11,28,29,30,31,16,17,18,19,20,21,22,23,24,25,26,27],[13,14,15,0,1,2,3,4,5,6,7,8,9,10,11,12,29,30,31,16,17,18,19,20,21,22,23,24,25,26,27,28],[14,15,0,1,2,3,4,5,6,7,8,9,10,11,12,13,30,31,16,17,18,19,20,21,22,23,24,25,26,27,28,29],[15,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,31,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30],[16,31,30,29,28,27,26,25,24,23,22,21,20,19,18,17,0,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1],[17,16,31,30,29,28,27,26,25,24,23,22,21,20,19,18,1,0,15,14,13,12,11,10,9,8,7,6,5,4,3,2],[18,17,16,31,30,29,28,27,26,25,24,23,22,21,20,19,2,1,0,15,14,13,12,11,10,9,8,7,6,5,4,3],[19,18,17,16,31,30,29,28,27,26,25,24,23,22,21,20,3,2,1,0,15,14,13,12,11,10,9,8,7,6,5,4],[20,19,18,17,16,31,30,29,28,27,26,25,24,23,22,21,4,3,2,1,0,15,14,13,12,11,10,9,8,7,6,5],[21,20,19,18,17,16,31,30,29,28,27,26,25,24,23,22,5,4,3,2,1,0,15,14,13,12,11,10,9,8,7,6],[22,21,20,19,18,17,16,31,30,29,28,27,26,25,24,23,6,5,4,3,2,1,0,15,14,13,12,11,10,9,8,7],[23,22,21,20,19,18,17,16,31,30,29,28,27,26,25,24,7,6,5,4,3,2,1,0,15,14,13,12,11,10,9,8],[24,23,22,21,20,19,18,17,16,31,30,29,28,27,26,25,8,7,6,5,4,3,2,1,0,15,14,13,12,11,10,9],[25,24,23,22,21,20,19,18,17,16,31,30,29,28,27,26,9,8,7,6,5,4,3,2,1,0,15,14,13,12,11,10],[26,25,24,23,22,21,20,19,18,17,16,31,30,29,28,27,10,9,8,7,6,5,4,3,2,1,0,15,14,13,12,11],[27,26,25,24,23,22,21,20,19,18,17,16,31,30,29,28,11,10,9,8,7,6,5,4,3,2,1,0,15,14,13,12],[28,27,26,25,24,23,22,21,20,19,18,17,16,31,30,29,12,11,10,9,8,7,6,5,4,3,2,1,0,15,14,13],[29,28,27,26,25,24,23,22,21,20,19,18,17,16,31,30,13,12,11,10,9,8,7,6,5,4,3,2,1,0,15,14],[30,29,28,27,26,25,24,23,22,21,20,19,18,17,16,31,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0,15],[31,30,29,28,27,26,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0]],"identity":0}。請依 [classes, partition_certificate, covered_element_count, group_order, certificate] 欄序回答。

查看答案與解釋([[0], [1, 15], [16, 18, 20, 22, 24, 26, 28, 30], [17, 19, 21, 23, 25, 27, 29, 31], [2, 14], [3, 13], [4, 12], [5, 11], [6, 10], [7, 9], [8]], 是, 32, 32, all_conjugacy_classes_are_equal_or_disjoint_and_cover_G)

Wave6第八層核對=([[0], [1, 15], [16, 18, 20, 22, 24, 26, 28, 30], [17, 19, 21, 23, 25, 27, 29, 31], [2, 14], [3, 13], [4, 12], [5, 11], [6, 10], [7, 9], [8]], 是, 32, 32, all_conjugacy_classes_are_equal_or_disjoint_and_cover_G)；依完整明示資料獨立重算；共軛類是element orbit並形成完整partition；singleton以forall g commute核對；共軛類不是coset或conjugate subgroup；不使用centralizer、class-size公式或類方程。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r03-finite-group-conjugacy-class-0064/)

有限群共軛類 · qf-mod45-conjugacy-partition-audit · candidate





## 65. 有限群共軛類

由完整Cayley table導出全部conjugation action與orbits。操作=conjugacy-partition-audit；資料={"group_table":[[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,0,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,17],[2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,0,1,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,17,18],[3,4,5,6,7,8,9,10,11,12,13,14,15,16,0,1,2,20,21,22,23,24,25,26,27,28,29,30,31,32,33,17,18,19],[4,5,6,7,8,9,10,11,12,13,14,15,16,0,1,2,3,21,22,23,24,25,26,27,28,29,30,31,32,33,17,18,19,20],[5,6,7,8,9,10,11,12,13,14,15,16,0,1,2,3,4,22,23,24,25,26,27,28,29,30,31,32,33,17,18,19,20,21],[6,7,8,9,10,11,12,13,14,15,16,0,1,2,3,4,5,23,24,25,26,27,28,29,30,31,32,33,17,18,19,20,21,22],[7,8,9,10,11,12,13,14,15,16,0,1,2,3,4,5,6,24,25,26,27,28,29,30,31,32,33,17,18,19,20,21,22,23],[8,9,10,11,12,13,14,15,16,0,1,2,3,4,5,6,7,25,26,27,28,29,30,31,32,33,17,18,19,20,21,22,23,24],[9,10,11,12,13,14,15,16,0,1,2,3,4,5,6,7,8,26,27,28,29,30,31,32,33,17,18,19,20,21,22,23,24,25],[10,11,12,13,14,15,16,0,1,2,3,4,5,6,7,8,9,27,28,29,30,31,32,33,17,18,19,20,21,22,23,24,25,26],[11,12,13,14,15,16,0,1,2,3,4,5,6,7,8,9,10,28,29,30,31,32,33,17,18,19,20,21,22,23,24,25,26,27],[12,13,14,15,16,0,1,2,3,4,5,6,7,8,9,10,11,29,30,31,32,33,17,18,19,20,21,22,23,24,25,26,27,28],[13,14,15,16,0,1,2,3,4,5,6,7,8,9,10,11,12,30,31,32,33,17,18,19,20,21,22,23,24,25,26,27,28,29],[14,15,16,0,1,2,3,4,5,6,7,8,9,10,11,12,13,31,32,33,17,18,19,20,21,22,23,24,25,26,27,28,29,30],[15,16,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,32,33,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31],[16,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,33,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32],[17,33,32,31,30,29,28,27,26,25,24,23,22,21,20,19,18,0,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1],[18,17,33,32,31,30,29,28,27,26,25,24,23,22,21,20,19,1,0,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2],[19,18,17,33,32,31,30,29,28,27,26,25,24,23,22,21,20,2,1,0,16,15,14,13,12,11,10,9,8,7,6,5,4,3],[20,19,18,17,33,32,31,30,29,28,27,26,25,24,23,22,21,3,2,1,0,16,15,14,13,12,11,10,9,8,7,6,5,4],[21,20,19,18,17,33,32,31,30,29,28,27,26,25,24,23,22,4,3,2,1,0,16,15,14,13,12,11,10,9,8,7,6,5],[22,21,20,19,18,17,33,32,31,30,29,28,27,26,25,24,23,5,4,3,2,1,0,16,15,14,13,12,11,10,9,8,7,6],[23,22,21,20,19,18,17,33,32,31,30,29,28,27,26,25,24,6,5,4,3,2,1,0,16,15,14,13,12,11,10,9,8,7],[24,23,22,21,20,19,18,17,33,32,31,30,29,28,27,26,25,7,6,5,4,3,2,1,0,16,15,14,13,12,11,10,9,8],[25,24,23,22,21,20,19,18,17,33,32,31,30,29,28,27,26,8,7,6,5,4,3,2,1,0,16,15,14,13,12,11,10,9],[26,25,24,23,22,21,20,19,18,17,33,32,31,30,29,28,27,9,8,7,6,5,4,3,2,1,0,16,15,14,13,12,11,10],[27,26,25,24,23,22,21,20,19,18,17,33,32,31,30,29,28,10,9,8,7,6,5,4,3,2,1,0,16,15,14,13,12,11],[28,27,26,25,24,23,22,21,20,19,18,17,33,32,31,30,29,11,10,9,8,7,6,5,4,3,2,1,0,16,15,14,13,12],[29,28,27,26,25,24,23,22,21,20,19,18,17,33,32,31,30,12,11,10,9,8,7,6,5,4,3,2,1,0,16,15,14,13],[30,29,28,27,26,25,24,23,22,21,20,19,18,17,33,32,31,13,12,11,10,9,8,7,6,5,4,3,2,1,0,16,15,14],[31,30,29,28,27,26,25,24,23,22,21,20,19,18,17,33,32,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0,16,15],[32,31,30,29,28,27,26,25,24,23,22,21,20,19,18,17,33,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0,16],[33,32,31,30,29,28,27,26,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0]],"identity":0}。請依 [classes, partition_certificate, covered_element_count, group_order, certificate] 欄序回答。

查看答案與解釋([[0], [1, 16], [17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33], [2, 15], [3, 14], [4, 13], [5, 12], [6, 11], [7, 10], [8, 9]], 是, 34, 34, all_conjugacy_classes_are_equal_or_disjoint_and_cover_G)

Wave6第八層核對=([[0], [1, 16], [17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33], [2, 15], [3, 14], [4, 13], [5, 12], [6, 11], [7, 10], [8, 9]], 是, 34, 34, all_conjugacy_classes_are_equal_or_disjoint_and_cover_G)；依完整明示資料獨立重算；共軛類是element orbit並形成完整partition；singleton以forall g commute核對；共軛類不是coset或conjugate subgroup；不使用centralizer、class-size公式或類方程。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r03-finite-group-conjugacy-class-0065/)

有限群共軛類 · qf-mod45-conjugacy-partition-audit · candidate





## 66. 有限群共軛類

由完整Cayley table導出全部conjugation action與orbits。操作=conjugacy-partition-audit；資料={"group_table":[[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,0,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,18],[2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,0,1,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,18,19],[3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,0,1,2,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,18,19,20],[4,5,6,7,8,9,10,11,12,13,14,15,16,17,0,1,2,3,22,23,24,25,26,27,28,29,30,31,32,33,34,35,18,19,20,21],[5,6,7,8,9,10,11,12,13,14,15,16,17,0,1,2,3,4,23,24,25,26,27,28,29,30,31,32,33,34,35,18,19,20,21,22],[6,7,8,9,10,11,12,13,14,15,16,17,0,1,2,3,4,5,24,25,26,27,28,29,30,31,32,33,34,35,18,19,20,21,22,23],[7,8,9,10,11,12,13,14,15,16,17,0,1,2,3,4,5,6,25,26,27,28,29,30,31,32,33,34,35,18,19,20,21,22,23,24],[8,9,10,11,12,13,14,15,16,17,0,1,2,3,4,5,6,7,26,27,28,29,30,31,32,33,34,35,18,19,20,21,22,23,24,25],[9,10,11,12,13,14,15,16,17,0,1,2,3,4,5,6,7,8,27,28,29,30,31,32,33,34,35,18,19,20,21,22,23,24,25,26],[10,11,12,13,14,15,16,17,0,1,2,3,4,5,6,7,8,9,28,29,30,31,32,33,34,35,18,19,20,21,22,23,24,25,26,27],[11,12,13,14,15,16,17,0,1,2,3,4,5,6,7,8,9,10,29,30,31,32,33,34,35,18,19,20,21,22,23,24,25,26,27,28],[12,13,14,15,16,17,0,1,2,3,4,5,6,7,8,9,10,11,30,31,32,33,34,35,18,19,20,21,22,23,24,25,26,27,28,29],[13,14,15,16,17,0,1,2,3,4,5,6,7,8,9,10,11,12,31,32,33,34,35,18,19,20,21,22,23,24,25,26,27,28,29,30],[14,15,16,17,0,1,2,3,4,5,6,7,8,9,10,11,12,13,32,33,34,35,18,19,20,21,22,23,24,25,26,27,28,29,30,31],[15,16,17,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,33,34,35,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32],[16,17,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,34,35,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33],[17,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,35,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34],[18,35,34,33,32,31,30,29,28,27,26,25,24,23,22,21,20,19,0,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1],[19,18,35,34,33,32,31,30,29,28,27,26,25,24,23,22,21,20,1,0,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2],[20,19,18,35,34,33,32,31,30,29,28,27,26,25,24,23,22,21,2,1,0,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3],[21,20,19,18,35,34,33,32,31,30,29,28,27,26,25,24,23,22,3,2,1,0,17,16,15,14,13,12,11,10,9,8,7,6,5,4],[22,21,20,19,18,35,34,33,32,31,30,29,28,27,26,25,24,23,4,3,2,1,0,17,16,15,14,13,12,11,10,9,8,7,6,5],[23,22,21,20,19,18,35,34,33,32,31,30,29,28,27,26,25,24,5,4,3,2,1,0,17,16,15,14,13,12,11,10,9,8,7,6],[24,23,22,21,20,19,18,35,34,33,32,31,30,29,28,27,26,25,6,5,4,3,2,1,0,17,16,15,14,13,12,11,10,9,8,7],[25,24,23,22,21,20,19,18,35,34,33,32,31,30,29,28,27,26,7,6,5,4,3,2,1,0,17,16,15,14,13,12,11,10,9,8],[26,25,24,23,22,21,20,19,18,35,34,33,32,31,30,29,28,27,8,7,6,5,4,3,2,1,0,17,16,15,14,13,12,11,10,9],[27,26,25,24,23,22,21,20,19,18,35,34,33,32,31,30,29,28,9,8,7,6,5,4,3,2,1,0,17,16,15,14,13,12,11,10],[28,27,26,25,24,23,22,21,20,19,18,35,34,33,32,31,30,29,10,9,8,7,6,5,4,3,2,1,0,17,16,15,14,13,12,11],[29,28,27,26,25,24,23,22,21,20,19,18,35,34,33,32,31,30,11,10,9,8,7,6,5,4,3,2,1,0,17,16,15,14,13,12],[30,29,28,27,26,25,24,23,22,21,20,19,18,35,34,33,32,31,12,11,10,9,8,7,6,5,4,3,2,1,0,17,16,15,14,13],[31,30,29,28,27,26,25,24,23,22,21,20,19,18,35,34,33,32,13,12,11,10,9,8,7,6,5,4,3,2,1,0,17,16,15,14],[32,31,30,29,28,27,26,25,24,23,22,21,20,19,18,35,34,33,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0,17,16,15],[33,32,31,30,29,28,27,26,25,24,23,22,21,20,19,18,35,34,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0,17,16],[34,33,32,31,30,29,28,27,26,25,24,23,22,21,20,19,18,35,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0,17],[35,34,33,32,31,30,29,28,27,26,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0]],"identity":0}。請依 [classes, partition_certificate, covered_element_count, group_order, certificate] 欄序回答。

查看答案與解釋([[0], [1, 17], [18, 20, 22, 24, 26, 28, 30, 32, 34], [19, 21, 23, 25, 27, 29, 31, 33, 35], [2, 16], [3, 15], [4, 14], [5, 13], [6, 12], [7, 11], [8, 10], [9]], 是, 36, 36, all_conjugacy_classes_are_equal_or_disjoint_and_cover_G)

Wave6第八層核對=([[0], [1, 17], [18, 20, 22, 24, 26, 28, 30, 32, 34], [19, 21, 23, 25, 27, 29, 31, 33, 35], [2, 16], [3, 15], [4, 14], [5, 13], [6, 12], [7, 11], [8, 10], [9]], 是, 36, 36, all_conjugacy_classes_are_equal_or_disjoint_and_cover_G)；依完整明示資料獨立重算；共軛類是element orbit並形成完整partition；singleton以forall g commute核對；共軛類不是coset或conjugate subgroup；不使用centralizer、class-size公式或類方程。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r03-finite-group-conjugacy-class-0066/)

有限群共軛類 · qf-mod45-conjugacy-partition-audit · candidate





## 67. 有限群共軛類

由完整Cayley table導出全部conjugation action與orbits。操作=conjugacy-partition-audit；資料={"group_table":[[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,0,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,19],[2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,0,1,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,19,20],[3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,0,1,2,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,19,20,21],[4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,0,1,2,3,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,19,20,21,22],[5,6,7,8,9,10,11,12,13,14,15,16,17,18,0,1,2,3,4,24,25,26,27,28,29,30,31,32,33,34,35,36,37,19,20,21,22,23],[6,7,8,9,10,11,12,13,14,15,16,17,18,0,1,2,3,4,5,25,26,27,28,29,30,31,32,33,34,35,36,37,19,20,21,22,23,24],[7,8,9,10,11,12,13,14,15,16,17,18,0,1,2,3,4,5,6,26,27,28,29,30,31,32,33,34,35,36,37,19,20,21,22,23,24,25],[8,9,10,11,12,13,14,15,16,17,18,0,1,2,3,4,5,6,7,27,28,29,30,31,32,33,34,35,36,37,19,20,21,22,23,24,25,26],[9,10,11,12,13,14,15,16,17,18,0,1,2,3,4,5,6,7,8,28,29,30,31,32,33,34,35,36,37,19,20,21,22,23,24,25,26,27],[10,11,12,13,14,15,16,17,18,0,1,2,3,4,5,6,7,8,9,29,30,31,32,33,34,35,36,37,19,20,21,22,23,24,25,26,27,28],[11,12,13,14,15,16,17,18,0,1,2,3,4,5,6,7,8,9,10,30,31,32,33,34,35,36,37,19,20,21,22,23,24,25,26,27,28,29],[12,13,14,15,16,17,18,0,1,2,3,4,5,6,7,8,9,10,11,31,32,33,34,35,36,37,19,20,21,22,23,24,25,26,27,28,29,30],[13,14,15,16,17,18,0,1,2,3,4,5,6,7,8,9,10,11,12,32,33,34,35,36,37,19,20,21,22,23,24,25,26,27,28,29,30,31],[14,15,16,17,18,0,1,2,3,4,5,6,7,8,9,10,11,12,13,33,34,35,36,37,19,20,21,22,23,24,25,26,27,28,29,30,31,32],[15,16,17,18,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,34,35,36,37,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33],[16,17,18,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,35,36,37,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34],[17,18,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,36,37,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35],[18,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,37,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36],[19,37,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,21,20,0,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1],[20,19,37,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,21,1,0,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2],[21,20,19,37,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,2,1,0,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3],[22,21,20,19,37,36,35,34,33,32,31,30,29,28,27,26,25,24,23,3,2,1,0,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4],[23,22,21,20,19,37,36,35,34,33,32,31,30,29,28,27,26,25,24,4,3,2,1,0,18,17,16,15,14,13,12,11,10,9,8,7,6,5],[24,23,22,21,20,19,37,36,35,34,33,32,31,30,29,28,27,26,25,5,4,3,2,1,0,18,17,16,15,14,13,12,11,10,9,8,7,6],[25,24,23,22,21,20,19,37,36,35,34,33,32,31,30,29,28,27,26,6,5,4,3,2,1,0,18,17,16,15,14,13,12,11,10,9,8,7],[26,25,24,23,22,21,20,19,37,36,35,34,33,32,31,30,29,28,27,7,6,5,4,3,2,1,0,18,17,16,15,14,13,12,11,10,9,8],[27,26,25,24,23,22,21,20,19,37,36,35,34,33,32,31,30,29,28,8,7,6,5,4,3,2,1,0,18,17,16,15,14,13,12,11,10,9],[28,27,26,25,24,23,22,21,20,19,37,36,35,34,33,32,31,30,29,9,8,7,6,5,4,3,2,1,0,18,17,16,15,14,13,12,11,10],[29,28,27,26,25,24,23,22,21,20,19,37,36,35,34,33,32,31,30,10,9,8,7,6,5,4,3,2,1,0,18,17,16,15,14,13,12,11],[30,29,28,27,26,25,24,23,22,21,20,19,37,36,35,34,33,32,31,11,10,9,8,7,6,5,4,3,2,1,0,18,17,16,15,14,13,12],[31,30,29,28,27,26,25,24,23,22,21,20,19,37,36,35,34,33,32,12,11,10,9,8,7,6,5,4,3,2,1,0,18,17,16,15,14,13],[32,31,30,29,28,27,26,25,24,23,22,21,20,19,37,36,35,34,33,13,12,11,10,9,8,7,6,5,4,3,2,1,0,18,17,16,15,14],[33,32,31,30,29,28,27,26,25,24,23,22,21,20,19,37,36,35,34,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0,18,17,16,15],[34,33,32,31,30,29,28,27,26,25,24,23,22,21,20,19,37,36,35,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0,18,17,16],[35,34,33,32,31,30,29,28,27,26,25,24,23,22,21,20,19,37,36,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0,18,17],[36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,21,20,19,37,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0,18],[37,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0]],"identity":0}。請依 [classes, partition_certificate, covered_element_count, group_order, certificate] 欄序回答。

查看答案與解釋([[0], [1, 18], [19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37], [2, 17], [3, 16], [4, 15], [5, 14], [6, 13], [7, 12], [8, 11], [9, 10]], 是, 38, 38, all_conjugacy_classes_are_equal_or_disjoint_and_cover_G)

Wave6第八層核對=([[0], [1, 18], [19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37], [2, 17], [3, 16], [4, 15], [5, 14], [6, 13], [7, 12], [8, 11], [9, 10]], 是, 38, 38, all_conjugacy_classes_are_equal_or_disjoint_and_cover_G)；依完整明示資料獨立重算；共軛類是element orbit並形成完整partition；singleton以forall g commute核對；共軛類不是coset或conjugate subgroup；不使用centralizer、class-size公式或類方程。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r03-finite-group-conjugacy-class-0067/)

有限群共軛類 · qf-mod45-conjugacy-partition-audit · candidate





## 68. 有限群共軛類

由完整Cayley table導出全部conjugation action與orbits。操作=conjugacy-partition-audit；資料={"group_table":[[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,0,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,20],[2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,0,1,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,20,21],[3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,0,1,2,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,20,21,22],[4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,0,1,2,3,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,20,21,22,23],[5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,0,1,2,3,4,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,20,21,22,23,24],[6,7,8,9,10,11,12,13,14,15,16,17,18,19,0,1,2,3,4,5,26,27,28,29,30,31,32,33,34,35,36,37,38,39,20,21,22,23,24,25],[7,8,9,10,11,12,13,14,15,16,17,18,19,0,1,2,3,4,5,6,27,28,29,30,31,32,33,34,35,36,37,38,39,20,21,22,23,24,25,26],[8,9,10,11,12,13,14,15,16,17,18,19,0,1,2,3,4,5,6,7,28,29,30,31,32,33,34,35,36,37,38,39,20,21,22,23,24,25,26,27],[9,10,11,12,13,14,15,16,17,18,19,0,1,2,3,4,5,6,7,8,29,30,31,32,33,34,35,36,37,38,39,20,21,22,23,24,25,26,27,28],[10,11,12,13,14,15,16,17,18,19,0,1,2,3,4,5,6,7,8,9,30,31,32,33,34,35,36,37,38,39,20,21,22,23,24,25,26,27,28,29],[11,12,13,14,15,16,17,18,19,0,1,2,3,4,5,6,7,8,9,10,31,32,33,34,35,36,37,38,39,20,21,22,23,24,25,26,27,28,29,30],[12,13,14,15,16,17,18,19,0,1,2,3,4,5,6,7,8,9,10,11,32,33,34,35,36,37,38,39,20,21,22,23,24,25,26,27,28,29,30,31],[13,14,15,16,17,18,19,0,1,2,3,4,5,6,7,8,9,10,11,12,33,34,35,36,37,38,39,20,21,22,23,24,25,26,27,28,29,30,31,32],[14,15,16,17,18,19,0,1,2,3,4,5,6,7,8,9,10,11,12,13,34,35,36,37,38,39,20,21,22,23,24,25,26,27,28,29,30,31,32,33],[15,16,17,18,19,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,35,36,37,38,39,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34],[16,17,18,19,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,36,37,38,39,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35],[17,18,19,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,37,38,39,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36],[18,19,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,38,39,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37],[19,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,39,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38],[20,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,21,0,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1],[21,20,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,1,0,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2],[22,21,20,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,23,2,1,0,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3],[23,22,21,20,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,3,2,1,0,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4],[24,23,22,21,20,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,4,3,2,1,0,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5],[25,24,23,22,21,20,39,38,37,36,35,34,33,32,31,30,29,28,27,26,5,4,3,2,1,0,19,18,17,16,15,14,13,12,11,10,9,8,7,6],[26,25,24,23,22,21,20,39,38,37,36,35,34,33,32,31,30,29,28,27,6,5,4,3,2,1,0,19,18,17,16,15,14,13,12,11,10,9,8,7],[27,26,25,24,23,22,21,20,39,38,37,36,35,34,33,32,31,30,29,28,7,6,5,4,3,2,1,0,19,18,17,16,15,14,13,12,11,10,9,8],[28,27,26,25,24,23,22,21,20,39,38,37,36,35,34,33,32,31,30,29,8,7,6,5,4,3,2,1,0,19,18,17,16,15,14,13,12,11,10,9],[29,28,27,26,25,24,23,22,21,20,39,38,37,36,35,34,33,32,31,30,9,8,7,6,5,4,3,2,1,0,19,18,17,16,15,14,13,12,11,10],[30,29,28,27,26,25,24,23,22,21,20,39,38,37,36,35,34,33,32,31,10,9,8,7,6,5,4,3,2,1,0,19,18,17,16,15,14,13,12,11],[31,30,29,28,27,26,25,24,23,22,21,20,39,38,37,36,35,34,33,32,11,10,9,8,7,6,5,4,3,2,1,0,19,18,17,16,15,14,13,12],[32,31,30,29,28,27,26,25,24,23,22,21,20,39,38,37,36,35,34,33,12,11,10,9,8,7,6,5,4,3,2,1,0,19,18,17,16,15,14,13],[33,32,31,30,29,28,27,26,25,24,23,22,21,20,39,38,37,36,35,34,13,12,11,10,9,8,7,6,5,4,3,2,1,0,19,18,17,16,15,14],[34,33,32,31,30,29,28,27,26,25,24,23,22,21,20,39,38,37,36,35,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0,19,18,17,16,15],[35,34,33,32,31,30,29,28,27,26,25,24,23,22,21,20,39,38,37,36,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0,19,18,17,16],[36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,21,20,39,38,37,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0,19,18,17],[37,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,21,20,39,38,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0,19,18],[38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,21,20,39,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0,19],[39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0]],"identity":0}。請依 [classes, partition_certificate, covered_element_count, group_order, certificate] 欄序回答。

查看答案與解釋([[0], [1, 19], [10], [2, 18], [20, 22, 24, 26, 28, 30, 32, 34, 36, 38], [21, 23, 25, 27, 29, 31, 33, 35, 37, 39], [3, 17], [4, 16], [5, 15], [6, 14], [7, 13], [8, 12], [9, 11]], 是, 40, 40, all_conjugacy_classes_are_equal_or_disjoint_and_cover_G)

Wave6第八層核對=([[0], [1, 19], [10], [2, 18], [20, 22, 24, 26, 28, 30, 32, 34, 36, 38], [21, 23, 25, 27, 29, 31, 33, 35, 37, 39], [3, 17], [4, 16], [5, 15], [6, 14], [7, 13], [8, 12], [9, 11]], 是, 40, 40, all_conjugacy_classes_are_equal_or_disjoint_and_cover_G)；依完整明示資料獨立重算；共軛類是element orbit並形成完整partition；singleton以forall g commute核對；共軛類不是coset或conjugate subgroup；不使用centralizer、class-size公式或類方程。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r03-finite-group-conjugacy-class-0068/)

有限群共軛類 · qf-mod45-conjugacy-partition-audit · candidate





## 69. 有限群共軛類

由完整Cayley table導出全部conjugation action與orbits。操作=conjugacy-partition-audit；資料={"group_table":[[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,0,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,21],[2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,0,1,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,21,22],[3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,0,1,2,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,21,22,23],[4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,0,1,2,3,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,21,22,23,24],[5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,0,1,2,3,4,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,21,22,23,24,25],[6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,0,1,2,3,4,5,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,21,22,23,24,25,26],[7,8,9,10,11,12,13,14,15,16,17,18,19,20,0,1,2,3,4,5,6,28,29,30,31,32,33,34,35,36,37,38,39,40,41,21,22,23,24,25,26,27],[8,9,10,11,12,13,14,15,16,17,18,19,20,0,1,2,3,4,5,6,7,29,30,31,32,33,34,35,36,37,38,39,40,41,21,22,23,24,25,26,27,28],[9,10,11,12,13,14,15,16,17,18,19,20,0,1,2,3,4,5,6,7,8,30,31,32,33,34,35,36,37,38,39,40,41,21,22,23,24,25,26,27,28,29],[10,11,12,13,14,15,16,17,18,19,20,0,1,2,3,4,5,6,7,8,9,31,32,33,34,35,36,37,38,39,40,41,21,22,23,24,25,26,27,28,29,30],[11,12,13,14,15,16,17,18,19,20,0,1,2,3,4,5,6,7,8,9,10,32,33,34,35,36,37,38,39,40,41,21,22,23,24,25,26,27,28,29,30,31],[12,13,14,15,16,17,18,19,20,0,1,2,3,4,5,6,7,8,9,10,11,33,34,35,36,37,38,39,40,41,21,22,23,24,25,26,27,28,29,30,31,32],[13,14,15,16,17,18,19,20,0,1,2,3,4,5,6,7,8,9,10,11,12,34,35,36,37,38,39,40,41,21,22,23,24,25,26,27,28,29,30,31,32,33],[14,15,16,17,18,19,20,0,1,2,3,4,5,6,7,8,9,10,11,12,13,35,36,37,38,39,40,41,21,22,23,24,25,26,27,28,29,30,31,32,33,34],[15,16,17,18,19,20,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,36,37,38,39,40,41,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35],[16,17,18,19,20,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,37,38,39,40,41,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36],[17,18,19,20,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,38,39,40,41,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37],[18,19,20,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,39,40,41,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38],[19,20,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,40,41,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39],[20,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,41,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40],[21,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,0,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1],[22,21,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,23,1,0,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2],[23,22,21,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,2,1,0,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3],[24,23,22,21,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,3,2,1,0,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4],[25,24,23,22,21,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,4,3,2,1,0,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5],[26,25,24,23,22,21,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,5,4,3,2,1,0,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6],[27,26,25,24,23,22,21,41,40,39,38,37,36,35,34,33,32,31,30,29,28,6,5,4,3,2,1,0,20,19,18,17,16,15,14,13,12,11,10,9,8,7],[28,27,26,25,24,23,22,21,41,40,39,38,37,36,35,34,33,32,31,30,29,7,6,5,4,3,2,1,0,20,19,18,17,16,15,14,13,12,11,10,9,8],[29,28,27,26,25,24,23,22,21,41,40,39,38,37,36,35,34,33,32,31,30,8,7,6,5,4,3,2,1,0,20,19,18,17,16,15,14,13,12,11,10,9],[30,29,28,27,26,25,24,23,22,21,41,40,39,38,37,36,35,34,33,32,31,9,8,7,6,5,4,3,2,1,0,20,19,18,17,16,15,14,13,12,11,10],[31,30,29,28,27,26,25,24,23,22,21,41,40,39,38,37,36,35,34,33,32,10,9,8,7,6,5,4,3,2,1,0,20,19,18,17,16,15,14,13,12,11],[32,31,30,29,28,27,26,25,24,23,22,21,41,40,39,38,37,36,35,34,33,11,10,9,8,7,6,5,4,3,2,1,0,20,19,18,17,16,15,14,13,12],[33,32,31,30,29,28,27,26,25,24,23,22,21,41,40,39,38,37,36,35,34,12,11,10,9,8,7,6,5,4,3,2,1,0,20,19,18,17,16,15,14,13],[34,33,32,31,30,29,28,27,26,25,24,23,22,21,41,40,39,38,37,36,35,13,12,11,10,9,8,7,6,5,4,3,2,1,0,20,19,18,17,16,15,14],[35,34,33,32,31,30,29,28,27,26,25,24,23,22,21,41,40,39,38,37,36,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0,20,19,18,17,16,15],[36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,21,41,40,39,38,37,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0,20,19,18,17,16],[37,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,21,41,40,39,38,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0,20,19,18,17],[38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,21,41,40,39,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0,20,19,18],[39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,21,41,40,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0,20,19],[40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,21,41,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0,20],[41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0]],"identity":0}。請依 [classes, partition_certificate, covered_element_count, group_order, certificate] 欄序回答。

查看答案與解釋([[0], [1, 20], [10, 11], [2, 19], [21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41], [3, 18], [4, 17], [5, 16], [6, 15], [7, 14], [8, 13], [9, 12]], 是, 42, 42, all_conjugacy_classes_are_equal_or_disjoint_and_cover_G)

Wave6第八層核對=([[0], [1, 20], [10, 11], [2, 19], [21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41], [3, 18], [4, 17], [5, 16], [6, 15], [7, 14], [8, 13], [9, 12]], 是, 42, 42, all_conjugacy_classes_are_equal_or_disjoint_and_cover_G)；依完整明示資料獨立重算；共軛類是element orbit並形成完整partition；singleton以forall g commute核對；共軛類不是coset或conjugate subgroup；不使用centralizer、class-size公式或類方程。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r03-finite-group-conjugacy-class-0069/)

有限群共軛類 · qf-mod45-conjugacy-partition-audit · candidate





## 70. 有限群共軛類

由完整Cayley table導出全部conjugation action與orbits。操作=conjugacy-partition-audit；資料={"group_table":[[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,0,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,22],[2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,0,1,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,22,23],[3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,0,1,2,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,22,23,24],[4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,0,1,2,3,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,22,23,24,25],[5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,0,1,2,3,4,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,22,23,24,25,26],[6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,0,1,2,3,4,5,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,22,23,24,25,26,27],[7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,0,1,2,3,4,5,6,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,22,23,24,25,26,27,28],[8,9,10,11,12,13,14,15,16,17,18,19,20,21,0,1,2,3,4,5,6,7,30,31,32,33,34,35,36,37,38,39,40,41,42,43,22,23,24,25,26,27,28,29],[9,10,11,12,13,14,15,16,17,18,19,20,21,0,1,2,3,4,5,6,7,8,31,32,33,34,35,36,37,38,39,40,41,42,43,22,23,24,25,26,27,28,29,30],[10,11,12,13,14,15,16,17,18,19,20,21,0,1,2,3,4,5,6,7,8,9,32,33,34,35,36,37,38,39,40,41,42,43,22,23,24,25,26,27,28,29,30,31],[11,12,13,14,15,16,17,18,19,20,21,0,1,2,3,4,5,6,7,8,9,10,33,34,35,36,37,38,39,40,41,42,43,22,23,24,25,26,27,28,29,30,31,32],[12,13,14,15,16,17,18,19,20,21,0,1,2,3,4,5,6,7,8,9,10,11,34,35,36,37,38,39,40,41,42,43,22,23,24,25,26,27,28,29,30,31,32,33],[13,14,15,16,17,18,19,20,21,0,1,2,3,4,5,6,7,8,9,10,11,12,35,36,37,38,39,40,41,42,43,22,23,24,25,26,27,28,29,30,31,32,33,34],[14,15,16,17,18,19,20,21,0,1,2,3,4,5,6,7,8,9,10,11,12,13,36,37,38,39,40,41,42,43,22,23,24,25,26,27,28,29,30,31,32,33,34,35],[15,16,17,18,19,20,21,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,37,38,39,40,41,42,43,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36],[16,17,18,19,20,21,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,38,39,40,41,42,43,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37],[17,18,19,20,21,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,39,40,41,42,43,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38],[18,19,20,21,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,40,41,42,43,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39],[19,20,21,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,41,42,43,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40],[20,21,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,42,43,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41],[21,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,43,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42],[22,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,23,0,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1],[23,22,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,1,0,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2],[24,23,22,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,2,1,0,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3],[25,24,23,22,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,3,2,1,0,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4],[26,25,24,23,22,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,4,3,2,1,0,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5],[27,26,25,24,23,22,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,5,4,3,2,1,0,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6],[28,27,26,25,24,23,22,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,6,5,4,3,2,1,0,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7],[29,28,27,26,25,24,23,22,43,42,41,40,39,38,37,36,35,34,33,32,31,30,7,6,5,4,3,2,1,0,21,20,19,18,17,16,15,14,13,12,11,10,9,8],[30,29,28,27,26,25,24,23,22,43,42,41,40,39,38,37,36,35,34,33,32,31,8,7,6,5,4,3,2,1,0,21,20,19,18,17,16,15,14,13,12,11,10,9],[31,30,29,28,27,26,25,24,23,22,43,42,41,40,39,38,37,36,35,34,33,32,9,8,7,6,5,4,3,2,1,0,21,20,19,18,17,16,15,14,13,12,11,10],[32,31,30,29,28,27,26,25,24,23,22,43,42,41,40,39,38,37,36,35,34,33,10,9,8,7,6,5,4,3,2,1,0,21,20,19,18,17,16,15,14,13,12,11],[33,32,31,30,29,28,27,26,25,24,23,22,43,42,41,40,39,38,37,36,35,34,11,10,9,8,7,6,5,4,3,2,1,0,21,20,19,18,17,16,15,14,13,12],[34,33,32,31,30,29,28,27,26,25,24,23,22,43,42,41,40,39,38,37,36,35,12,11,10,9,8,7,6,5,4,3,2,1,0,21,20,19,18,17,16,15,14,13],[35,34,33,32,31,30,29,28,27,26,25,24,23,22,43,42,41,40,39,38,37,36,13,12,11,10,9,8,7,6,5,4,3,2,1,0,21,20,19,18,17,16,15,14],[36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,43,42,41,40,39,38,37,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0,21,20,19,18,17,16,15],[37,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,43,42,41,40,39,38,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0,21,20,19,18,17,16],[38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,43,42,41,40,39,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0,21,20,19,18,17],[39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,43,42,41,40,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0,21,20,19,18],[40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,43,42,41,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0,21,20,19],[41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,43,42,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0,21,20],[42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,43,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0,21],[43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0]],"identity":0}。請依 [classes, partition_certificate, covered_element_count, group_order, certificate] 欄序回答。

查看答案與解釋([[0], [1, 21], [10, 12], [11], [2, 20], [22, 24, 26, 28, 30, 32, 34, 36, 38, 40, 42], [23, 25, 27, 29, 31, 33, 35, 37, 39, 41, 43], [3, 19], [4, 18], [5, 17], [6, 16], [7, 15], [8, 14], [9, 13]], 是, 44, 44, all_conjugacy_classes_are_equal_or_disjoint_and_cover_G)

Wave6第八層核對=([[0], [1, 21], [10, 12], [11], [2, 20], [22, 24, 26, 28, 30, 32, 34, 36, 38, 40, 42], [23, 25, 27, 29, 31, 33, 35, 37, 39, 41, 43], [3, 19], [4, 18], [5, 17], [6, 16], [7, 15], [8, 14], [9, 13]], 是, 44, 44, all_conjugacy_classes_are_equal_or_disjoint_and_cover_G)；依完整明示資料獨立重算；共軛類是element orbit並形成完整partition；singleton以forall g commute核對；共軛類不是coset或conjugate subgroup；不使用centralizer、class-size公式或類方程。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r03-finite-group-conjugacy-class-0070/)

有限群共軛類 · qf-mod45-conjugacy-partition-audit · candidate





## 71. 有限群共軛類

由完整Cayley table導出全部conjugation action與orbits。操作=conjugacy-partition-audit；資料={"group_table":[[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,0,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,23],[2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,0,1,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,23,24],[3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,0,1,2,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,23,24,25],[4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,0,1,2,3,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,23,24,25,26],[5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,0,1,2,3,4,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,23,24,25,26,27],[6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,0,1,2,3,4,5,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,23,24,25,26,27,28],[7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,0,1,2,3,4,5,6,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,23,24,25,26,27,28,29],[8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,0,1,2,3,4,5,6,7,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,23,24,25,26,27,28,29,30],[9,10,11,12,13,14,15,16,17,18,19,20,21,22,0,1,2,3,4,5,6,7,8,32,33,34,35,36,37,38,39,40,41,42,43,44,45,23,24,25,26,27,28,29,30,31],[10,11,12,13,14,15,16,17,18,19,20,21,22,0,1,2,3,4,5,6,7,8,9,33,34,35,36,37,38,39,40,41,42,43,44,45,23,24,25,26,27,28,29,30,31,32],[11,12,13,14,15,16,17,18,19,20,21,22,0,1,2,3,4,5,6,7,8,9,10,34,35,36,37,38,39,40,41,42,43,44,45,23,24,25,26,27,28,29,30,31,32,33],[12,13,14,15,16,17,18,19,20,21,22,0,1,2,3,4,5,6,7,8,9,10,11,35,36,37,38,39,40,41,42,43,44,45,23,24,25,26,27,28,29,30,31,32,33,34],[13,14,15,16,17,18,19,20,21,22,0,1,2,3,4,5,6,7,8,9,10,11,12,36,37,38,39,40,41,42,43,44,45,23,24,25,26,27,28,29,30,31,32,33,34,35],[14,15,16,17,18,19,20,21,22,0,1,2,3,4,5,6,7,8,9,10,11,12,13,37,38,39,40,41,42,43,44,45,23,24,25,26,27,28,29,30,31,32,33,34,35,36],[15,16,17,18,19,20,21,22,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,38,39,40,41,42,43,44,45,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37],[16,17,18,19,20,21,22,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,39,40,41,42,43,44,45,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38],[17,18,19,20,21,22,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,40,41,42,43,44,45,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39],[18,19,20,21,22,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,41,42,43,44,45,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40],[19,20,21,22,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,42,43,44,45,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41],[20,21,22,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,43,44,45,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42],[21,22,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,44,45,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],[22,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,45,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44],[23,45,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,0,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1],[24,23,45,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,1,0,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2],[25,24,23,45,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,2,1,0,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3],[26,25,24,23,45,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,3,2,1,0,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4],[27,26,25,24,23,45,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,4,3,2,1,0,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5],[28,27,26,25,24,23,45,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,5,4,3,2,1,0,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6],[29,28,27,26,25,24,23,45,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,6,5,4,3,2,1,0,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7],[30,29,28,27,26,25,24,23,45,44,43,42,41,40,39,38,37,36,35,34,33,32,31,7,6,5,4,3,2,1,0,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8],[31,30,29,28,27,26,25,24,23,45,44,43,42,41,40,39,38,37,36,35,34,33,32,8,7,6,5,4,3,2,1,0,22,21,20,19,18,17,16,15,14,13,12,11,10,9],[32,31,30,29,28,27,26,25,24,23,45,44,43,42,41,40,39,38,37,36,35,34,33,9,8,7,6,5,4,3,2,1,0,22,21,20,19,18,17,16,15,14,13,12,11,10],[33,32,31,30,29,28,27,26,25,24,23,45,44,43,42,41,40,39,38,37,36,35,34,10,9,8,7,6,5,4,3,2,1,0,22,21,20,19,18,17,16,15,14,13,12,11],[34,33,32,31,30,29,28,27,26,25,24,23,45,44,43,42,41,40,39,38,37,36,35,11,10,9,8,7,6,5,4,3,2,1,0,22,21,20,19,18,17,16,15,14,13,12],[35,34,33,32,31,30,29,28,27,26,25,24,23,45,44,43,42,41,40,39,38,37,36,12,11,10,9,8,7,6,5,4,3,2,1,0,22,21,20,19,18,17,16,15,14,13],[36,35,34,33,32,31,30,29,28,27,26,25,24,23,45,44,43,42,41,40,39,38,37,13,12,11,10,9,8,7,6,5,4,3,2,1,0,22,21,20,19,18,17,16,15,14],[37,36,35,34,33,32,31,30,29,28,27,26,25,24,23,45,44,43,42,41,40,39,38,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0,22,21,20,19,18,17,16,15],[38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,23,45,44,43,42,41,40,39,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0,22,21,20,19,18,17,16],[39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,23,45,44,43,42,41,40,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0,22,21,20,19,18,17],[40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,23,45,44,43,42,41,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0,22,21,20,19,18],[41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,23,45,44,43,42,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0,22,21,20,19],[42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,23,45,44,43,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0,22,21,20],[43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,23,45,44,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0,22,21],[44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,23,45,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0,22],[45,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0]],"identity":0}。請依 [classes, partition_certificate, covered_element_count, group_order, certificate] 欄序回答。

查看答案與解釋([[0], [1, 22], [10, 13], [11, 12], [2, 21], [23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45], [3, 20], [4, 19], [5, 18], [6, 17], [7, 16], [8, 15], [9, 14]], 是, 46, 46, all_conjugacy_classes_are_equal_or_disjoint_and_cover_G)

Wave6第八層核對=([[0], [1, 22], [10, 13], [11, 12], [2, 21], [23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45], [3, 20], [4, 19], [5, 18], [6, 17], [7, 16], [8, 15], [9, 14]], 是, 46, 46, all_conjugacy_classes_are_equal_or_disjoint_and_cover_G)；依完整明示資料獨立重算；共軛類是element orbit並形成完整partition；singleton以forall g commute核對；共軛類不是coset或conjugate subgroup；不使用centralizer、class-size公式或類方程。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r03-finite-group-conjugacy-class-0071/)

有限群共軛類 · qf-mod45-conjugacy-partition-audit · candidate





## 72. 有限群共軛類

由完整Cayley table導出全部conjugation action與orbits。操作=conjugacy-partition-audit；資料={"group_table":[[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,0,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,24],[2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,0,1,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,24,25],[3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,0,1,2,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,24,25,26],[4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,0,1,2,3,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,24,25,26,27],[5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,0,1,2,3,4,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,24,25,26,27,28],[6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,0,1,2,3,4,5,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,24,25,26,27,28,29],[7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,0,1,2,3,4,5,6,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,24,25,26,27,28,29,30],[8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,0,1,2,3,4,5,6,7,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,24,25,26,27,28,29,30,31],[9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,0,1,2,3,4,5,6,7,8,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,24,25,26,27,28,29,30,31,32],[10,11,12,13,14,15,16,17,18,19,20,21,22,23,0,1,2,3,4,5,6,7,8,9,34,35,36,37,38,39,40,41,42,43,44,45,46,47,24,25,26,27,28,29,30,31,32,33],[11,12,13,14,15,16,17,18,19,20,21,22,23,0,1,2,3,4,5,6,7,8,9,10,35,36,37,38,39,40,41,42,43,44,45,46,47,24,25,26,27,28,29,30,31,32,33,34],[12,13,14,15,16,17,18,19,20,21,22,23,0,1,2,3,4,5,6,7,8,9,10,11,36,37,38,39,40,41,42,43,44,45,46,47,24,25,26,27,28,29,30,31,32,33,34,35],[13,14,15,16,17,18,19,20,21,22,23,0,1,2,3,4,5,6,7,8,9,10,11,12,37,38,39,40,41,42,43,44,45,46,47,24,25,26,27,28,29,30,31,32,33,34,35,36],[14,15,16,17,18,19,20,21,22,23,0,1,2,3,4,5,6,7,8,9,10,11,12,13,38,39,40,41,42,43,44,45,46,47,24,25,26,27,28,29,30,31,32,33,34,35,36,37],[15,16,17,18,19,20,21,22,23,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,39,40,41,42,43,44,45,46,47,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38],[16,17,18,19,20,21,22,23,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,40,41,42,43,44,45,46,47,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39],[17,18,19,20,21,22,23,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,41,42,43,44,45,46,47,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40],[18,19,20,21,22,23,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,42,43,44,45,46,47,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41],[19,20,21,22,23,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,43,44,45,46,47,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42],[20,21,22,23,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,44,45,46,47,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],[21,22,23,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,45,46,47,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44],[22,23,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,46,47,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45],[23,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,47,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46],[24,47,46,45,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,0,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1],[25,24,47,46,45,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,1,0,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2],[26,25,24,47,46,45,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,2,1,0,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3],[27,26,25,24,47,46,45,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,3,2,1,0,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4],[28,27,26,25,24,47,46,45,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,4,3,2,1,0,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5],[29,28,27,26,25,24,47,46,45,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,5,4,3,2,1,0,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6],[30,29,28,27,26,25,24,47,46,45,44,43,42,41,40,39,38,37,36,35,34,33,32,31,6,5,4,3,2,1,0,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7],[31,30,29,28,27,26,25,24,47,46,45,44,43,42,41,40,39,38,37,36,35,34,33,32,7,6,5,4,3,2,1,0,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8],[32,31,30,29,28,27,26,25,24,47,46,45,44,43,42,41,40,39,38,37,36,35,34,33,8,7,6,5,4,3,2,1,0,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9],[33,32,31,30,29,28,27,26,25,24,47,46,45,44,43,42,41,40,39,38,37,36,35,34,9,8,7,6,5,4,3,2,1,0,23,22,21,20,19,18,17,16,15,14,13,12,11,10],[34,33,32,31,30,29,28,27,26,25,24,47,46,45,44,43,42,41,40,39,38,37,36,35,10,9,8,7,6,5,4,3,2,1,0,23,22,21,20,19,18,17,16,15,14,13,12,11],[35,34,33,32,31,30,29,28,27,26,25,24,47,46,45,44,43,42,41,40,39,38,37,36,11,10,9,8,7,6,5,4,3,2,1,0,23,22,21,20,19,18,17,16,15,14,13,12],[36,35,34,33,32,31,30,29,28,27,26,25,24,47,46,45,44,43,42,41,40,39,38,37,12,11,10,9,8,7,6,5,4,3,2,1,0,23,22,21,20,19,18,17,16,15,14,13],[37,36,35,34,33,32,31,30,29,28,27,26,25,24,47,46,45,44,43,42,41,40,39,38,13,12,11,10,9,8,7,6,5,4,3,2,1,0,23,22,21,20,19,18,17,16,15,14],[38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,47,46,45,44,43,42,41,40,39,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0,23,22,21,20,19,18,17,16,15],[39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,47,46,45,44,43,42,41,40,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0,23,22,21,20,19,18,17,16],[40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,47,46,45,44,43,42,41,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0,23,22,21,20,19,18,17],[41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,47,46,45,44,43,42,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0,23,22,21,20,19,18],[42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,47,46,45,44,43,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0,23,22,21,20,19],[43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,47,46,45,44,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0,23,22,21,20],[44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,47,46,45,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0,23,22,21],[45,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,47,46,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0,23,22],[46,45,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,47,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0,23],[47,46,45,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0]],"identity":0}。請依 [classes, partition_certificate, covered_element_count, group_order, certificate] 欄序回答。

查看答案與解釋([[0], [1, 23], [10, 14], [11, 13], [12], [2, 22], [24, 26, 28, 30, 32, 34, 36, 38, 40, 42, 44, 46], [25, 27, 29, 31, 33, 35, 37, 39, 41, 43, 45, 47], [3, 21], [4, 20], [5, 19], [6, 18], [7, 17], [8, 16], [9, 15]], 是, 48, 48, all_conjugacy_classes_are_equal_or_disjoint_and_cover_G)

Wave6第八層核對=([[0], [1, 23], [10, 14], [11, 13], [12], [2, 22], [24, 26, 28, 30, 32, 34, 36, 38, 40, 42, 44, 46], [25, 27, 29, 31, 33, 35, 37, 39, 41, 43, 45, 47], [3, 21], [4, 20], [5, 19], [6, 18], [7, 17], [8, 16], [9, 15]], 是, 48, 48, all_conjugacy_classes_are_equal_or_disjoint_and_cover_G)；依完整明示資料獨立重算；共軛類是element orbit並形成完整partition；singleton以forall g commute核對；共軛類不是coset或conjugate subgroup；不使用centralizer、class-size公式或類方程。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r03-finite-group-conjugacy-class-0072/)

有限群共軛類 · qf-mod45-conjugacy-partition-audit · candidate





## 73. 有限群共軛類

由完整Cayley table導出全部conjugation action與orbits。操作=conjugacy-partition-audit；資料={"group_table":[[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,0,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,25],[2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,0,1,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,25,26],[3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,0,1,2,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,25,26,27],[4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,0,1,2,3,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,25,26,27,28],[5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,0,1,2,3,4,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,25,26,27,28,29],[6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,0,1,2,3,4,5,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,25,26,27,28,29,30],[7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,0,1,2,3,4,5,6,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,25,26,27,28,29,30,31],[8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,0,1,2,3,4,5,6,7,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,25,26,27,28,29,30,31,32],[9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,0,1,2,3,4,5,6,7,8,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,25,26,27,28,29,30,31,32,33],[10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,0,1,2,3,4,5,6,7,8,9,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,25,26,27,28,29,30,31,32,33,34],[11,12,13,14,15,16,17,18,19,20,21,22,23,24,0,1,2,3,4,5,6,7,8,9,10,36,37,38,39,40,41,42,43,44,45,46,47,48,49,25,26,27,28,29,30,31,32,33,34,35],[12,13,14,15,16,17,18,19,20,21,22,23,24,0,1,2,3,4,5,6,7,8,9,10,11,37,38,39,40,41,42,43,44,45,46,47,48,49,25,26,27,28,29,30,31,32,33,34,35,36],[13,14,15,16,17,18,19,20,21,22,23,24,0,1,2,3,4,5,6,7,8,9,10,11,12,38,39,40,41,42,43,44,45,46,47,48,49,25,26,27,28,29,30,31,32,33,34,35,36,37],[14,15,16,17,18,19,20,21,22,23,24,0,1,2,3,4,5,6,7,8,9,10,11,12,13,39,40,41,42,43,44,45,46,47,48,49,25,26,27,28,29,30,31,32,33,34,35,36,37,38],[15,16,17,18,19,20,21,22,23,24,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,40,41,42,43,44,45,46,47,48,49,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39],[16,17,18,19,20,21,22,23,24,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,41,42,43,44,45,46,47,48,49,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40],[17,18,19,20,21,22,23,24,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,42,43,44,45,46,47,48,49,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41],[18,19,20,21,22,23,24,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,43,44,45,46,47,48,49,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42],[19,20,21,22,23,24,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,44,45,46,47,48,49,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],[20,21,22,23,24,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,45,46,47,48,49,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44],[21,22,23,24,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,46,47,48,49,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45],[22,23,24,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,47,48,49,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46],[23,24,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,48,49,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47],[24,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,49,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48],[25,49,48,47,46,45,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,0,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1],[26,25,49,48,47,46,45,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,1,0,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2],[27,26,25,49,48,47,46,45,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,2,1,0,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3],[28,27,26,25,49,48,47,46,45,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,3,2,1,0,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4],[29,28,27,26,25,49,48,47,46,45,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,4,3,2,1,0,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5],[30,29,28,27,26,25,49,48,47,46,45,44,43,42,41,40,39,38,37,36,35,34,33,32,31,5,4,3,2,1,0,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6],[31,30,29,28,27,26,25,49,48,47,46,45,44,43,42,41,40,39,38,37,36,35,34,33,32,6,5,4,3,2,1,0,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7],[32,31,30,29,28,27,26,25,49,48,47,46,45,44,43,42,41,40,39,38,37,36,35,34,33,7,6,5,4,3,2,1,0,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8],[33,32,31,30,29,28,27,26,25,49,48,47,46,45,44,43,42,41,40,39,38,37,36,35,34,8,7,6,5,4,3,2,1,0,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9],[34,33,32,31,30,29,28,27,26,25,49,48,47,46,45,44,43,42,41,40,39,38,37,36,35,9,8,7,6,5,4,3,2,1,0,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10],[35,34,33,32,31,30,29,28,27,26,25,49,48,47,46,45,44,43,42,41,40,39,38,37,36,10,9,8,7,6,5,4,3,2,1,0,24,23,22,21,20,19,18,17,16,15,14,13,12,11],[36,35,34,33,32,31,30,29,28,27,26,25,49,48,47,46,45,44,43,42,41,40,39,38,37,11,10,9,8,7,6,5,4,3,2,1,0,24,23,22,21,20,19,18,17,16,15,14,13,12],[37,36,35,34,33,32,31,30,29,28,27,26,25,49,48,47,46,45,44,43,42,41,40,39,38,12,11,10,9,8,7,6,5,4,3,2,1,0,24,23,22,21,20,19,18,17,16,15,14,13],[38,37,36,35,34,33,32,31,30,29,28,27,26,25,49,48,47,46,45,44,43,42,41,40,39,13,12,11,10,9,8,7,6,5,4,3,2,1,0,24,23,22,21,20,19,18,17,16,15,14],[39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,49,48,47,46,45,44,43,42,41,40,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0,24,23,22,21,20,19,18,17,16,15],[40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,49,48,47,46,45,44,43,42,41,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0,24,23,22,21,20,19,18,17,16],[41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,49,48,47,46,45,44,43,42,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0,24,23,22,21,20,19,18,17],[42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,49,48,47,46,45,44,43,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0,24,23,22,21,20,19,18],[43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,49,48,47,46,45,44,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0,24,23,22,21,20,19],[44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,49,48,47,46,45,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0,24,23,22,21,20],[45,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,49,48,47,46,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0,24,23,22,21],[46,45,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,49,48,47,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0,24,23,22],[47,46,45,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,49,48,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0,24,23],[48,47,46,45,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,49,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0,24],[49,48,47,46,45,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0]],"identity":0}。請依 [classes, partition_certificate, covered_element_count, group_order, certificate] 欄序回答。

查看答案與解釋([[0], [1, 24], [10, 15], [11, 14], [12, 13], [2, 23], [25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49], [3, 22], [4, 21], [5, 20], [6, 19], [7, 18], [8, 17], [9, 16]], 是, 50, 50, all_conjugacy_classes_are_equal_or_disjoint_and_cover_G)

Wave6第八層核對=([[0], [1, 24], [10, 15], [11, 14], [12, 13], [2, 23], [25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49], [3, 22], [4, 21], [5, 20], [6, 19], [7, 18], [8, 17], [9, 16]], 是, 50, 50, all_conjugacy_classes_are_equal_or_disjoint_and_cover_G)；依完整明示資料獨立重算；共軛類是element orbit並形成完整partition；singleton以forall g commute核對；共軛類不是coset或conjugate subgroup；不使用centralizer、class-size公式或類方程。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r03-finite-group-conjugacy-class-0073/)

有限群共軛類 · qf-mod45-conjugacy-partition-audit · candidate





## 74. 有限群共軛類

由完整Cayley table導出全部conjugation action與orbits。操作=conjugacy-partition-audit；資料={"group_table":[[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,0,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,26],[2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,0,1,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,26,27],[3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,0,1,2,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,26,27,28],[4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,0,1,2,3,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,26,27,28,29],[5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,0,1,2,3,4,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,26,27,28,29,30],[6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,0,1,2,3,4,5,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,26,27,28,29,30,31],[7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,0,1,2,3,4,5,6,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,26,27,28,29,30,31,32],[8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,0,1,2,3,4,5,6,7,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,26,27,28,29,30,31,32,33],[9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,0,1,2,3,4,5,6,7,8,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,26,27,28,29,30,31,32,33,34],[10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,0,1,2,3,4,5,6,7,8,9,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,26,27,28,29,30,31,32,33,34,35],[11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,0,1,2,3,4,5,6,7,8,9,10,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,26,27,28,29,30,31,32,33,34,35,36],[12,13,14,15,16,17,18,19,20,21,22,23,24,25,0,1,2,3,4,5,6,7,8,9,10,11,38,39,40,41,42,43,44,45,46,47,48,49,50,51,26,27,28,29,30,31,32,33,34,35,36,37],[13,14,15,16,17,18,19,20,21,22,23,24,25,0,1,2,3,4,5,6,7,8,9,10,11,12,39,40,41,42,43,44,45,46,47,48,49,50,51,26,27,28,29,30,31,32,33,34,35,36,37,38],[14,15,16,17,18,19,20,21,22,23,24,25,0,1,2,3,4,5,6,7,8,9,10,11,12,13,40,41,42,43,44,45,46,47,48,49,50,51,26,27,28,29,30,31,32,33,34,35,36,37,38,39],[15,16,17,18,19,20,21,22,23,24,25,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,41,42,43,44,45,46,47,48,49,50,51,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40],[16,17,18,19,20,21,22,23,24,25,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,42,43,44,45,46,47,48,49,50,51,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41],[17,18,19,20,21,22,23,24,25,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,43,44,45,46,47,48,49,50,51,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42],[18,19,20,21,22,23,24,25,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,44,45,46,47,48,49,50,51,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],[19,20,21,22,23,24,25,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,45,46,47,48,49,50,51,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44],[20,21,22,23,24,25,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,46,47,48,49,50,51,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45],[21,22,23,24,25,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,47,48,49,50,51,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46],[22,23,24,25,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,48,49,50,51,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47],[23,24,25,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,49,50,51,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48],[24,25,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,50,51,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49],[25,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,51,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50],[26,51,50,49,48,47,46,45,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,0,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1],[27,26,51,50,49,48,47,46,45,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,1,0,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2],[28,27,26,51,50,49,48,47,46,45,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,2,1,0,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3],[29,28,27,26,51,50,49,48,47,46,45,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,3,2,1,0,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4],[30,29,28,27,26,51,50,49,48,47,46,45,44,43,42,41,40,39,38,37,36,35,34,33,32,31,4,3,2,1,0,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5],[31,30,29,28,27,26,51,50,49,48,47,46,45,44,43,42,41,40,39,38,37,36,35,34,33,32,5,4,3,2,1,0,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6],[32,31,30,29,28,27,26,51,50,49,48,47,46,45,44,43,42,41,40,39,38,37,36,35,34,33,6,5,4,3,2,1,0,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7],[33,32,31,30,29,28,27,26,51,50,49,48,47,46,45,44,43,42,41,40,39,38,37,36,35,34,7,6,5,4,3,2,1,0,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8],[34,33,32,31,30,29,28,27,26,51,50,49,48,47,46,45,44,43,42,41,40,39,38,37,36,35,8,7,6,5,4,3,2,1,0,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9],[35,34,33,32,31,30,29,28,27,26,51,50,49,48,47,46,45,44,43,42,41,40,39,38,37,36,9,8,7,6,5,4,3,2,1,0,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10],[36,35,34,33,32,31,30,29,28,27,26,51,50,49,48,47,46,45,44,43,42,41,40,39,38,37,10,9,8,7,6,5,4,3,2,1,0,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11],[37,36,35,34,33,32,31,30,29,28,27,26,51,50,49,48,47,46,45,44,43,42,41,40,39,38,11,10,9,8,7,6,5,4,3,2,1,0,25,24,23,22,21,20,19,18,17,16,15,14,13,12],[38,37,36,35,34,33,32,31,30,29,28,27,26,51,50,49,48,47,46,45,44,43,42,41,40,39,12,11,10,9,8,7,6,5,4,3,2,1,0,25,24,23,22,21,20,19,18,17,16,15,14,13],[39,38,37,36,35,34,33,32,31,30,29,28,27,26,51,50,49,48,47,46,45,44,43,42,41,40,13,12,11,10,9,8,7,6,5,4,3,2,1,0,25,24,23,22,21,20,19,18,17,16,15,14],[40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,51,50,49,48,47,46,45,44,43,42,41,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0,25,24,23,22,21,20,19,18,17,16,15],[41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,51,50,49,48,47,46,45,44,43,42,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0,25,24,23,22,21,20,19,18,17,16],[42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,51,50,49,48,47,46,45,44,43,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0,25,24,23,22,21,20,19,18,17],[43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,51,50,49,48,47,46,45,44,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0,25,24,23,22,21,20,19,18],[44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,51,50,49,48,47,46,45,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0,25,24,23,22,21,20,19],[45,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,51,50,49,48,47,46,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0,25,24,23,22,21,20],[46,45,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,51,50,49,48,47,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0,25,24,23,22,21],[47,46,45,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,51,50,49,48,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0,25,24,23,22],[48,47,46,45,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,51,50,49,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0,25,24,23],[49,48,47,46,45,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,51,50,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0,25,24],[50,49,48,47,46,45,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,51,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0,25],[51,50,49,48,47,46,45,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0]],"identity":0}。請依 [classes, partition_certificate, covered_element_count, group_order, certificate] 欄序回答。

查看答案與解釋([[0], [1, 25], [10, 16], [11, 15], [12, 14], [13], [2, 24], [26, 28, 30, 32, 34, 36, 38, 40, 42, 44, 46, 48, 50], [27, 29, 31, 33, 35, 37, 39, 41, 43, 45, 47, 49, 51], [3, 23], [4, 22], [5, 21], [6, 20], [7, 19], [8, 18], [9, 17]], 是, 52, 52, all_conjugacy_classes_are_equal_or_disjoint_and_cover_G)

Wave6第八層核對=([[0], [1, 25], [10, 16], [11, 15], [12, 14], [13], [2, 24], [26, 28, 30, 32, 34, 36, 38, 40, 42, 44, 46, 48, 50], [27, 29, 31, 33, 35, 37, 39, 41, 43, 45, 47, 49, 51], [3, 23], [4, 22], [5, 21], [6, 20], [7, 19], [8, 18], [9, 17]], 是, 52, 52, all_conjugacy_classes_are_equal_or_disjoint_and_cover_G)；依完整明示資料獨立重算；共軛類是element orbit並形成完整partition；singleton以forall g commute核對；共軛類不是coset或conjugate subgroup；不使用centralizer、class-size公式或類方程。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r03-finite-group-conjugacy-class-0074/)

有限群共軛類 · qf-mod45-conjugacy-partition-audit · candidate





## 75. 有限群共軛類

由完整Cayley table導出全部conjugation action與orbits。操作=conjugacy-partition-audit；資料={"group_table":[[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,0,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,27],[2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,0,1,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,27,28],[3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,0,1,2,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,27,28,29],[4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,0,1,2,3,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,27,28,29,30],[5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,0,1,2,3,4,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,27,28,29,30,31],[6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,0,1,2,3,4,5,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,27,28,29,30,31,32],[7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,0,1,2,3,4,5,6,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,27,28,29,30,31,32,33],[8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,0,1,2,3,4,5,6,7,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,27,28,29,30,31,32,33,34],[9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,0,1,2,3,4,5,6,7,8,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,27,28,29,30,31,32,33,34,35],[10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,0,1,2,3,4,5,6,7,8,9,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,27,28,29,30,31,32,33,34,35,36],[11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,0,1,2,3,4,5,6,7,8,9,10,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,27,28,29,30,31,32,33,34,35,36,37],[12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,0,1,2,3,4,5,6,7,8,9,10,11,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,27,28,29,30,31,32,33,34,35,36,37,38],[13,14,15,16,17,18,19,20,21,22,23,24,25,26,0,1,2,3,4,5,6,7,8,9,10,11,12,40,41,42,43,44,45,46,47,48,49,50,51,52,53,27,28,29,30,31,32,33,34,35,36,37,38,39],[14,15,16,17,18,19,20,21,22,23,24,25,26,0,1,2,3,4,5,6,7,8,9,10,11,12,13,41,42,43,44,45,46,47,48,49,50,51,52,53,27,28,29,30,31,32,33,34,35,36,37,38,39,40],[15,16,17,18,19,20,21,22,23,24,25,26,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,42,43,44,45,46,47,48,49,50,51,52,53,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41],[16,17,18,19,20,21,22,23,24,25,26,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,43,44,45,46,47,48,49,50,51,52,53,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42],[17,18,19,20,21,22,23,24,25,26,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,44,45,46,47,48,49,50,51,52,53,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],[18,19,20,21,22,23,24,25,26,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,45,46,47,48,49,50,51,52,53,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44],[19,20,21,22,23,24,25,26,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,46,47,48,49,50,51,52,53,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45],[20,21,22,23,24,25,26,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,47,48,49,50,51,52,53,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46],[21,22,23,24,25,26,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,48,49,50,51,52,53,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47],[22,23,24,25,26,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,49,50,51,52,53,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48],[23,24,25,26,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,50,51,52,53,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49],[24,25,26,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,51,52,53,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50],[25,26,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,52,53,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51],[26,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,53,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52],[27,53,52,51,50,49,48,47,46,45,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,0,26,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1],[28,27,53,52,51,50,49,48,47,46,45,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,1,0,26,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2],[29,28,27,53,52,51,50,49,48,47,46,45,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,2,1,0,26,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3],[30,29,28,27,53,52,51,50,49,48,47,46,45,44,43,42,41,40,39,38,37,36,35,34,33,32,31,3,2,1,0,26,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4],[31,30,29,28,27,53,52,51,50,49,48,47,46,45,44,43,42,41,40,39,38,37,36,35,34,33,32,4,3,2,1,0,26,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5],[32,31,30,29,28,27,53,52,51,50,49,48,47,46,45,44,43,42,41,40,39,38,37,36,35,34,33,5,4,3,2,1,0,26,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6],[33,32,31,30,29,28,27,53,52,51,50,49,48,47,46,45,44,43,42,41,40,39,38,37,36,35,34,6,5,4,3,2,1,0,26,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7],[34,33,32,31,30,29,28,27,53,52,51,50,49,48,47,46,45,44,43,42,41,40,39,38,37,36,35,7,6,5,4,3,2,1,0,26,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8],[35,34,33,32,31,30,29,28,27,53,52,51,50,49,48,47,46,45,44,43,42,41,40,39,38,37,36,8,7,6,5,4,3,2,1,0,26,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9],[36,35,34,33,32,31,30,29,28,27,53,52,51,50,49,48,47,46,45,44,43,42,41,40,39,38,37,9,8,7,6,5,4,3,2,1,0,26,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10],[37,36,35,34,33,32,31,30,29,28,27,53,52,51,50,49,48,47,46,45,44,43,42,41,40,39,38,10,9,8,7,6,5,4,3,2,1,0,26,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11],[38,37,36,35,34,33,32,31,30,29,28,27,53,52,51,50,49,48,47,46,45,44,43,42,41,40,39,11,10,9,8,7,6,5,4,3,2,1,0,26,25,24,23,22,21,20,19,18,17,16,15,14,13,12],[39,38,37,36,35,34,33,32,31,30,29,28,27,53,52,51,50,49,48,47,46,45,44,43,42,41,40,12,11,10,9,8,7,6,5,4,3,2,1,0,26,25,24,23,22,21,20,19,18,17,16,15,14,13],[40,39,38,37,36,35,34,33,32,31,30,29,28,27,53,52,51,50,49,48,47,46,45,44,43,42,41,13,12,11,10,9,8,7,6,5,4,3,2,1,0,26,25,24,23,22,21,20,19,18,17,16,15,14],[41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,53,52,51,50,49,48,47,46,45,44,43,42,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0,26,25,24,23,22,21,20,19,18,17,16,15],[42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,53,52,51,50,49,48,47,46,45,44,43,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0,26,25,24,23,22,21,20,19,18,17,16],[43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,53,52,51,50,49,48,47,46,45,44,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0,26,25,24,23,22,21,20,19,18,17],[44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,53,52,51,50,49,48,47,46,45,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0,26,25,24,23,22,21,20,19,18],[45,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,53,52,51,50,49,48,47,46,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0,26,25,24,23,22,21,20,19],[46,45,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,53,52,51,50,49,48,47,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0,26,25,24,23,22,21,20],[47,46,45,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,53,52,51,50,49,48,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0,26,25,24,23,22,21],[48,47,46,45,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,53,52,51,50,49,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0,26,25,24,23,22],[49,48,47,46,45,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,53,52,51,50,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0,26,25,24,23],[50,49,48,47,46,45,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,53,52,51,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0,26,25,24],[51,50,49,48,47,46,45,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,53,52,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0,26,25],[52,51,50,49,48,47,46,45,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,53,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0,26],[53,52,51,50,49,48,47,46,45,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0]],"identity":0}。請依 [classes, partition_certificate, covered_element_count, group_order, certificate] 欄序回答。

查看答案與解釋([[0], [1, 26], [10, 17], [11, 16], [12, 15], [13, 14], [2, 25], [27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53], [3, 24], [4, 23], [5, 22], [6, 21], [7, 20], [8, 19], [9, 18]], 是, 54, 54, all_conjugacy_classes_are_equal_or_disjoint_and_cover_G)

Wave6第八層核對=([[0], [1, 26], [10, 17], [11, 16], [12, 15], [13, 14], [2, 25], [27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53], [3, 24], [4, 23], [5, 22], [6, 21], [7, 20], [8, 19], [9, 18]], 是, 54, 54, all_conjugacy_classes_are_equal_or_disjoint_and_cover_G)；依完整明示資料獨立重算；共軛類是element orbit並形成完整partition；singleton以forall g commute核對；共軛類不是coset或conjugate subgroup；不使用centralizer、class-size公式或類方程。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r03-finite-group-conjugacy-class-0075/)

有限群共軛類 · qf-mod45-conjugacy-partition-audit · candidate





## 76. 有限群共軛類

由完整Cayley table導出全部conjugation action與orbits。操作=conjugacy-singleton-nonconjugate-boundary；資料={"group_table":[[0,1,2,3,4,5],[1,2,0,4,5,3],[2,0,1,5,3,4],[3,5,4,0,2,1],[4,3,5,1,0,2],[5,4,3,2,1,0]],"identity":0,"element":0,"other":3}。請依 [element, singleton_class, commutes_with_all, other, conjugate_to_other, nonconjugate_certificate, boundary] 欄序回答。

查看答案與解釋(0, [0], 是, 3, 否, 是, singleton_class_iff_commutes_with_every_g_and_other_outside_class_is_nonconjugate_without_class_size_formula)

Wave6第八層核對=(0, [0], 是, 3, 否, 是, singleton_class_iff_commutes_with_every_g_and_other_outside_class_is_nonconjugate_without_class_size_formula)；依完整明示資料獨立重算；共軛類是element orbit並形成完整partition；singleton以forall g commute核對；共軛類不是coset或conjugate subgroup；不使用centralizer、class-size公式或類方程。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r03-finite-group-conjugacy-class-0076/)

有限群共軛類 · qf-mod45-conjugacy-singleton-nonconjugate-boundary · candidate





## 77. 有限群共軛類

由完整Cayley table導出全部conjugation action與orbits。操作=conjugacy-singleton-nonconjugate-boundary；資料={"group_table":[[0,1,2,3,4,5,6,7],[1,2,3,0,5,6,7,4],[2,3,0,1,6,7,4,5],[3,0,1,2,7,4,5,6],[4,7,6,5,0,3,2,1],[5,4,7,6,1,0,3,2],[6,5,4,7,2,1,0,3],[7,6,5,4,3,2,1,0]],"identity":0,"element":0,"other":4}。請依 [element, singleton_class, commutes_with_all, other, conjugate_to_other, nonconjugate_certificate, boundary] 欄序回答。

查看答案與解釋(0, [0], 是, 4, 否, 是, singleton_class_iff_commutes_with_every_g_and_other_outside_class_is_nonconjugate_without_class_size_formula)

Wave6第八層核對=(0, [0], 是, 4, 否, 是, singleton_class_iff_commutes_with_every_g_and_other_outside_class_is_nonconjugate_without_class_size_formula)；依完整明示資料獨立重算；共軛類是element orbit並形成完整partition；singleton以forall g commute核對；共軛類不是coset或conjugate subgroup；不使用centralizer、class-size公式或類方程。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r03-finite-group-conjugacy-class-0077/)

有限群共軛類 · qf-mod45-conjugacy-singleton-nonconjugate-boundary · candidate





## 78. 有限群共軛類

由完整Cayley table導出全部conjugation action與orbits。操作=conjugacy-singleton-nonconjugate-boundary；資料={"group_table":[[0,1,2,3,4,5,6,7,8,9],[1,2,3,4,0,6,7,8,9,5],[2,3,4,0,1,7,8,9,5,6],[3,4,0,1,2,8,9,5,6,7],[4,0,1,2,3,9,5,6,7,8],[5,9,8,7,6,0,4,3,2,1],[6,5,9,8,7,1,0,4,3,2],[7,6,5,9,8,2,1,0,4,3],[8,7,6,5,9,3,2,1,0,4],[9,8,7,6,5,4,3,2,1,0]],"identity":0,"element":0,"other":5}。請依 [element, singleton_class, commutes_with_all, other, conjugate_to_other, nonconjugate_certificate, boundary] 欄序回答。

查看答案與解釋(0, [0], 是, 5, 否, 是, singleton_class_iff_commutes_with_every_g_and_other_outside_class_is_nonconjugate_without_class_size_formula)

Wave6第八層核對=(0, [0], 是, 5, 否, 是, singleton_class_iff_commutes_with_every_g_and_other_outside_class_is_nonconjugate_without_class_size_formula)；依完整明示資料獨立重算；共軛類是element orbit並形成完整partition；singleton以forall g commute核對；共軛類不是coset或conjugate subgroup；不使用centralizer、class-size公式或類方程。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r03-finite-group-conjugacy-class-0078/)

有限群共軛類 · qf-mod45-conjugacy-singleton-nonconjugate-boundary · candidate





## 79. 有限群共軛類

由完整Cayley table導出全部conjugation action與orbits。操作=conjugacy-singleton-nonconjugate-boundary；資料={"group_table":[[0,1,2,3,4,5,6,7,8,9,10,11],[1,2,3,4,5,0,7,8,9,10,11,6],[2,3,4,5,0,1,8,9,10,11,6,7],[3,4,5,0,1,2,9,10,11,6,7,8],[4,5,0,1,2,3,10,11,6,7,8,9],[5,0,1,2,3,4,11,6,7,8,9,10],[6,11,10,9,8,7,0,5,4,3,2,1],[7,6,11,10,9,8,1,0,5,4,3,2],[8,7,6,11,10,9,2,1,0,5,4,3],[9,8,7,6,11,10,3,2,1,0,5,4],[10,9,8,7,6,11,4,3,2,1,0,5],[11,10,9,8,7,6,5,4,3,2,1,0]],"identity":0,"element":0,"other":6}。請依 [element, singleton_class, commutes_with_all, other, conjugate_to_other, nonconjugate_certificate, boundary] 欄序回答。

查看答案與解釋(0, [0], 是, 6, 否, 是, singleton_class_iff_commutes_with_every_g_and_other_outside_class_is_nonconjugate_without_class_size_formula)

Wave6第八層核對=(0, [0], 是, 6, 否, 是, singleton_class_iff_commutes_with_every_g_and_other_outside_class_is_nonconjugate_without_class_size_formula)；依完整明示資料獨立重算；共軛類是element orbit並形成完整partition；singleton以forall g commute核對；共軛類不是coset或conjugate subgroup；不使用centralizer、class-size公式或類方程。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r03-finite-group-conjugacy-class-0079/)

有限群共軛類 · qf-mod45-conjugacy-singleton-nonconjugate-boundary · candidate





## 80. 有限群共軛類

由完整Cayley table導出全部conjugation action與orbits。操作=conjugacy-singleton-nonconjugate-boundary；資料={"group_table":[[0,1,2,3,4,5,6,7,8,9,10,11,12,13],[1,2,3,4,5,6,0,8,9,10,11,12,13,7],[2,3,4,5,6,0,1,9,10,11,12,13,7,8],[3,4,5,6,0,1,2,10,11,12,13,7,8,9],[4,5,6,0,1,2,3,11,12,13,7,8,9,10],[5,6,0,1,2,3,4,12,13,7,8,9,10,11],[6,0,1,2,3,4,5,13,7,8,9,10,11,12],[7,13,12,11,10,9,8,0,6,5,4,3,2,1],[8,7,13,12,11,10,9,1,0,6,5,4,3,2],[9,8,7,13,12,11,10,2,1,0,6,5,4,3],[10,9,8,7,13,12,11,3,2,1,0,6,5,4],[11,10,9,8,7,13,12,4,3,2,1,0,6,5],[12,11,10,9,8,7,13,5,4,3,2,1,0,6],[13,12,11,10,9,8,7,6,5,4,3,2,1,0]],"identity":0,"element":0,"other":7}。請依 [element, singleton_class, commutes_with_all, other, conjugate_to_other, nonconjugate_certificate, boundary] 欄序回答。

查看答案與解釋(0, [0], 是, 7, 否, 是, singleton_class_iff_commutes_with_every_g_and_other_outside_class_is_nonconjugate_without_class_size_formula)

Wave6第八層核對=(0, [0], 是, 7, 否, 是, singleton_class_iff_commutes_with_every_g_and_other_outside_class_is_nonconjugate_without_class_size_formula)；依完整明示資料獨立重算；共軛類是element orbit並形成完整partition；singleton以forall g commute核對；共軛類不是coset或conjugate subgroup；不使用centralizer、class-size公式或類方程。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r03-finite-group-conjugacy-class-0080/)

有限群共軛類 · qf-mod45-conjugacy-singleton-nonconjugate-boundary · candidate





## 81. 有限群共軛類

由完整Cayley table導出全部conjugation action與orbits。操作=conjugacy-singleton-nonconjugate-boundary；資料={"group_table":[[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15],[1,2,3,4,5,6,7,0,9,10,11,12,13,14,15,8],[2,3,4,5,6,7,0,1,10,11,12,13,14,15,8,9],[3,4,5,6,7,0,1,2,11,12,13,14,15,8,9,10],[4,5,6,7,0,1,2,3,12,13,14,15,8,9,10,11],[5,6,7,0,1,2,3,4,13,14,15,8,9,10,11,12],[6,7,0,1,2,3,4,5,14,15,8,9,10,11,12,13],[7,0,1,2,3,4,5,6,15,8,9,10,11,12,13,14],[8,15,14,13,12,11,10,9,0,7,6,5,4,3,2,1],[9,8,15,14,13,12,11,10,1,0,7,6,5,4,3,2],[10,9,8,15,14,13,12,11,2,1,0,7,6,5,4,3],[11,10,9,8,15,14,13,12,3,2,1,0,7,6,5,4],[12,11,10,9,8,15,14,13,4,3,2,1,0,7,6,5],[13,12,11,10,9,8,15,14,5,4,3,2,1,0,7,6],[14,13,12,11,10,9,8,15,6,5,4,3,2,1,0,7],[15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0]],"identity":0,"element":0,"other":8}。請依 [element, singleton_class, commutes_with_all, other, conjugate_to_other, nonconjugate_certificate, boundary] 欄序回答。

查看答案與解釋(0, [0], 是, 8, 否, 是, singleton_class_iff_commutes_with_every_g_and_other_outside_class_is_nonconjugate_without_class_size_formula)

Wave6第八層核對=(0, [0], 是, 8, 否, 是, singleton_class_iff_commutes_with_every_g_and_other_outside_class_is_nonconjugate_without_class_size_formula)；依完整明示資料獨立重算；共軛類是element orbit並形成完整partition；singleton以forall g commute核對；共軛類不是coset或conjugate subgroup；不使用centralizer、class-size公式或類方程。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r03-finite-group-conjugacy-class-0081/)

有限群共軛類 · qf-mod45-conjugacy-singleton-nonconjugate-boundary · candidate





## 82. 有限群共軛類

由完整Cayley table導出全部conjugation action與orbits。操作=conjugacy-singleton-nonconjugate-boundary；資料={"group_table":[[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17],[1,2,3,4,5,6,7,8,0,10,11,12,13,14,15,16,17,9],[2,3,4,5,6,7,8,0,1,11,12,13,14,15,16,17,9,10],[3,4,5,6,7,8,0,1,2,12,13,14,15,16,17,9,10,11],[4,5,6,7,8,0,1,2,3,13,14,15,16,17,9,10,11,12],[5,6,7,8,0,1,2,3,4,14,15,16,17,9,10,11,12,13],[6,7,8,0,1,2,3,4,5,15,16,17,9,10,11,12,13,14],[7,8,0,1,2,3,4,5,6,16,17,9,10,11,12,13,14,15],[8,0,1,2,3,4,5,6,7,17,9,10,11,12,13,14,15,16],[9,17,16,15,14,13,12,11,10,0,8,7,6,5,4,3,2,1],[10,9,17,16,15,14,13,12,11,1,0,8,7,6,5,4,3,2],[11,10,9,17,16,15,14,13,12,2,1,0,8,7,6,5,4,3],[12,11,10,9,17,16,15,14,13,3,2,1,0,8,7,6,5,4],[13,12,11,10,9,17,16,15,14,4,3,2,1,0,8,7,6,5],[14,13,12,11,10,9,17,16,15,5,4,3,2,1,0,8,7,6],[15,14,13,12,11,10,9,17,16,6,5,4,3,2,1,0,8,7],[16,15,14,13,12,11,10,9,17,7,6,5,4,3,2,1,0,8],[17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0]],"identity":0,"element":0,"other":9}。請依 [element, singleton_class, commutes_with_all, other, conjugate_to_other, nonconjugate_certificate, boundary] 欄序回答。

查看答案與解釋(0, [0], 是, 9, 否, 是, singleton_class_iff_commutes_with_every_g_and_other_outside_class_is_nonconjugate_without_class_size_formula)

Wave6第八層核對=(0, [0], 是, 9, 否, 是, singleton_class_iff_commutes_with_every_g_and_other_outside_class_is_nonconjugate_without_class_size_formula)；依完整明示資料獨立重算；共軛類是element orbit並形成完整partition；singleton以forall g commute核對；共軛類不是coset或conjugate subgroup；不使用centralizer、class-size公式或類方程。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r03-finite-group-conjugacy-class-0082/)

有限群共軛類 · qf-mod45-conjugacy-singleton-nonconjugate-boundary · candidate





## 83. 有限群共軛類

由完整Cayley table導出全部conjugation action與orbits。操作=conjugacy-singleton-nonconjugate-boundary；資料={"group_table":[[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19],[1,2,3,4,5,6,7,8,9,0,11,12,13,14,15,16,17,18,19,10],[2,3,4,5,6,7,8,9,0,1,12,13,14,15,16,17,18,19,10,11],[3,4,5,6,7,8,9,0,1,2,13,14,15,16,17,18,19,10,11,12],[4,5,6,7,8,9,0,1,2,3,14,15,16,17,18,19,10,11,12,13],[5,6,7,8,9,0,1,2,3,4,15,16,17,18,19,10,11,12,13,14],[6,7,8,9,0,1,2,3,4,5,16,17,18,19,10,11,12,13,14,15],[7,8,9,0,1,2,3,4,5,6,17,18,19,10,11,12,13,14,15,16],[8,9,0,1,2,3,4,5,6,7,18,19,10,11,12,13,14,15,16,17],[9,0,1,2,3,4,5,6,7,8,19,10,11,12,13,14,15,16,17,18],[10,19,18,17,16,15,14,13,12,11,0,9,8,7,6,5,4,3,2,1],[11,10,19,18,17,16,15,14,13,12,1,0,9,8,7,6,5,4,3,2],[12,11,10,19,18,17,16,15,14,13,2,1,0,9,8,7,6,5,4,3],[13,12,11,10,19,18,17,16,15,14,3,2,1,0,9,8,7,6,5,4],[14,13,12,11,10,19,18,17,16,15,4,3,2,1,0,9,8,7,6,5],[15,14,13,12,11,10,19,18,17,16,5,4,3,2,1,0,9,8,7,6],[16,15,14,13,12,11,10,19,18,17,6,5,4,3,2,1,0,9,8,7],[17,16,15,14,13,12,11,10,19,18,7,6,5,4,3,2,1,0,9,8],[18,17,16,15,14,13,12,11,10,19,8,7,6,5,4,3,2,1,0,9],[19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0]],"identity":0,"element":0,"other":10}。請依 [element, singleton_class, commutes_with_all, other, conjugate_to_other, nonconjugate_certificate, boundary] 欄序回答。

查看答案與解釋(0, [0], 是, 10, 否, 是, singleton_class_iff_commutes_with_every_g_and_other_outside_class_is_nonconjugate_without_class_size_formula)

Wave6第八層核對=(0, [0], 是, 10, 否, 是, singleton_class_iff_commutes_with_every_g_and_other_outside_class_is_nonconjugate_without_class_size_formula)；依完整明示資料獨立重算；共軛類是element orbit並形成完整partition；singleton以forall g commute核對；共軛類不是coset或conjugate subgroup；不使用centralizer、class-size公式或類方程。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r03-finite-group-conjugacy-class-0083/)

有限群共軛類 · qf-mod45-conjugacy-singleton-nonconjugate-boundary · candidate





## 84. 有限群共軛類

由完整Cayley table導出全部conjugation action與orbits。操作=conjugacy-singleton-nonconjugate-boundary；資料={"group_table":[[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21],[1,2,3,4,5,6,7,8,9,10,0,12,13,14,15,16,17,18,19,20,21,11],[2,3,4,5,6,7,8,9,10,0,1,13,14,15,16,17,18,19,20,21,11,12],[3,4,5,6,7,8,9,10,0,1,2,14,15,16,17,18,19,20,21,11,12,13],[4,5,6,7,8,9,10,0,1,2,3,15,16,17,18,19,20,21,11,12,13,14],[5,6,7,8,9,10,0,1,2,3,4,16,17,18,19,20,21,11,12,13,14,15],[6,7,8,9,10,0,1,2,3,4,5,17,18,19,20,21,11,12,13,14,15,16],[7,8,9,10,0,1,2,3,4,5,6,18,19,20,21,11,12,13,14,15,16,17],[8,9,10,0,1,2,3,4,5,6,7,19,20,21,11,12,13,14,15,16,17,18],[9,10,0,1,2,3,4,5,6,7,8,20,21,11,12,13,14,15,16,17,18,19],[10,0,1,2,3,4,5,6,7,8,9,21,11,12,13,14,15,16,17,18,19,20],[11,21,20,19,18,17,16,15,14,13,12,0,10,9,8,7,6,5,4,3,2,1],[12,11,21,20,19,18,17,16,15,14,13,1,0,10,9,8,7,6,5,4,3,2],[13,12,11,21,20,19,18,17,16,15,14,2,1,0,10,9,8,7,6,5,4,3],[14,13,12,11,21,20,19,18,17,16,15,3,2,1,0,10,9,8,7,6,5,4],[15,14,13,12,11,21,20,19,18,17,16,4,3,2,1,0,10,9,8,7,6,5],[16,15,14,13,12,11,21,20,19,18,17,5,4,3,2,1,0,10,9,8,7,6],[17,16,15,14,13,12,11,21,20,19,18,6,5,4,3,2,1,0,10,9,8,7],[18,17,16,15,14,13,12,11,21,20,19,7,6,5,4,3,2,1,0,10,9,8],[19,18,17,16,15,14,13,12,11,21,20,8,7,6,5,4,3,2,1,0,10,9],[20,19,18,17,16,15,14,13,12,11,21,9,8,7,6,5,4,3,2,1,0,10],[21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0]],"identity":0,"element":0,"other":11}。請依 [element, singleton_class, commutes_with_all, other, conjugate_to_other, nonconjugate_certificate, boundary] 欄序回答。

查看答案與解釋(0, [0], 是, 11, 否, 是, singleton_class_iff_commutes_with_every_g_and_other_outside_class_is_nonconjugate_without_class_size_formula)

Wave6第八層核對=(0, [0], 是, 11, 否, 是, singleton_class_iff_commutes_with_every_g_and_other_outside_class_is_nonconjugate_without_class_size_formula)；依完整明示資料獨立重算；共軛類是element orbit並形成完整partition；singleton以forall g commute核對；共軛類不是coset或conjugate subgroup；不使用centralizer、class-size公式或類方程。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r03-finite-group-conjugacy-class-0084/)

有限群共軛類 · qf-mod45-conjugacy-singleton-nonconjugate-boundary · candidate





## 85. 有限群共軛類

由完整Cayley table導出全部conjugation action與orbits。操作=conjugacy-singleton-nonconjugate-boundary；資料={"group_table":[[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23],[1,2,3,4,5,6,7,8,9,10,11,0,13,14,15,16,17,18,19,20,21,22,23,12],[2,3,4,5,6,7,8,9,10,11,0,1,14,15,16,17,18,19,20,21,22,23,12,13],[3,4,5,6,7,8,9,10,11,0,1,2,15,16,17,18,19,20,21,22,23,12,13,14],[4,5,6,7,8,9,10,11,0,1,2,3,16,17,18,19,20,21,22,23,12,13,14,15],[5,6,7,8,9,10,11,0,1,2,3,4,17,18,19,20,21,22,23,12,13,14,15,16],[6,7,8,9,10,11,0,1,2,3,4,5,18,19,20,21,22,23,12,13,14,15,16,17],[7,8,9,10,11,0,1,2,3,4,5,6,19,20,21,22,23,12,13,14,15,16,17,18],[8,9,10,11,0,1,2,3,4,5,6,7,20,21,22,23,12,13,14,15,16,17,18,19],[9,10,11,0,1,2,3,4,5,6,7,8,21,22,23,12,13,14,15,16,17,18,19,20],[10,11,0,1,2,3,4,5,6,7,8,9,22,23,12,13,14,15,16,17,18,19,20,21],[11,0,1,2,3,4,5,6,7,8,9,10,23,12,13,14,15,16,17,18,19,20,21,22],[12,23,22,21,20,19,18,17,16,15,14,13,0,11,10,9,8,7,6,5,4,3,2,1],[13,12,23,22,21,20,19,18,17,16,15,14,1,0,11,10,9,8,7,6,5,4,3,2],[14,13,12,23,22,21,20,19,18,17,16,15,2,1,0,11,10,9,8,7,6,5,4,3],[15,14,13,12,23,22,21,20,19,18,17,16,3,2,1,0,11,10,9,8,7,6,5,4],[16,15,14,13,12,23,22,21,20,19,18,17,4,3,2,1,0,11,10,9,8,7,6,5],[17,16,15,14,13,12,23,22,21,20,19,18,5,4,3,2,1,0,11,10,9,8,7,6],[18,17,16,15,14,13,12,23,22,21,20,19,6,5,4,3,2,1,0,11,10,9,8,7],[19,18,17,16,15,14,13,12,23,22,21,20,7,6,5,4,3,2,1,0,11,10,9,8],[20,19,18,17,16,15,14,13,12,23,22,21,8,7,6,5,4,3,2,1,0,11,10,9],[21,20,19,18,17,16,15,14,13,12,23,22,9,8,7,6,5,4,3,2,1,0,11,10],[22,21,20,19,18,17,16,15,14,13,12,23,10,9,8,7,6,5,4,3,2,1,0,11],[23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0]],"identity":0,"element":0,"other":12}。請依 [element, singleton_class, commutes_with_all, other, conjugate_to_other, nonconjugate_certificate, boundary] 欄序回答。

查看答案與解釋(0, [0], 是, 12, 否, 是, singleton_class_iff_commutes_with_every_g_and_other_outside_class_is_nonconjugate_without_class_size_formula)

Wave6第八層核對=(0, [0], 是, 12, 否, 是, singleton_class_iff_commutes_with_every_g_and_other_outside_class_is_nonconjugate_without_class_size_formula)；依完整明示資料獨立重算；共軛類是element orbit並形成完整partition；singleton以forall g commute核對；共軛類不是coset或conjugate subgroup；不使用centralizer、class-size公式或類方程。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r03-finite-group-conjugacy-class-0085/)

有限群共軛類 · qf-mod45-conjugacy-singleton-nonconjugate-boundary · candidate





## 86. 有限群共軛類

由完整Cayley table導出全部conjugation action與orbits。操作=conjugacy-singleton-nonconjugate-boundary；資料={"group_table":[[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25],[1,2,3,4,5,6,7,8,9,10,11,12,0,14,15,16,17,18,19,20,21,22,23,24,25,13],[2,3,4,5,6,7,8,9,10,11,12,0,1,15,16,17,18,19,20,21,22,23,24,25,13,14],[3,4,5,6,7,8,9,10,11,12,0,1,2,16,17,18,19,20,21,22,23,24,25,13,14,15],[4,5,6,7,8,9,10,11,12,0,1,2,3,17,18,19,20,21,22,23,24,25,13,14,15,16],[5,6,7,8,9,10,11,12,0,1,2,3,4,18,19,20,21,22,23,24,25,13,14,15,16,17],[6,7,8,9,10,11,12,0,1,2,3,4,5,19,20,21,22,23,24,25,13,14,15,16,17,18],[7,8,9,10,11,12,0,1,2,3,4,5,6,20,21,22,23,24,25,13,14,15,16,17,18,19],[8,9,10,11,12,0,1,2,3,4,5,6,7,21,22,23,24,25,13,14,15,16,17,18,19,20],[9,10,11,12,0,1,2,3,4,5,6,7,8,22,23,24,25,13,14,15,16,17,18,19,20,21],[10,11,12,0,1,2,3,4,5,6,7,8,9,23,24,25,13,14,15,16,17,18,19,20,21,22],[11,12,0,1,2,3,4,5,6,7,8,9,10,24,25,13,14,15,16,17,18,19,20,21,22,23],[12,0,1,2,3,4,5,6,7,8,9,10,11,25,13,14,15,16,17,18,19,20,21,22,23,24],[13,25,24,23,22,21,20,19,18,17,16,15,14,0,12,11,10,9,8,7,6,5,4,3,2,1],[14,13,25,24,23,22,21,20,19,18,17,16,15,1,0,12,11,10,9,8,7,6,5,4,3,2],[15,14,13,25,24,23,22,21,20,19,18,17,16,2,1,0,12,11,10,9,8,7,6,5,4,3],[16,15,14,13,25,24,23,22,21,20,19,18,17,3,2,1,0,12,11,10,9,8,7,6,5,4],[17,16,15,14,13,25,24,23,22,21,20,19,18,4,3,2,1,0,12,11,10,9,8,7,6,5],[18,17,16,15,14,13,25,24,23,22,21,20,19,5,4,3,2,1,0,12,11,10,9,8,7,6],[19,18,17,16,15,14,13,25,24,23,22,21,20,6,5,4,3,2,1,0,12,11,10,9,8,7],[20,19,18,17,16,15,14,13,25,24,23,22,21,7,6,5,4,3,2,1,0,12,11,10,9,8],[21,20,19,18,17,16,15,14,13,25,24,23,22,8,7,6,5,4,3,2,1,0,12,11,10,9],[22,21,20,19,18,17,16,15,14,13,25,24,23,9,8,7,6,5,4,3,2,1,0,12,11,10],[23,22,21,20,19,18,17,16,15,14,13,25,24,10,9,8,7,6,5,4,3,2,1,0,12,11],[24,23,22,21,20,19,18,17,16,15,14,13,25,11,10,9,8,7,6,5,4,3,2,1,0,12],[25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0]],"identity":0,"element":0,"other":13}。請依 [element, singleton_class, commutes_with_all, other, conjugate_to_other, nonconjugate_certificate, boundary] 欄序回答。

查看答案與解釋(0, [0], 是, 13, 否, 是, singleton_class_iff_commutes_with_every_g_and_other_outside_class_is_nonconjugate_without_class_size_formula)

Wave6第八層核對=(0, [0], 是, 13, 否, 是, singleton_class_iff_commutes_with_every_g_and_other_outside_class_is_nonconjugate_without_class_size_formula)；依完整明示資料獨立重算；共軛類是element orbit並形成完整partition；singleton以forall g commute核對；共軛類不是coset或conjugate subgroup；不使用centralizer、class-size公式或類方程。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r03-finite-group-conjugacy-class-0086/)

有限群共軛類 · qf-mod45-conjugacy-singleton-nonconjugate-boundary · candidate





## 87. 有限群共軛類

由完整Cayley table導出全部conjugation action與orbits。操作=conjugacy-singleton-nonconjugate-boundary；資料={"group_table":[[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27],[1,2,3,4,5,6,7,8,9,10,11,12,13,0,15,16,17,18,19,20,21,22,23,24,25,26,27,14],[2,3,4,5,6,7,8,9,10,11,12,13,0,1,16,17,18,19,20,21,22,23,24,25,26,27,14,15],[3,4,5,6,7,8,9,10,11,12,13,0,1,2,17,18,19,20,21,22,23,24,25,26,27,14,15,16],[4,5,6,7,8,9,10,11,12,13,0,1,2,3,18,19,20,21,22,23,24,25,26,27,14,15,16,17],[5,6,7,8,9,10,11,12,13,0,1,2,3,4,19,20,21,22,23,24,25,26,27,14,15,16,17,18],[6,7,8,9,10,11,12,13,0,1,2,3,4,5,20,21,22,23,24,25,26,27,14,15,16,17,18,19],[7,8,9,10,11,12,13,0,1,2,3,4,5,6,21,22,23,24,25,26,27,14,15,16,17,18,19,20],[8,9,10,11,12,13,0,1,2,3,4,5,6,7,22,23,24,25,26,27,14,15,16,17,18,19,20,21],[9,10,11,12,13,0,1,2,3,4,5,6,7,8,23,24,25,26,27,14,15,16,17,18,19,20,21,22],[10,11,12,13,0,1,2,3,4,5,6,7,8,9,24,25,26,27,14,15,16,17,18,19,20,21,22,23],[11,12,13,0,1,2,3,4,5,6,7,8,9,10,25,26,27,14,15,16,17,18,19,20,21,22,23,24],[12,13,0,1,2,3,4,5,6,7,8,9,10,11,26,27,14,15,16,17,18,19,20,21,22,23,24,25],[13,0,1,2,3,4,5,6,7,8,9,10,11,12,27,14,15,16,17,18,19,20,21,22,23,24,25,26],[14,27,26,25,24,23,22,21,20,19,18,17,16,15,0,13,12,11,10,9,8,7,6,5,4,3,2,1],[15,14,27,26,25,24,23,22,21,20,19,18,17,16,1,0,13,12,11,10,9,8,7,6,5,4,3,2],[16,15,14,27,26,25,24,23,22,21,20,19,18,17,2,1,0,13,12,11,10,9,8,7,6,5,4,3],[17,16,15,14,27,26,25,24,23,22,21,20,19,18,3,2,1,0,13,12,11,10,9,8,7,6,5,4],[18,17,16,15,14,27,26,25,24,23,22,21,20,19,4,3,2,1,0,13,12,11,10,9,8,7,6,5],[19,18,17,16,15,14,27,26,25,24,23,22,21,20,5,4,3,2,1,0,13,12,11,10,9,8,7,6],[20,19,18,17,16,15,14,27,26,25,24,23,22,21,6,5,4,3,2,1,0,13,12,11,10,9,8,7],[21,20,19,18,17,16,15,14,27,26,25,24,23,22,7,6,5,4,3,2,1,0,13,12,11,10,9,8],[22,21,20,19,18,17,16,15,14,27,26,25,24,23,8,7,6,5,4,3,2,1,0,13,12,11,10,9],[23,22,21,20,19,18,17,16,15,14,27,26,25,24,9,8,7,6,5,4,3,2,1,0,13,12,11,10],[24,23,22,21,20,19,18,17,16,15,14,27,26,25,10,9,8,7,6,5,4,3,2,1,0,13,12,11],[25,24,23,22,21,20,19,18,17,16,15,14,27,26,11,10,9,8,7,6,5,4,3,2,1,0,13,12],[26,25,24,23,22,21,20,19,18,17,16,15,14,27,12,11,10,9,8,7,6,5,4,3,2,1,0,13],[27,26,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0]],"identity":0,"element":0,"other":14}。請依 [element, singleton_class, commutes_with_all, other, conjugate_to_other, nonconjugate_certificate, boundary] 欄序回答。

查看答案與解釋(0, [0], 是, 14, 否, 是, singleton_class_iff_commutes_with_every_g_and_other_outside_class_is_nonconjugate_without_class_size_formula)

Wave6第八層核對=(0, [0], 是, 14, 否, 是, singleton_class_iff_commutes_with_every_g_and_other_outside_class_is_nonconjugate_without_class_size_formula)；依完整明示資料獨立重算；共軛類是element orbit並形成完整partition；singleton以forall g commute核對；共軛類不是coset或conjugate subgroup；不使用centralizer、class-size公式或類方程。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r03-finite-group-conjugacy-class-0087/)

有限群共軛類 · qf-mod45-conjugacy-singleton-nonconjugate-boundary · candidate





## 88. 有限群共軛類

由完整Cayley table導出全部conjugation action與orbits。操作=conjugacy-singleton-nonconjugate-boundary；資料={"group_table":[[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,0,16,17,18,19,20,21,22,23,24,25,26,27,28,29,15],[2,3,4,5,6,7,8,9,10,11,12,13,14,0,1,17,18,19,20,21,22,23,24,25,26,27,28,29,15,16],[3,4,5,6,7,8,9,10,11,12,13,14,0,1,2,18,19,20,21,22,23,24,25,26,27,28,29,15,16,17],[4,5,6,7,8,9,10,11,12,13,14,0,1,2,3,19,20,21,22,23,24,25,26,27,28,29,15,16,17,18],[5,6,7,8,9,10,11,12,13,14,0,1,2,3,4,20,21,22,23,24,25,26,27,28,29,15,16,17,18,19],[6,7,8,9,10,11,12,13,14,0,1,2,3,4,5,21,22,23,24,25,26,27,28,29,15,16,17,18,19,20],[7,8,9,10,11,12,13,14,0,1,2,3,4,5,6,22,23,24,25,26,27,28,29,15,16,17,18,19,20,21],[8,9,10,11,12,13,14,0,1,2,3,4,5,6,7,23,24,25,26,27,28,29,15,16,17,18,19,20,21,22],[9,10,11,12,13,14,0,1,2,3,4,5,6,7,8,24,25,26,27,28,29,15,16,17,18,19,20,21,22,23],[10,11,12,13,14,0,1,2,3,4,5,6,7,8,9,25,26,27,28,29,15,16,17,18,19,20,21,22,23,24],[11,12,13,14,0,1,2,3,4,5,6,7,8,9,10,26,27,28,29,15,16,17,18,19,20,21,22,23,24,25],[12,13,14,0,1,2,3,4,5,6,7,8,9,10,11,27,28,29,15,16,17,18,19,20,21,22,23,24,25,26],[13,14,0,1,2,3,4,5,6,7,8,9,10,11,12,28,29,15,16,17,18,19,20,21,22,23,24,25,26,27],[14,0,1,2,3,4,5,6,7,8,9,10,11,12,13,29,15,16,17,18,19,20,21,22,23,24,25,26,27,28],[15,29,28,27,26,25,24,23,22,21,20,19,18,17,16,0,14,13,12,11,10,9,8,7,6,5,4,3,2,1],[16,15,29,28,27,26,25,24,23,22,21,20,19,18,17,1,0,14,13,12,11,10,9,8,7,6,5,4,3,2],[17,16,15,29,28,27,26,25,24,23,22,21,20,19,18,2,1,0,14,13,12,11,10,9,8,7,6,5,4,3],[18,17,16,15,29,28,27,26,25,24,23,22,21,20,19,3,2,1,0,14,13,12,11,10,9,8,7,6,5,4],[19,18,17,16,15,29,28,27,26,25,24,23,22,21,20,4,3,2,1,0,14,13,12,11,10,9,8,7,6,5],[20,19,18,17,16,15,29,28,27,26,25,24,23,22,21,5,4,3,2,1,0,14,13,12,11,10,9,8,7,6],[21,20,19,18,17,16,15,29,28,27,26,25,24,23,22,6,5,4,3,2,1,0,14,13,12,11,10,9,8,7],[22,21,20,19,18,17,16,15,29,28,27,26,25,24,23,7,6,5,4,3,2,1,0,14,13,12,11,10,9,8],[23,22,21,20,19,18,17,16,15,29,28,27,26,25,24,8,7,6,5,4,3,2,1,0,14,13,12,11,10,9],[24,23,22,21,20,19,18,17,16,15,29,28,27,26,25,9,8,7,6,5,4,3,2,1,0,14,13,12,11,10],[25,24,23,22,21,20,19,18,17,16,15,29,28,27,26,10,9,8,7,6,5,4,3,2,1,0,14,13,12,11],[26,25,24,23,22,21,20,19,18,17,16,15,29,28,27,11,10,9,8,7,6,5,4,3,2,1,0,14,13,12],[27,26,25,24,23,22,21,20,19,18,17,16,15,29,28,12,11,10,9,8,7,6,5,4,3,2,1,0,14,13],[28,27,26,25,24,23,22,21,20,19,18,17,16,15,29,13,12,11,10,9,8,7,6,5,4,3,2,1,0,14],[29,28,27,26,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0]],"identity":0,"element":0,"other":15}。請依 [element, singleton_class, commutes_with_all, other, conjugate_to_other, nonconjugate_certificate, boundary] 欄序回答。

查看答案與解釋(0, [0], 是, 15, 否, 是, singleton_class_iff_commutes_with_every_g_and_other_outside_class_is_nonconjugate_without_class_size_formula)

Wave6第八層核對=(0, [0], 是, 15, 否, 是, singleton_class_iff_commutes_with_every_g_and_other_outside_class_is_nonconjugate_without_class_size_formula)；依完整明示資料獨立重算；共軛類是element orbit並形成完整partition；singleton以forall g commute核對；共軛類不是coset或conjugate subgroup；不使用centralizer、class-size公式或類方程。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r03-finite-group-conjugacy-class-0088/)

有限群共軛類 · qf-mod45-conjugacy-singleton-nonconjugate-boundary · candidate





## 89. 有限群共軛類

由完整Cayley table導出全部conjugation action與orbits。操作=conjugacy-singleton-nonconjugate-boundary；資料={"group_table":[[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,0,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,16],[2,3,4,5,6,7,8,9,10,11,12,13,14,15,0,1,18,19,20,21,22,23,24,25,26,27,28,29,30,31,16,17],[3,4,5,6,7,8,9,10,11,12,13,14,15,0,1,2,19,20,21,22,23,24,25,26,27,28,29,30,31,16,17,18],[4,5,6,7,8,9,10,11,12,13,14,15,0,1,2,3,20,21,22,23,24,25,26,27,28,29,30,31,16,17,18,19],[5,6,7,8,9,10,11,12,13,14,15,0,1,2,3,4,21,22,23,24,25,26,27,28,29,30,31,16,17,18,19,20],[6,7,8,9,10,11,12,13,14,15,0,1,2,3,4,5,22,23,24,25,26,27,28,29,30,31,16,17,18,19,20,21],[7,8,9,10,11,12,13,14,15,0,1,2,3,4,5,6,23,24,25,26,27,28,29,30,31,16,17,18,19,20,21,22],[8,9,10,11,12,13,14,15,0,1,2,3,4,5,6,7,24,25,26,27,28,29,30,31,16,17,18,19,20,21,22,23],[9,10,11,12,13,14,15,0,1,2,3,4,5,6,7,8,25,26,27,28,29,30,31,16,17,18,19,20,21,22,23,24],[10,11,12,13,14,15,0,1,2,3,4,5,6,7,8,9,26,27,28,29,30,31,16,17,18,19,20,21,22,23,24,25],[11,12,13,14,15,0,1,2,3,4,5,6,7,8,9,10,27,28,29,30,31,16,17,18,19,20,21,22,23,24,25,26],[12,13,14,15,0,1,2,3,4,5,6,7,8,9,10,11,28,29,30,31,16,17,18,19,20,21,22,23,24,25,26,27],[13,14,15,0,1,2,3,4,5,6,7,8,9,10,11,12,29,30,31,16,17,18,19,20,21,22,23,24,25,26,27,28],[14,15,0,1,2,3,4,5,6,7,8,9,10,11,12,13,30,31,16,17,18,19,20,21,22,23,24,25,26,27,28,29],[15,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,31,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30],[16,31,30,29,28,27,26,25,24,23,22,21,20,19,18,17,0,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1],[17,16,31,30,29,28,27,26,25,24,23,22,21,20,19,18,1,0,15,14,13,12,11,10,9,8,7,6,5,4,3,2],[18,17,16,31,30,29,28,27,26,25,24,23,22,21,20,19,2,1,0,15,14,13,12,11,10,9,8,7,6,5,4,3],[19,18,17,16,31,30,29,28,27,26,25,24,23,22,21,20,3,2,1,0,15,14,13,12,11,10,9,8,7,6,5,4],[20,19,18,17,16,31,30,29,28,27,26,25,24,23,22,21,4,3,2,1,0,15,14,13,12,11,10,9,8,7,6,5],[21,20,19,18,17,16,31,30,29,28,27,26,25,24,23,22,5,4,3,2,1,0,15,14,13,12,11,10,9,8,7,6],[22,21,20,19,18,17,16,31,30,29,28,27,26,25,24,23,6,5,4,3,2,1,0,15,14,13,12,11,10,9,8,7],[23,22,21,20,19,18,17,16,31,30,29,28,27,26,25,24,7,6,5,4,3,2,1,0,15,14,13,12,11,10,9,8],[24,23,22,21,20,19,18,17,16,31,30,29,28,27,26,25,8,7,6,5,4,3,2,1,0,15,14,13,12,11,10,9],[25,24,23,22,21,20,19,18,17,16,31,30,29,28,27,26,9,8,7,6,5,4,3,2,1,0,15,14,13,12,11,10],[26,25,24,23,22,21,20,19,18,17,16,31,30,29,28,27,10,9,8,7,6,5,4,3,2,1,0,15,14,13,12,11],[27,26,25,24,23,22,21,20,19,18,17,16,31,30,29,28,11,10,9,8,7,6,5,4,3,2,1,0,15,14,13,12],[28,27,26,25,24,23,22,21,20,19,18,17,16,31,30,29,12,11,10,9,8,7,6,5,4,3,2,1,0,15,14,13],[29,28,27,26,25,24,23,22,21,20,19,18,17,16,31,30,13,12,11,10,9,8,7,6,5,4,3,2,1,0,15,14],[30,29,28,27,26,25,24,23,22,21,20,19,18,17,16,31,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0,15],[31,30,29,28,27,26,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0]],"identity":0,"element":0,"other":16}。請依 [element, singleton_class, commutes_with_all, other, conjugate_to_other, nonconjugate_certificate, boundary] 欄序回答。

查看答案與解釋(0, [0], 是, 16, 否, 是, singleton_class_iff_commutes_with_every_g_and_other_outside_class_is_nonconjugate_without_class_size_formula)

Wave6第八層核對=(0, [0], 是, 16, 否, 是, singleton_class_iff_commutes_with_every_g_and_other_outside_class_is_nonconjugate_without_class_size_formula)；依完整明示資料獨立重算；共軛類是element orbit並形成完整partition；singleton以forall g commute核對；共軛類不是coset或conjugate subgroup；不使用centralizer、class-size公式或類方程。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r03-finite-group-conjugacy-class-0089/)

有限群共軛類 · qf-mod45-conjugacy-singleton-nonconjugate-boundary · candidate





## 90. 有限群共軛類

由完整Cayley table導出全部conjugation action與orbits。操作=conjugacy-singleton-nonconjugate-boundary；資料={"group_table":[[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,0,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,17],[2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,0,1,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,17,18],[3,4,5,6,7,8,9,10,11,12,13,14,15,16,0,1,2,20,21,22,23,24,25,26,27,28,29,30,31,32,33,17,18,19],[4,5,6,7,8,9,10,11,12,13,14,15,16,0,1,2,3,21,22,23,24,25,26,27,28,29,30,31,32,33,17,18,19,20],[5,6,7,8,9,10,11,12,13,14,15,16,0,1,2,3,4,22,23,24,25,26,27,28,29,30,31,32,33,17,18,19,20,21],[6,7,8,9,10,11,12,13,14,15,16,0,1,2,3,4,5,23,24,25,26,27,28,29,30,31,32,33,17,18,19,20,21,22],[7,8,9,10,11,12,13,14,15,16,0,1,2,3,4,5,6,24,25,26,27,28,29,30,31,32,33,17,18,19,20,21,22,23],[8,9,10,11,12,13,14,15,16,0,1,2,3,4,5,6,7,25,26,27,28,29,30,31,32,33,17,18,19,20,21,22,23,24],[9,10,11,12,13,14,15,16,0,1,2,3,4,5,6,7,8,26,27,28,29,30,31,32,33,17,18,19,20,21,22,23,24,25],[10,11,12,13,14,15,16,0,1,2,3,4,5,6,7,8,9,27,28,29,30,31,32,33,17,18,19,20,21,22,23,24,25,26],[11,12,13,14,15,16,0,1,2,3,4,5,6,7,8,9,10,28,29,30,31,32,33,17,18,19,20,21,22,23,24,25,26,27],[12,13,14,15,16,0,1,2,3,4,5,6,7,8,9,10,11,29,30,31,32,33,17,18,19,20,21,22,23,24,25,26,27,28],[13,14,15,16,0,1,2,3,4,5,6,7,8,9,10,11,12,30,31,32,33,17,18,19,20,21,22,23,24,25,26,27,28,29],[14,15,16,0,1,2,3,4,5,6,7,8,9,10,11,12,13,31,32,33,17,18,19,20,21,22,23,24,25,26,27,28,29,30],[15,16,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,32,33,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31],[16,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,33,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32],[17,33,32,31,30,29,28,27,26,25,24,23,22,21,20,19,18,0,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1],[18,17,33,32,31,30,29,28,27,26,25,24,23,22,21,20,19,1,0,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2],[19,18,17,33,32,31,30,29,28,27,26,25,24,23,22,21,20,2,1,0,16,15,14,13,12,11,10,9,8,7,6,5,4,3],[20,19,18,17,33,32,31,30,29,28,27,26,25,24,23,22,21,3,2,1,0,16,15,14,13,12,11,10,9,8,7,6,5,4],[21,20,19,18,17,33,32,31,30,29,28,27,26,25,24,23,22,4,3,2,1,0,16,15,14,13,12,11,10,9,8,7,6,5],[22,21,20,19,18,17,33,32,31,30,29,28,27,26,25,24,23,5,4,3,2,1,0,16,15,14,13,12,11,10,9,8,7,6],[23,22,21,20,19,18,17,33,32,31,30,29,28,27,26,25,24,6,5,4,3,2,1,0,16,15,14,13,12,11,10,9,8,7],[24,23,22,21,20,19,18,17,33,32,31,30,29,28,27,26,25,7,6,5,4,3,2,1,0,16,15,14,13,12,11,10,9,8],[25,24,23,22,21,20,19,18,17,33,32,31,30,29,28,27,26,8,7,6,5,4,3,2,1,0,16,15,14,13,12,11,10,9],[26,25,24,23,22,21,20,19,18,17,33,32,31,30,29,28,27,9,8,7,6,5,4,3,2,1,0,16,15,14,13,12,11,10],[27,26,25,24,23,22,21,20,19,18,17,33,32,31,30,29,28,10,9,8,7,6,5,4,3,2,1,0,16,15,14,13,12,11],[28,27,26,25,24,23,22,21,20,19,18,17,33,32,31,30,29,11,10,9,8,7,6,5,4,3,2,1,0,16,15,14,13,12],[29,28,27,26,25,24,23,22,21,20,19,18,17,33,32,31,30,12,11,10,9,8,7,6,5,4,3,2,1,0,16,15,14,13],[30,29,28,27,26,25,24,23,22,21,20,19,18,17,33,32,31,13,12,11,10,9,8,7,6,5,4,3,2,1,0,16,15,14],[31,30,29,28,27,26,25,24,23,22,21,20,19,18,17,33,32,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0,16,15],[32,31,30,29,28,27,26,25,24,23,22,21,20,19,18,17,33,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0,16],[33,32,31,30,29,28,27,26,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0]],"identity":0,"element":0,"other":17}。請依 [element, singleton_class, commutes_with_all, other, conjugate_to_other, nonconjugate_certificate, boundary] 欄序回答。

查看答案與解釋(0, [0], 是, 17, 否, 是, singleton_class_iff_commutes_with_every_g_and_other_outside_class_is_nonconjugate_without_class_size_formula)

Wave6第八層核對=(0, [0], 是, 17, 否, 是, singleton_class_iff_commutes_with_every_g_and_other_outside_class_is_nonconjugate_without_class_size_formula)；依完整明示資料獨立重算；共軛類是element orbit並形成完整partition；singleton以forall g commute核對；共軛類不是coset或conjugate subgroup；不使用centralizer、class-size公式或類方程。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r03-finite-group-conjugacy-class-0090/)

有限群共軛類 · qf-mod45-conjugacy-singleton-nonconjugate-boundary · candidate





## 91. 有限群共軛類

由完整Cayley table導出全部conjugation action與orbits。操作=conjugacy-singleton-nonconjugate-boundary；資料={"group_table":[[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,0,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,18],[2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,0,1,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,18,19],[3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,0,1,2,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,18,19,20],[4,5,6,7,8,9,10,11,12,13,14,15,16,17,0,1,2,3,22,23,24,25,26,27,28,29,30,31,32,33,34,35,18,19,20,21],[5,6,7,8,9,10,11,12,13,14,15,16,17,0,1,2,3,4,23,24,25,26,27,28,29,30,31,32,33,34,35,18,19,20,21,22],[6,7,8,9,10,11,12,13,14,15,16,17,0,1,2,3,4,5,24,25,26,27,28,29,30,31,32,33,34,35,18,19,20,21,22,23],[7,8,9,10,11,12,13,14,15,16,17,0,1,2,3,4,5,6,25,26,27,28,29,30,31,32,33,34,35,18,19,20,21,22,23,24],[8,9,10,11,12,13,14,15,16,17,0,1,2,3,4,5,6,7,26,27,28,29,30,31,32,33,34,35,18,19,20,21,22,23,24,25],[9,10,11,12,13,14,15,16,17,0,1,2,3,4,5,6,7,8,27,28,29,30,31,32,33,34,35,18,19,20,21,22,23,24,25,26],[10,11,12,13,14,15,16,17,0,1,2,3,4,5,6,7,8,9,28,29,30,31,32,33,34,35,18,19,20,21,22,23,24,25,26,27],[11,12,13,14,15,16,17,0,1,2,3,4,5,6,7,8,9,10,29,30,31,32,33,34,35,18,19,20,21,22,23,24,25,26,27,28],[12,13,14,15,16,17,0,1,2,3,4,5,6,7,8,9,10,11,30,31,32,33,34,35,18,19,20,21,22,23,24,25,26,27,28,29],[13,14,15,16,17,0,1,2,3,4,5,6,7,8,9,10,11,12,31,32,33,34,35,18,19,20,21,22,23,24,25,26,27,28,29,30],[14,15,16,17,0,1,2,3,4,5,6,7,8,9,10,11,12,13,32,33,34,35,18,19,20,21,22,23,24,25,26,27,28,29,30,31],[15,16,17,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,33,34,35,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32],[16,17,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,34,35,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33],[17,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,35,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34],[18,35,34,33,32,31,30,29,28,27,26,25,24,23,22,21,20,19,0,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1],[19,18,35,34,33,32,31,30,29,28,27,26,25,24,23,22,21,20,1,0,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2],[20,19,18,35,34,33,32,31,30,29,28,27,26,25,24,23,22,21,2,1,0,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3],[21,20,19,18,35,34,33,32,31,30,29,28,27,26,25,24,23,22,3,2,1,0,17,16,15,14,13,12,11,10,9,8,7,6,5,4],[22,21,20,19,18,35,34,33,32,31,30,29,28,27,26,25,24,23,4,3,2,1,0,17,16,15,14,13,12,11,10,9,8,7,6,5],[23,22,21,20,19,18,35,34,33,32,31,30,29,28,27,26,25,24,5,4,3,2,1,0,17,16,15,14,13,12,11,10,9,8,7,6],[24,23,22,21,20,19,18,35,34,33,32,31,30,29,28,27,26,25,6,5,4,3,2,1,0,17,16,15,14,13,12,11,10,9,8,7],[25,24,23,22,21,20,19,18,35,34,33,32,31,30,29,28,27,26,7,6,5,4,3,2,1,0,17,16,15,14,13,12,11,10,9,8],[26,25,24,23,22,21,20,19,18,35,34,33,32,31,30,29,28,27,8,7,6,5,4,3,2,1,0,17,16,15,14,13,12,11,10,9],[27,26,25,24,23,22,21,20,19,18,35,34,33,32,31,30,29,28,9,8,7,6,5,4,3,2,1,0,17,16,15,14,13,12,11,10],[28,27,26,25,24,23,22,21,20,19,18,35,34,33,32,31,30,29,10,9,8,7,6,5,4,3,2,1,0,17,16,15,14,13,12,11],[29,28,27,26,25,24,23,22,21,20,19,18,35,34,33,32,31,30,11,10,9,8,7,6,5,4,3,2,1,0,17,16,15,14,13,12],[30,29,28,27,26,25,24,23,22,21,20,19,18,35,34,33,32,31,12,11,10,9,8,7,6,5,4,3,2,1,0,17,16,15,14,13],[31,30,29,28,27,26,25,24,23,22,21,20,19,18,35,34,33,32,13,12,11,10,9,8,7,6,5,4,3,2,1,0,17,16,15,14],[32,31,30,29,28,27,26,25,24,23,22,21,20,19,18,35,34,33,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0,17,16,15],[33,32,31,30,29,28,27,26,25,24,23,22,21,20,19,18,35,34,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0,17,16],[34,33,32,31,30,29,28,27,26,25,24,23,22,21,20,19,18,35,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0,17],[35,34,33,32,31,30,29,28,27,26,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0]],"identity":0,"element":0,"other":18}。請依 [element, singleton_class, commutes_with_all, other, conjugate_to_other, nonconjugate_certificate, boundary] 欄序回答。

查看答案與解釋(0, [0], 是, 18, 否, 是, singleton_class_iff_commutes_with_every_g_and_other_outside_class_is_nonconjugate_without_class_size_formula)

Wave6第八層核對=(0, [0], 是, 18, 否, 是, singleton_class_iff_commutes_with_every_g_and_other_outside_class_is_nonconjugate_without_class_size_formula)；依完整明示資料獨立重算；共軛類是element orbit並形成完整partition；singleton以forall g commute核對；共軛類不是coset或conjugate subgroup；不使用centralizer、class-size公式或類方程。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r03-finite-group-conjugacy-class-0091/)

有限群共軛類 · qf-mod45-conjugacy-singleton-nonconjugate-boundary · candidate





## 92. 有限群共軛類

由完整Cayley table導出全部conjugation action與orbits。操作=conjugacy-singleton-nonconjugate-boundary；資料={"group_table":[[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,0,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,19],[2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,0,1,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,19,20],[3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,0,1,2,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,19,20,21],[4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,0,1,2,3,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,19,20,21,22],[5,6,7,8,9,10,11,12,13,14,15,16,17,18,0,1,2,3,4,24,25,26,27,28,29,30,31,32,33,34,35,36,37,19,20,21,22,23],[6,7,8,9,10,11,12,13,14,15,16,17,18,0,1,2,3,4,5,25,26,27,28,29,30,31,32,33,34,35,36,37,19,20,21,22,23,24],[7,8,9,10,11,12,13,14,15,16,17,18,0,1,2,3,4,5,6,26,27,28,29,30,31,32,33,34,35,36,37,19,20,21,22,23,24,25],[8,9,10,11,12,13,14,15,16,17,18,0,1,2,3,4,5,6,7,27,28,29,30,31,32,33,34,35,36,37,19,20,21,22,23,24,25,26],[9,10,11,12,13,14,15,16,17,18,0,1,2,3,4,5,6,7,8,28,29,30,31,32,33,34,35,36,37,19,20,21,22,23,24,25,26,27],[10,11,12,13,14,15,16,17,18,0,1,2,3,4,5,6,7,8,9,29,30,31,32,33,34,35,36,37,19,20,21,22,23,24,25,26,27,28],[11,12,13,14,15,16,17,18,0,1,2,3,4,5,6,7,8,9,10,30,31,32,33,34,35,36,37,19,20,21,22,23,24,25,26,27,28,29],[12,13,14,15,16,17,18,0,1,2,3,4,5,6,7,8,9,10,11,31,32,33,34,35,36,37,19,20,21,22,23,24,25,26,27,28,29,30],[13,14,15,16,17,18,0,1,2,3,4,5,6,7,8,9,10,11,12,32,33,34,35,36,37,19,20,21,22,23,24,25,26,27,28,29,30,31],[14,15,16,17,18,0,1,2,3,4,5,6,7,8,9,10,11,12,13,33,34,35,36,37,19,20,21,22,23,24,25,26,27,28,29,30,31,32],[15,16,17,18,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,34,35,36,37,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33],[16,17,18,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,35,36,37,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34],[17,18,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,36,37,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35],[18,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,37,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36],[19,37,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,21,20,0,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1],[20,19,37,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,21,1,0,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2],[21,20,19,37,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,2,1,0,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3],[22,21,20,19,37,36,35,34,33,32,31,30,29,28,27,26,25,24,23,3,2,1,0,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4],[23,22,21,20,19,37,36,35,34,33,32,31,30,29,28,27,26,25,24,4,3,2,1,0,18,17,16,15,14,13,12,11,10,9,8,7,6,5],[24,23,22,21,20,19,37,36,35,34,33,32,31,30,29,28,27,26,25,5,4,3,2,1,0,18,17,16,15,14,13,12,11,10,9,8,7,6],[25,24,23,22,21,20,19,37,36,35,34,33,32,31,30,29,28,27,26,6,5,4,3,2,1,0,18,17,16,15,14,13,12,11,10,9,8,7],[26,25,24,23,22,21,20,19,37,36,35,34,33,32,31,30,29,28,27,7,6,5,4,3,2,1,0,18,17,16,15,14,13,12,11,10,9,8],[27,26,25,24,23,22,21,20,19,37,36,35,34,33,32,31,30,29,28,8,7,6,5,4,3,2,1,0,18,17,16,15,14,13,12,11,10,9],[28,27,26,25,24,23,22,21,20,19,37,36,35,34,33,32,31,30,29,9,8,7,6,5,4,3,2,1,0,18,17,16,15,14,13,12,11,10],[29,28,27,26,25,24,23,22,21,20,19,37,36,35,34,33,32,31,30,10,9,8,7,6,5,4,3,2,1,0,18,17,16,15,14,13,12,11],[30,29,28,27,26,25,24,23,22,21,20,19,37,36,35,34,33,32,31,11,10,9,8,7,6,5,4,3,2,1,0,18,17,16,15,14,13,12],[31,30,29,28,27,26,25,24,23,22,21,20,19,37,36,35,34,33,32,12,11,10,9,8,7,6,5,4,3,2,1,0,18,17,16,15,14,13],[32,31,30,29,28,27,26,25,24,23,22,21,20,19,37,36,35,34,33,13,12,11,10,9,8,7,6,5,4,3,2,1,0,18,17,16,15,14],[33,32,31,30,29,28,27,26,25,24,23,22,21,20,19,37,36,35,34,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0,18,17,16,15],[34,33,32,31,30,29,28,27,26,25,24,23,22,21,20,19,37,36,35,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0,18,17,16],[35,34,33,32,31,30,29,28,27,26,25,24,23,22,21,20,19,37,36,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0,18,17],[36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,21,20,19,37,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0,18],[37,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0]],"identity":0,"element":0,"other":19}。請依 [element, singleton_class, commutes_with_all, other, conjugate_to_other, nonconjugate_certificate, boundary] 欄序回答。

查看答案與解釋(0, [0], 是, 19, 否, 是, singleton_class_iff_commutes_with_every_g_and_other_outside_class_is_nonconjugate_without_class_size_formula)

Wave6第八層核對=(0, [0], 是, 19, 否, 是, singleton_class_iff_commutes_with_every_g_and_other_outside_class_is_nonconjugate_without_class_size_formula)；依完整明示資料獨立重算；共軛類是element orbit並形成完整partition；singleton以forall g commute核對；共軛類不是coset或conjugate subgroup；不使用centralizer、class-size公式或類方程。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r03-finite-group-conjugacy-class-0092/)

有限群共軛類 · qf-mod45-conjugacy-singleton-nonconjugate-boundary · candidate





## 93. 有限群共軛類

由完整Cayley table導出全部conjugation action與orbits。操作=conjugacy-singleton-nonconjugate-boundary；資料={"group_table":[[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,0,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,20],[2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,0,1,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,20,21],[3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,0,1,2,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,20,21,22],[4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,0,1,2,3,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,20,21,22,23],[5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,0,1,2,3,4,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,20,21,22,23,24],[6,7,8,9,10,11,12,13,14,15,16,17,18,19,0,1,2,3,4,5,26,27,28,29,30,31,32,33,34,35,36,37,38,39,20,21,22,23,24,25],[7,8,9,10,11,12,13,14,15,16,17,18,19,0,1,2,3,4,5,6,27,28,29,30,31,32,33,34,35,36,37,38,39,20,21,22,23,24,25,26],[8,9,10,11,12,13,14,15,16,17,18,19,0,1,2,3,4,5,6,7,28,29,30,31,32,33,34,35,36,37,38,39,20,21,22,23,24,25,26,27],[9,10,11,12,13,14,15,16,17,18,19,0,1,2,3,4,5,6,7,8,29,30,31,32,33,34,35,36,37,38,39,20,21,22,23,24,25,26,27,28],[10,11,12,13,14,15,16,17,18,19,0,1,2,3,4,5,6,7,8,9,30,31,32,33,34,35,36,37,38,39,20,21,22,23,24,25,26,27,28,29],[11,12,13,14,15,16,17,18,19,0,1,2,3,4,5,6,7,8,9,10,31,32,33,34,35,36,37,38,39,20,21,22,23,24,25,26,27,28,29,30],[12,13,14,15,16,17,18,19,0,1,2,3,4,5,6,7,8,9,10,11,32,33,34,35,36,37,38,39,20,21,22,23,24,25,26,27,28,29,30,31],[13,14,15,16,17,18,19,0,1,2,3,4,5,6,7,8,9,10,11,12,33,34,35,36,37,38,39,20,21,22,23,24,25,26,27,28,29,30,31,32],[14,15,16,17,18,19,0,1,2,3,4,5,6,7,8,9,10,11,12,13,34,35,36,37,38,39,20,21,22,23,24,25,26,27,28,29,30,31,32,33],[15,16,17,18,19,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,35,36,37,38,39,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34],[16,17,18,19,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,36,37,38,39,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35],[17,18,19,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,37,38,39,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36],[18,19,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,38,39,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37],[19,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,39,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38],[20,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,21,0,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1],[21,20,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,1,0,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2],[22,21,20,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,23,2,1,0,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3],[23,22,21,20,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,3,2,1,0,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4],[24,23,22,21,20,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,4,3,2,1,0,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5],[25,24,23,22,21,20,39,38,37,36,35,34,33,32,31,30,29,28,27,26,5,4,3,2,1,0,19,18,17,16,15,14,13,12,11,10,9,8,7,6],[26,25,24,23,22,21,20,39,38,37,36,35,34,33,32,31,30,29,28,27,6,5,4,3,2,1,0,19,18,17,16,15,14,13,12,11,10,9,8,7],[27,26,25,24,23,22,21,20,39,38,37,36,35,34,33,32,31,30,29,28,7,6,5,4,3,2,1,0,19,18,17,16,15,14,13,12,11,10,9,8],[28,27,26,25,24,23,22,21,20,39,38,37,36,35,34,33,32,31,30,29,8,7,6,5,4,3,2,1,0,19,18,17,16,15,14,13,12,11,10,9],[29,28,27,26,25,24,23,22,21,20,39,38,37,36,35,34,33,32,31,30,9,8,7,6,5,4,3,2,1,0,19,18,17,16,15,14,13,12,11,10],[30,29,28,27,26,25,24,23,22,21,20,39,38,37,36,35,34,33,32,31,10,9,8,7,6,5,4,3,2,1,0,19,18,17,16,15,14,13,12,11],[31,30,29,28,27,26,25,24,23,22,21,20,39,38,37,36,35,34,33,32,11,10,9,8,7,6,5,4,3,2,1,0,19,18,17,16,15,14,13,12],[32,31,30,29,28,27,26,25,24,23,22,21,20,39,38,37,36,35,34,33,12,11,10,9,8,7,6,5,4,3,2,1,0,19,18,17,16,15,14,13],[33,32,31,30,29,28,27,26,25,24,23,22,21,20,39,38,37,36,35,34,13,12,11,10,9,8,7,6,5,4,3,2,1,0,19,18,17,16,15,14],[34,33,32,31,30,29,28,27,26,25,24,23,22,21,20,39,38,37,36,35,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0,19,18,17,16,15],[35,34,33,32,31,30,29,28,27,26,25,24,23,22,21,20,39,38,37,36,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0,19,18,17,16],[36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,21,20,39,38,37,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0,19,18,17],[37,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,21,20,39,38,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0,19,18],[38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,21,20,39,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0,19],[39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0]],"identity":0,"element":0,"other":20}。請依 [element, singleton_class, commutes_with_all, other, conjugate_to_other, nonconjugate_certificate, boundary] 欄序回答。

查看答案與解釋(0, [0], 是, 20, 否, 是, singleton_class_iff_commutes_with_every_g_and_other_outside_class_is_nonconjugate_without_class_size_formula)

Wave6第八層核對=(0, [0], 是, 20, 否, 是, singleton_class_iff_commutes_with_every_g_and_other_outside_class_is_nonconjugate_without_class_size_formula)；依完整明示資料獨立重算；共軛類是element orbit並形成完整partition；singleton以forall g commute核對；共軛類不是coset或conjugate subgroup；不使用centralizer、class-size公式或類方程。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r03-finite-group-conjugacy-class-0093/)

有限群共軛類 · qf-mod45-conjugacy-singleton-nonconjugate-boundary · candidate





## 94. 有限群共軛類

由完整Cayley table導出全部conjugation action與orbits。操作=conjugacy-singleton-nonconjugate-boundary；資料={"group_table":[[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,0,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,21],[2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,0,1,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,21,22],[3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,0,1,2,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,21,22,23],[4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,0,1,2,3,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,21,22,23,24],[5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,0,1,2,3,4,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,21,22,23,24,25],[6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,0,1,2,3,4,5,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,21,22,23,24,25,26],[7,8,9,10,11,12,13,14,15,16,17,18,19,20,0,1,2,3,4,5,6,28,29,30,31,32,33,34,35,36,37,38,39,40,41,21,22,23,24,25,26,27],[8,9,10,11,12,13,14,15,16,17,18,19,20,0,1,2,3,4,5,6,7,29,30,31,32,33,34,35,36,37,38,39,40,41,21,22,23,24,25,26,27,28],[9,10,11,12,13,14,15,16,17,18,19,20,0,1,2,3,4,5,6,7,8,30,31,32,33,34,35,36,37,38,39,40,41,21,22,23,24,25,26,27,28,29],[10,11,12,13,14,15,16,17,18,19,20,0,1,2,3,4,5,6,7,8,9,31,32,33,34,35,36,37,38,39,40,41,21,22,23,24,25,26,27,28,29,30],[11,12,13,14,15,16,17,18,19,20,0,1,2,3,4,5,6,7,8,9,10,32,33,34,35,36,37,38,39,40,41,21,22,23,24,25,26,27,28,29,30,31],[12,13,14,15,16,17,18,19,20,0,1,2,3,4,5,6,7,8,9,10,11,33,34,35,36,37,38,39,40,41,21,22,23,24,25,26,27,28,29,30,31,32],[13,14,15,16,17,18,19,20,0,1,2,3,4,5,6,7,8,9,10,11,12,34,35,36,37,38,39,40,41,21,22,23,24,25,26,27,28,29,30,31,32,33],[14,15,16,17,18,19,20,0,1,2,3,4,5,6,7,8,9,10,11,12,13,35,36,37,38,39,40,41,21,22,23,24,25,26,27,28,29,30,31,32,33,34],[15,16,17,18,19,20,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,36,37,38,39,40,41,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35],[16,17,18,19,20,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,37,38,39,40,41,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36],[17,18,19,20,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,38,39,40,41,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37],[18,19,20,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,39,40,41,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38],[19,20,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,40,41,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39],[20,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,41,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40],[21,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,0,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1],[22,21,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,23,1,0,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2],[23,22,21,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,2,1,0,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3],[24,23,22,21,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,3,2,1,0,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4],[25,24,23,22,21,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,4,3,2,1,0,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5],[26,25,24,23,22,21,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,5,4,3,2,1,0,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6],[27,26,25,24,23,22,21,41,40,39,38,37,36,35,34,33,32,31,30,29,28,6,5,4,3,2,1,0,20,19,18,17,16,15,14,13,12,11,10,9,8,7],[28,27,26,25,24,23,22,21,41,40,39,38,37,36,35,34,33,32,31,30,29,7,6,5,4,3,2,1,0,20,19,18,17,16,15,14,13,12,11,10,9,8],[29,28,27,26,25,24,23,22,21,41,40,39,38,37,36,35,34,33,32,31,30,8,7,6,5,4,3,2,1,0,20,19,18,17,16,15,14,13,12,11,10,9],[30,29,28,27,26,25,24,23,22,21,41,40,39,38,37,36,35,34,33,32,31,9,8,7,6,5,4,3,2,1,0,20,19,18,17,16,15,14,13,12,11,10],[31,30,29,28,27,26,25,24,23,22,21,41,40,39,38,37,36,35,34,33,32,10,9,8,7,6,5,4,3,2,1,0,20,19,18,17,16,15,14,13,12,11],[32,31,30,29,28,27,26,25,24,23,22,21,41,40,39,38,37,36,35,34,33,11,10,9,8,7,6,5,4,3,2,1,0,20,19,18,17,16,15,14,13,12],[33,32,31,30,29,28,27,26,25,24,23,22,21,41,40,39,38,37,36,35,34,12,11,10,9,8,7,6,5,4,3,2,1,0,20,19,18,17,16,15,14,13],[34,33,32,31,30,29,28,27,26,25,24,23,22,21,41,40,39,38,37,36,35,13,12,11,10,9,8,7,6,5,4,3,2,1,0,20,19,18,17,16,15,14],[35,34,33,32,31,30,29,28,27,26,25,24,23,22,21,41,40,39,38,37,36,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0,20,19,18,17,16,15],[36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,21,41,40,39,38,37,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0,20,19,18,17,16],[37,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,21,41,40,39,38,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0,20,19,18,17],[38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,21,41,40,39,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0,20,19,18],[39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,21,41,40,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0,20,19],[40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,21,41,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0,20],[41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0]],"identity":0,"element":0,"other":21}。請依 [element, singleton_class, commutes_with_all, other, conjugate_to_other, nonconjugate_certificate, boundary] 欄序回答。

查看答案與解釋(0, [0], 是, 21, 否, 是, singleton_class_iff_commutes_with_every_g_and_other_outside_class_is_nonconjugate_without_class_size_formula)

Wave6第八層核對=(0, [0], 是, 21, 否, 是, singleton_class_iff_commutes_with_every_g_and_other_outside_class_is_nonconjugate_without_class_size_formula)；依完整明示資料獨立重算；共軛類是element orbit並形成完整partition；singleton以forall g commute核對；共軛類不是coset或conjugate subgroup；不使用centralizer、class-size公式或類方程。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r03-finite-group-conjugacy-class-0094/)

有限群共軛類 · qf-mod45-conjugacy-singleton-nonconjugate-boundary · candidate





## 95. 有限群共軛類

由完整Cayley table導出全部conjugation action與orbits。操作=conjugacy-singleton-nonconjugate-boundary；資料={"group_table":[[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,0,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,22],[2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,0,1,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,22,23],[3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,0,1,2,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,22,23,24],[4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,0,1,2,3,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,22,23,24,25],[5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,0,1,2,3,4,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,22,23,24,25,26],[6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,0,1,2,3,4,5,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,22,23,24,25,26,27],[7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,0,1,2,3,4,5,6,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,22,23,24,25,26,27,28],[8,9,10,11,12,13,14,15,16,17,18,19,20,21,0,1,2,3,4,5,6,7,30,31,32,33,34,35,36,37,38,39,40,41,42,43,22,23,24,25,26,27,28,29],[9,10,11,12,13,14,15,16,17,18,19,20,21,0,1,2,3,4,5,6,7,8,31,32,33,34,35,36,37,38,39,40,41,42,43,22,23,24,25,26,27,28,29,30],[10,11,12,13,14,15,16,17,18,19,20,21,0,1,2,3,4,5,6,7,8,9,32,33,34,35,36,37,38,39,40,41,42,43,22,23,24,25,26,27,28,29,30,31],[11,12,13,14,15,16,17,18,19,20,21,0,1,2,3,4,5,6,7,8,9,10,33,34,35,36,37,38,39,40,41,42,43,22,23,24,25,26,27,28,29,30,31,32],[12,13,14,15,16,17,18,19,20,21,0,1,2,3,4,5,6,7,8,9,10,11,34,35,36,37,38,39,40,41,42,43,22,23,24,25,26,27,28,29,30,31,32,33],[13,14,15,16,17,18,19,20,21,0,1,2,3,4,5,6,7,8,9,10,11,12,35,36,37,38,39,40,41,42,43,22,23,24,25,26,27,28,29,30,31,32,33,34],[14,15,16,17,18,19,20,21,0,1,2,3,4,5,6,7,8,9,10,11,12,13,36,37,38,39,40,41,42,43,22,23,24,25,26,27,28,29,30,31,32,33,34,35],[15,16,17,18,19,20,21,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,37,38,39,40,41,42,43,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36],[16,17,18,19,20,21,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,38,39,40,41,42,43,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37],[17,18,19,20,21,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,39,40,41,42,43,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38],[18,19,20,21,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,40,41,42,43,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39],[19,20,21,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,41,42,43,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40],[20,21,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,42,43,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41],[21,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,43,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42],[22,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,23,0,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1],[23,22,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,1,0,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2],[24,23,22,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,2,1,0,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3],[25,24,23,22,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,3,2,1,0,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4],[26,25,24,23,22,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,4,3,2,1,0,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5],[27,26,25,24,23,22,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,5,4,3,2,1,0,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6],[28,27,26,25,24,23,22,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,6,5,4,3,2,1,0,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7],[29,28,27,26,25,24,23,22,43,42,41,40,39,38,37,36,35,34,33,32,31,30,7,6,5,4,3,2,1,0,21,20,19,18,17,16,15,14,13,12,11,10,9,8],[30,29,28,27,26,25,24,23,22,43,42,41,40,39,38,37,36,35,34,33,32,31,8,7,6,5,4,3,2,1,0,21,20,19,18,17,16,15,14,13,12,11,10,9],[31,30,29,28,27,26,25,24,23,22,43,42,41,40,39,38,37,36,35,34,33,32,9,8,7,6,5,4,3,2,1,0,21,20,19,18,17,16,15,14,13,12,11,10],[32,31,30,29,28,27,26,25,24,23,22,43,42,41,40,39,38,37,36,35,34,33,10,9,8,7,6,5,4,3,2,1,0,21,20,19,18,17,16,15,14,13,12,11],[33,32,31,30,29,28,27,26,25,24,23,22,43,42,41,40,39,38,37,36,35,34,11,10,9,8,7,6,5,4,3,2,1,0,21,20,19,18,17,16,15,14,13,12],[34,33,32,31,30,29,28,27,26,25,24,23,22,43,42,41,40,39,38,37,36,35,12,11,10,9,8,7,6,5,4,3,2,1,0,21,20,19,18,17,16,15,14,13],[35,34,33,32,31,30,29,28,27,26,25,24,23,22,43,42,41,40,39,38,37,36,13,12,11,10,9,8,7,6,5,4,3,2,1,0,21,20,19,18,17,16,15,14],[36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,43,42,41,40,39,38,37,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0,21,20,19,18,17,16,15],[37,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,43,42,41,40,39,38,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0,21,20,19,18,17,16],[38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,43,42,41,40,39,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0,21,20,19,18,17],[39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,43,42,41,40,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0,21,20,19,18],[40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,43,42,41,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0,21,20,19],[41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,43,42,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0,21,20],[42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,43,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0,21],[43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0]],"identity":0,"element":0,"other":22}。請依 [element, singleton_class, commutes_with_all, other, conjugate_to_other, nonconjugate_certificate, boundary] 欄序回答。

查看答案與解釋(0, [0], 是, 22, 否, 是, singleton_class_iff_commutes_with_every_g_and_other_outside_class_is_nonconjugate_without_class_size_formula)

Wave6第八層核對=(0, [0], 是, 22, 否, 是, singleton_class_iff_commutes_with_every_g_and_other_outside_class_is_nonconjugate_without_class_size_formula)；依完整明示資料獨立重算；共軛類是element orbit並形成完整partition；singleton以forall g commute核對；共軛類不是coset或conjugate subgroup；不使用centralizer、class-size公式或類方程。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r03-finite-group-conjugacy-class-0095/)

有限群共軛類 · qf-mod45-conjugacy-singleton-nonconjugate-boundary · candidate





## 96. 有限群共軛類

由完整Cayley table導出全部conjugation action與orbits。操作=conjugacy-singleton-nonconjugate-boundary；資料={"group_table":[[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,0,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,23],[2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,0,1,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,23,24],[3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,0,1,2,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,23,24,25],[4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,0,1,2,3,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,23,24,25,26],[5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,0,1,2,3,4,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,23,24,25,26,27],[6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,0,1,2,3,4,5,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,23,24,25,26,27,28],[7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,0,1,2,3,4,5,6,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,23,24,25,26,27,28,29],[8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,0,1,2,3,4,5,6,7,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,23,24,25,26,27,28,29,30],[9,10,11,12,13,14,15,16,17,18,19,20,21,22,0,1,2,3,4,5,6,7,8,32,33,34,35,36,37,38,39,40,41,42,43,44,45,23,24,25,26,27,28,29,30,31],[10,11,12,13,14,15,16,17,18,19,20,21,22,0,1,2,3,4,5,6,7,8,9,33,34,35,36,37,38,39,40,41,42,43,44,45,23,24,25,26,27,28,29,30,31,32],[11,12,13,14,15,16,17,18,19,20,21,22,0,1,2,3,4,5,6,7,8,9,10,34,35,36,37,38,39,40,41,42,43,44,45,23,24,25,26,27,28,29,30,31,32,33],[12,13,14,15,16,17,18,19,20,21,22,0,1,2,3,4,5,6,7,8,9,10,11,35,36,37,38,39,40,41,42,43,44,45,23,24,25,26,27,28,29,30,31,32,33,34],[13,14,15,16,17,18,19,20,21,22,0,1,2,3,4,5,6,7,8,9,10,11,12,36,37,38,39,40,41,42,43,44,45,23,24,25,26,27,28,29,30,31,32,33,34,35],[14,15,16,17,18,19,20,21,22,0,1,2,3,4,5,6,7,8,9,10,11,12,13,37,38,39,40,41,42,43,44,45,23,24,25,26,27,28,29,30,31,32,33,34,35,36],[15,16,17,18,19,20,21,22,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,38,39,40,41,42,43,44,45,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37],[16,17,18,19,20,21,22,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,39,40,41,42,43,44,45,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38],[17,18,19,20,21,22,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,40,41,42,43,44,45,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39],[18,19,20,21,22,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,41,42,43,44,45,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40],[19,20,21,22,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,42,43,44,45,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41],[20,21,22,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,43,44,45,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42],[21,22,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,44,45,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],[22,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,45,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44],[23,45,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,0,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1],[24,23,45,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,1,0,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2],[25,24,23,45,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,2,1,0,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3],[26,25,24,23,45,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,3,2,1,0,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4],[27,26,25,24,23,45,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,4,3,2,1,0,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5],[28,27,26,25,24,23,45,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,5,4,3,2,1,0,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6],[29,28,27,26,25,24,23,45,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,6,5,4,3,2,1,0,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7],[30,29,28,27,26,25,24,23,45,44,43,42,41,40,39,38,37,36,35,34,33,32,31,7,6,5,4,3,2,1,0,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8],[31,30,29,28,27,26,25,24,23,45,44,43,42,41,40,39,38,37,36,35,34,33,32,8,7,6,5,4,3,2,1,0,22,21,20,19,18,17,16,15,14,13,12,11,10,9],[32,31,30,29,28,27,26,25,24,23,45,44,43,42,41,40,39,38,37,36,35,34,33,9,8,7,6,5,4,3,2,1,0,22,21,20,19,18,17,16,15,14,13,12,11,10],[33,32,31,30,29,28,27,26,25,24,23,45,44,43,42,41,40,39,38,37,36,35,34,10,9,8,7,6,5,4,3,2,1,0,22,21,20,19,18,17,16,15,14,13,12,11],[34,33,32,31,30,29,28,27,26,25,24,23,45,44,43,42,41,40,39,38,37,36,35,11,10,9,8,7,6,5,4,3,2,1,0,22,21,20,19,18,17,16,15,14,13,12],[35,34,33,32,31,30,29,28,27,26,25,24,23,45,44,43,42,41,40,39,38,37,36,12,11,10,9,8,7,6,5,4,3,2,1,0,22,21,20,19,18,17,16,15,14,13],[36,35,34,33,32,31,30,29,28,27,26,25,24,23,45,44,43,42,41,40,39,38,37,13,12,11,10,9,8,7,6,5,4,3,2,1,0,22,21,20,19,18,17,16,15,14],[37,36,35,34,33,32,31,30,29,28,27,26,25,24,23,45,44,43,42,41,40,39,38,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0,22,21,20,19,18,17,16,15],[38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,23,45,44,43,42,41,40,39,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0,22,21,20,19,18,17,16],[39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,23,45,44,43,42,41,40,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0,22,21,20,19,18,17],[40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,23,45,44,43,42,41,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0,22,21,20,19,18],[41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,23,45,44,43,42,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0,22,21,20,19],[42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,23,45,44,43,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0,22,21,20],[43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,23,45,44,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0,22,21],[44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,23,45,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0,22],[45,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0]],"identity":0,"element":0,"other":23}。請依 [element, singleton_class, commutes_with_all, other, conjugate_to_other, nonconjugate_certificate, boundary] 欄序回答。

查看答案與解釋(0, [0], 是, 23, 否, 是, singleton_class_iff_commutes_with_every_g_and_other_outside_class_is_nonconjugate_without_class_size_formula)

Wave6第八層核對=(0, [0], 是, 23, 否, 是, singleton_class_iff_commutes_with_every_g_and_other_outside_class_is_nonconjugate_without_class_size_formula)；依完整明示資料獨立重算；共軛類是element orbit並形成完整partition；singleton以forall g commute核對；共軛類不是coset或conjugate subgroup；不使用centralizer、class-size公式或類方程。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r03-finite-group-conjugacy-class-0096/)

有限群共軛類 · qf-mod45-conjugacy-singleton-nonconjugate-boundary · candidate





## 97. 有限群共軛類

由完整Cayley table導出全部conjugation action與orbits。操作=conjugacy-singleton-nonconjugate-boundary；資料={"group_table":[[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,0,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,24],[2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,0,1,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,24,25],[3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,0,1,2,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,24,25,26],[4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,0,1,2,3,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,24,25,26,27],[5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,0,1,2,3,4,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,24,25,26,27,28],[6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,0,1,2,3,4,5,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,24,25,26,27,28,29],[7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,0,1,2,3,4,5,6,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,24,25,26,27,28,29,30],[8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,0,1,2,3,4,5,6,7,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,24,25,26,27,28,29,30,31],[9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,0,1,2,3,4,5,6,7,8,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,24,25,26,27,28,29,30,31,32],[10,11,12,13,14,15,16,17,18,19,20,21,22,23,0,1,2,3,4,5,6,7,8,9,34,35,36,37,38,39,40,41,42,43,44,45,46,47,24,25,26,27,28,29,30,31,32,33],[11,12,13,14,15,16,17,18,19,20,21,22,23,0,1,2,3,4,5,6,7,8,9,10,35,36,37,38,39,40,41,42,43,44,45,46,47,24,25,26,27,28,29,30,31,32,33,34],[12,13,14,15,16,17,18,19,20,21,22,23,0,1,2,3,4,5,6,7,8,9,10,11,36,37,38,39,40,41,42,43,44,45,46,47,24,25,26,27,28,29,30,31,32,33,34,35],[13,14,15,16,17,18,19,20,21,22,23,0,1,2,3,4,5,6,7,8,9,10,11,12,37,38,39,40,41,42,43,44,45,46,47,24,25,26,27,28,29,30,31,32,33,34,35,36],[14,15,16,17,18,19,20,21,22,23,0,1,2,3,4,5,6,7,8,9,10,11,12,13,38,39,40,41,42,43,44,45,46,47,24,25,26,27,28,29,30,31,32,33,34,35,36,37],[15,16,17,18,19,20,21,22,23,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,39,40,41,42,43,44,45,46,47,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38],[16,17,18,19,20,21,22,23,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,40,41,42,43,44,45,46,47,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39],[17,18,19,20,21,22,23,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,41,42,43,44,45,46,47,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40],[18,19,20,21,22,23,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,42,43,44,45,46,47,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41],[19,20,21,22,23,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,43,44,45,46,47,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42],[20,21,22,23,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,44,45,46,47,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],[21,22,23,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,45,46,47,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44],[22,23,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,46,47,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45],[23,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,47,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46],[24,47,46,45,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,0,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1],[25,24,47,46,45,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,1,0,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2],[26,25,24,47,46,45,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,2,1,0,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3],[27,26,25,24,47,46,45,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,3,2,1,0,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4],[28,27,26,25,24,47,46,45,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,4,3,2,1,0,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5],[29,28,27,26,25,24,47,46,45,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,5,4,3,2,1,0,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6],[30,29,28,27,26,25,24,47,46,45,44,43,42,41,40,39,38,37,36,35,34,33,32,31,6,5,4,3,2,1,0,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7],[31,30,29,28,27,26,25,24,47,46,45,44,43,42,41,40,39,38,37,36,35,34,33,32,7,6,5,4,3,2,1,0,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8],[32,31,30,29,28,27,26,25,24,47,46,45,44,43,42,41,40,39,38,37,36,35,34,33,8,7,6,5,4,3,2,1,0,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9],[33,32,31,30,29,28,27,26,25,24,47,46,45,44,43,42,41,40,39,38,37,36,35,34,9,8,7,6,5,4,3,2,1,0,23,22,21,20,19,18,17,16,15,14,13,12,11,10],[34,33,32,31,30,29,28,27,26,25,24,47,46,45,44,43,42,41,40,39,38,37,36,35,10,9,8,7,6,5,4,3,2,1,0,23,22,21,20,19,18,17,16,15,14,13,12,11],[35,34,33,32,31,30,29,28,27,26,25,24,47,46,45,44,43,42,41,40,39,38,37,36,11,10,9,8,7,6,5,4,3,2,1,0,23,22,21,20,19,18,17,16,15,14,13,12],[36,35,34,33,32,31,30,29,28,27,26,25,24,47,46,45,44,43,42,41,40,39,38,37,12,11,10,9,8,7,6,5,4,3,2,1,0,23,22,21,20,19,18,17,16,15,14,13],[37,36,35,34,33,32,31,30,29,28,27,26,25,24,47,46,45,44,43,42,41,40,39,38,13,12,11,10,9,8,7,6,5,4,3,2,1,0,23,22,21,20,19,18,17,16,15,14],[38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,47,46,45,44,43,42,41,40,39,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0,23,22,21,20,19,18,17,16,15],[39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,47,46,45,44,43,42,41,40,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0,23,22,21,20,19,18,17,16],[40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,47,46,45,44,43,42,41,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0,23,22,21,20,19,18,17],[41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,47,46,45,44,43,42,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0,23,22,21,20,19,18],[42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,47,46,45,44,43,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0,23,22,21,20,19],[43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,47,46,45,44,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0,23,22,21,20],[44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,47,46,45,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0,23,22,21],[45,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,47,46,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0,23,22],[46,45,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,47,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0,23],[47,46,45,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0]],"identity":0,"element":0,"other":24}。請依 [element, singleton_class, commutes_with_all, other, conjugate_to_other, nonconjugate_certificate, boundary] 欄序回答。

查看答案與解釋(0, [0], 是, 24, 否, 是, singleton_class_iff_commutes_with_every_g_and_other_outside_class_is_nonconjugate_without_class_size_formula)

Wave6第八層核對=(0, [0], 是, 24, 否, 是, singleton_class_iff_commutes_with_every_g_and_other_outside_class_is_nonconjugate_without_class_size_formula)；依完整明示資料獨立重算；共軛類是element orbit並形成完整partition；singleton以forall g commute核對；共軛類不是coset或conjugate subgroup；不使用centralizer、class-size公式或類方程。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r03-finite-group-conjugacy-class-0097/)

有限群共軛類 · qf-mod45-conjugacy-singleton-nonconjugate-boundary · candidate





## 98. 有限群共軛類

由完整Cayley table導出全部conjugation action與orbits。操作=conjugacy-singleton-nonconjugate-boundary；資料={"group_table":[[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,0,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,25],[2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,0,1,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,25,26],[3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,0,1,2,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,25,26,27],[4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,0,1,2,3,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,25,26,27,28],[5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,0,1,2,3,4,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,25,26,27,28,29],[6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,0,1,2,3,4,5,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,25,26,27,28,29,30],[7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,0,1,2,3,4,5,6,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,25,26,27,28,29,30,31],[8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,0,1,2,3,4,5,6,7,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,25,26,27,28,29,30,31,32],[9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,0,1,2,3,4,5,6,7,8,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,25,26,27,28,29,30,31,32,33],[10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,0,1,2,3,4,5,6,7,8,9,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,25,26,27,28,29,30,31,32,33,34],[11,12,13,14,15,16,17,18,19,20,21,22,23,24,0,1,2,3,4,5,6,7,8,9,10,36,37,38,39,40,41,42,43,44,45,46,47,48,49,25,26,27,28,29,30,31,32,33,34,35],[12,13,14,15,16,17,18,19,20,21,22,23,24,0,1,2,3,4,5,6,7,8,9,10,11,37,38,39,40,41,42,43,44,45,46,47,48,49,25,26,27,28,29,30,31,32,33,34,35,36],[13,14,15,16,17,18,19,20,21,22,23,24,0,1,2,3,4,5,6,7,8,9,10,11,12,38,39,40,41,42,43,44,45,46,47,48,49,25,26,27,28,29,30,31,32,33,34,35,36,37],[14,15,16,17,18,19,20,21,22,23,24,0,1,2,3,4,5,6,7,8,9,10,11,12,13,39,40,41,42,43,44,45,46,47,48,49,25,26,27,28,29,30,31,32,33,34,35,36,37,38],[15,16,17,18,19,20,21,22,23,24,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,40,41,42,43,44,45,46,47,48,49,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39],[16,17,18,19,20,21,22,23,24,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,41,42,43,44,45,46,47,48,49,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40],[17,18,19,20,21,22,23,24,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,42,43,44,45,46,47,48,49,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41],[18,19,20,21,22,23,24,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,43,44,45,46,47,48,49,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42],[19,20,21,22,23,24,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,44,45,46,47,48,49,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],[20,21,22,23,24,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,45,46,47,48,49,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44],[21,22,23,24,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,46,47,48,49,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45],[22,23,24,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,47,48,49,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46],[23,24,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,48,49,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47],[24,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,49,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48],[25,49,48,47,46,45,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,0,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1],[26,25,49,48,47,46,45,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,1,0,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2],[27,26,25,49,48,47,46,45,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,2,1,0,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3],[28,27,26,25,49,48,47,46,45,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,3,2,1,0,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4],[29,28,27,26,25,49,48,47,46,45,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,4,3,2,1,0,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5],[30,29,28,27,26,25,49,48,47,46,45,44,43,42,41,40,39,38,37,36,35,34,33,32,31,5,4,3,2,1,0,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6],[31,30,29,28,27,26,25,49,48,47,46,45,44,43,42,41,40,39,38,37,36,35,34,33,32,6,5,4,3,2,1,0,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7],[32,31,30,29,28,27,26,25,49,48,47,46,45,44,43,42,41,40,39,38,37,36,35,34,33,7,6,5,4,3,2,1,0,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8],[33,32,31,30,29,28,27,26,25,49,48,47,46,45,44,43,42,41,40,39,38,37,36,35,34,8,7,6,5,4,3,2,1,0,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9],[34,33,32,31,30,29,28,27,26,25,49,48,47,46,45,44,43,42,41,40,39,38,37,36,35,9,8,7,6,5,4,3,2,1,0,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10],[35,34,33,32,31,30,29,28,27,26,25,49,48,47,46,45,44,43,42,41,40,39,38,37,36,10,9,8,7,6,5,4,3,2,1,0,24,23,22,21,20,19,18,17,16,15,14,13,12,11],[36,35,34,33,32,31,30,29,28,27,26,25,49,48,47,46,45,44,43,42,41,40,39,38,37,11,10,9,8,7,6,5,4,3,2,1,0,24,23,22,21,20,19,18,17,16,15,14,13,12],[37,36,35,34,33,32,31,30,29,28,27,26,25,49,48,47,46,45,44,43,42,41,40,39,38,12,11,10,9,8,7,6,5,4,3,2,1,0,24,23,22,21,20,19,18,17,16,15,14,13],[38,37,36,35,34,33,32,31,30,29,28,27,26,25,49,48,47,46,45,44,43,42,41,40,39,13,12,11,10,9,8,7,6,5,4,3,2,1,0,24,23,22,21,20,19,18,17,16,15,14],[39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,49,48,47,46,45,44,43,42,41,40,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0,24,23,22,21,20,19,18,17,16,15],[40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,49,48,47,46,45,44,43,42,41,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0,24,23,22,21,20,19,18,17,16],[41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,49,48,47,46,45,44,43,42,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0,24,23,22,21,20,19,18,17],[42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,49,48,47,46,45,44,43,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0,24,23,22,21,20,19,18],[43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,49,48,47,46,45,44,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0,24,23,22,21,20,19],[44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,49,48,47,46,45,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0,24,23,22,21,20],[45,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,49,48,47,46,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0,24,23,22,21],[46,45,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,49,48,47,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0,24,23,22],[47,46,45,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,49,48,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0,24,23],[48,47,46,45,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,49,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0,24],[49,48,47,46,45,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0]],"identity":0,"element":0,"other":25}。請依 [element, singleton_class, commutes_with_all, other, conjugate_to_other, nonconjugate_certificate, boundary] 欄序回答。

查看答案與解釋(0, [0], 是, 25, 否, 是, singleton_class_iff_commutes_with_every_g_and_other_outside_class_is_nonconjugate_without_class_size_formula)

Wave6第八層核對=(0, [0], 是, 25, 否, 是, singleton_class_iff_commutes_with_every_g_and_other_outside_class_is_nonconjugate_without_class_size_formula)；依完整明示資料獨立重算；共軛類是element orbit並形成完整partition；singleton以forall g commute核對；共軛類不是coset或conjugate subgroup；不使用centralizer、class-size公式或類方程。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r03-finite-group-conjugacy-class-0098/)

有限群共軛類 · qf-mod45-conjugacy-singleton-nonconjugate-boundary · candidate





## 99. 有限群共軛類

由完整Cayley table導出全部conjugation action與orbits。操作=conjugacy-singleton-nonconjugate-boundary；資料={"group_table":[[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,0,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,26],[2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,0,1,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,26,27],[3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,0,1,2,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,26,27,28],[4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,0,1,2,3,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,26,27,28,29],[5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,0,1,2,3,4,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,26,27,28,29,30],[6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,0,1,2,3,4,5,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,26,27,28,29,30,31],[7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,0,1,2,3,4,5,6,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,26,27,28,29,30,31,32],[8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,0,1,2,3,4,5,6,7,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,26,27,28,29,30,31,32,33],[9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,0,1,2,3,4,5,6,7,8,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,26,27,28,29,30,31,32,33,34],[10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,0,1,2,3,4,5,6,7,8,9,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,26,27,28,29,30,31,32,33,34,35],[11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,0,1,2,3,4,5,6,7,8,9,10,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,26,27,28,29,30,31,32,33,34,35,36],[12,13,14,15,16,17,18,19,20,21,22,23,24,25,0,1,2,3,4,5,6,7,8,9,10,11,38,39,40,41,42,43,44,45,46,47,48,49,50,51,26,27,28,29,30,31,32,33,34,35,36,37],[13,14,15,16,17,18,19,20,21,22,23,24,25,0,1,2,3,4,5,6,7,8,9,10,11,12,39,40,41,42,43,44,45,46,47,48,49,50,51,26,27,28,29,30,31,32,33,34,35,36,37,38],[14,15,16,17,18,19,20,21,22,23,24,25,0,1,2,3,4,5,6,7,8,9,10,11,12,13,40,41,42,43,44,45,46,47,48,49,50,51,26,27,28,29,30,31,32,33,34,35,36,37,38,39],[15,16,17,18,19,20,21,22,23,24,25,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,41,42,43,44,45,46,47,48,49,50,51,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40],[16,17,18,19,20,21,22,23,24,25,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,42,43,44,45,46,47,48,49,50,51,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41],[17,18,19,20,21,22,23,24,25,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,43,44,45,46,47,48,49,50,51,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42],[18,19,20,21,22,23,24,25,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,44,45,46,47,48,49,50,51,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],[19,20,21,22,23,24,25,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,45,46,47,48,49,50,51,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44],[20,21,22,23,24,25,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,46,47,48,49,50,51,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45],[21,22,23,24,25,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,47,48,49,50,51,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46],[22,23,24,25,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,48,49,50,51,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47],[23,24,25,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,49,50,51,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48],[24,25,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,50,51,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49],[25,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,51,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50],[26,51,50,49,48,47,46,45,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,0,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1],[27,26,51,50,49,48,47,46,45,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,1,0,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2],[28,27,26,51,50,49,48,47,46,45,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,2,1,0,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3],[29,28,27,26,51,50,49,48,47,46,45,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,3,2,1,0,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4],[30,29,28,27,26,51,50,49,48,47,46,45,44,43,42,41,40,39,38,37,36,35,34,33,32,31,4,3,2,1,0,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5],[31,30,29,28,27,26,51,50,49,48,47,46,45,44,43,42,41,40,39,38,37,36,35,34,33,32,5,4,3,2,1,0,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6],[32,31,30,29,28,27,26,51,50,49,48,47,46,45,44,43,42,41,40,39,38,37,36,35,34,33,6,5,4,3,2,1,0,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7],[33,32,31,30,29,28,27,26,51,50,49,48,47,46,45,44,43,42,41,40,39,38,37,36,35,34,7,6,5,4,3,2,1,0,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8],[34,33,32,31,30,29,28,27,26,51,50,49,48,47,46,45,44,43,42,41,40,39,38,37,36,35,8,7,6,5,4,3,2,1,0,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9],[35,34,33,32,31,30,29,28,27,26,51,50,49,48,47,46,45,44,43,42,41,40,39,38,37,36,9,8,7,6,5,4,3,2,1,0,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10],[36,35,34,33,32,31,30,29,28,27,26,51,50,49,48,47,46,45,44,43,42,41,40,39,38,37,10,9,8,7,6,5,4,3,2,1,0,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11],[37,36,35,34,33,32,31,30,29,28,27,26,51,50,49,48,47,46,45,44,43,42,41,40,39,38,11,10,9,8,7,6,5,4,3,2,1,0,25,24,23,22,21,20,19,18,17,16,15,14,13,12],[38,37,36,35,34,33,32,31,30,29,28,27,26,51,50,49,48,47,46,45,44,43,42,41,40,39,12,11,10,9,8,7,6,5,4,3,2,1,0,25,24,23,22,21,20,19,18,17,16,15,14,13],[39,38,37,36,35,34,33,32,31,30,29,28,27,26,51,50,49,48,47,46,45,44,43,42,41,40,13,12,11,10,9,8,7,6,5,4,3,2,1,0,25,24,23,22,21,20,19,18,17,16,15,14],[40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,51,50,49,48,47,46,45,44,43,42,41,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0,25,24,23,22,21,20,19,18,17,16,15],[41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,51,50,49,48,47,46,45,44,43,42,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0,25,24,23,22,21,20,19,18,17,16],[42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,51,50,49,48,47,46,45,44,43,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0,25,24,23,22,21,20,19,18,17],[43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,51,50,49,48,47,46,45,44,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0,25,24,23,22,21,20,19,18],[44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,51,50,49,48,47,46,45,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0,25,24,23,22,21,20,19],[45,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,51,50,49,48,47,46,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0,25,24,23,22,21,20],[46,45,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,51,50,49,48,47,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0,25,24,23,22,21],[47,46,45,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,51,50,49,48,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0,25,24,23,22],[48,47,46,45,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,51,50,49,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0,25,24,23],[49,48,47,46,45,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,51,50,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0,25,24],[50,49,48,47,46,45,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,51,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0,25],[51,50,49,48,47,46,45,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0]],"identity":0,"element":0,"other":26}。請依 [element, singleton_class, commutes_with_all, other, conjugate_to_other, nonconjugate_certificate, boundary] 欄序回答。

查看答案與解釋(0, [0], 是, 26, 否, 是, singleton_class_iff_commutes_with_every_g_and_other_outside_class_is_nonconjugate_without_class_size_formula)

Wave6第八層核對=(0, [0], 是, 26, 否, 是, singleton_class_iff_commutes_with_every_g_and_other_outside_class_is_nonconjugate_without_class_size_formula)；依完整明示資料獨立重算；共軛類是element orbit並形成完整partition；singleton以forall g commute核對；共軛類不是coset或conjugate subgroup；不使用centralizer、class-size公式或類方程。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r03-finite-group-conjugacy-class-0099/)

有限群共軛類 · qf-mod45-conjugacy-singleton-nonconjugate-boundary · candidate





## 100. 有限群共軛類

由完整Cayley table導出全部conjugation action與orbits。操作=conjugacy-singleton-nonconjugate-boundary；資料={"group_table":[[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,0,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,27],[2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,0,1,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,27,28],[3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,0,1,2,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,27,28,29],[4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,0,1,2,3,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,27,28,29,30],[5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,0,1,2,3,4,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,27,28,29,30,31],[6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,0,1,2,3,4,5,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,27,28,29,30,31,32],[7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,0,1,2,3,4,5,6,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,27,28,29,30,31,32,33],[8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,0,1,2,3,4,5,6,7,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,27,28,29,30,31,32,33,34],[9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,0,1,2,3,4,5,6,7,8,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,27,28,29,30,31,32,33,34,35],[10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,0,1,2,3,4,5,6,7,8,9,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,27,28,29,30,31,32,33,34,35,36],[11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,0,1,2,3,4,5,6,7,8,9,10,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,27,28,29,30,31,32,33,34,35,36,37],[12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,0,1,2,3,4,5,6,7,8,9,10,11,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,27,28,29,30,31,32,33,34,35,36,37,38],[13,14,15,16,17,18,19,20,21,22,23,24,25,26,0,1,2,3,4,5,6,7,8,9,10,11,12,40,41,42,43,44,45,46,47,48,49,50,51,52,53,27,28,29,30,31,32,33,34,35,36,37,38,39],[14,15,16,17,18,19,20,21,22,23,24,25,26,0,1,2,3,4,5,6,7,8,9,10,11,12,13,41,42,43,44,45,46,47,48,49,50,51,52,53,27,28,29,30,31,32,33,34,35,36,37,38,39,40],[15,16,17,18,19,20,21,22,23,24,25,26,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,42,43,44,45,46,47,48,49,50,51,52,53,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41],[16,17,18,19,20,21,22,23,24,25,26,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,43,44,45,46,47,48,49,50,51,52,53,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42],[17,18,19,20,21,22,23,24,25,26,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,44,45,46,47,48,49,50,51,52,53,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],[18,19,20,21,22,23,24,25,26,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,45,46,47,48,49,50,51,52,53,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44],[19,20,21,22,23,24,25,26,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,46,47,48,49,50,51,52,53,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45],[20,21,22,23,24,25,26,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,47,48,49,50,51,52,53,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46],[21,22,23,24,25,26,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,48,49,50,51,52,53,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47],[22,23,24,25,26,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,49,50,51,52,53,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48],[23,24,25,26,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,50,51,52,53,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49],[24,25,26,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,51,52,53,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50],[25,26,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,52,53,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51],[26,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,53,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52],[27,53,52,51,50,49,48,47,46,45,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,0,26,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1],[28,27,53,52,51,50,49,48,47,46,45,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,1,0,26,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2],[29,28,27,53,52,51,50,49,48,47,46,45,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,2,1,0,26,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3],[30,29,28,27,53,52,51,50,49,48,47,46,45,44,43,42,41,40,39,38,37,36,35,34,33,32,31,3,2,1,0,26,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4],[31,30,29,28,27,53,52,51,50,49,48,47,46,45,44,43,42,41,40,39,38,37,36,35,34,33,32,4,3,2,1,0,26,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5],[32,31,30,29,28,27,53,52,51,50,49,48,47,46,45,44,43,42,41,40,39,38,37,36,35,34,33,5,4,3,2,1,0,26,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6],[33,32,31,30,29,28,27,53,52,51,50,49,48,47,46,45,44,43,42,41,40,39,38,37,36,35,34,6,5,4,3,2,1,0,26,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7],[34,33,32,31,30,29,28,27,53,52,51,50,49,48,47,46,45,44,43,42,41,40,39,38,37,36,35,7,6,5,4,3,2,1,0,26,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8],[35,34,33,32,31,30,29,28,27,53,52,51,50,49,48,47,46,45,44,43,42,41,40,39,38,37,36,8,7,6,5,4,3,2,1,0,26,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9],[36,35,34,33,32,31,30,29,28,27,53,52,51,50,49,48,47,46,45,44,43,42,41,40,39,38,37,9,8,7,6,5,4,3,2,1,0,26,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10],[37,36,35,34,33,32,31,30,29,28,27,53,52,51,50,49,48,47,46,45,44,43,42,41,40,39,38,10,9,8,7,6,5,4,3,2,1,0,26,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11],[38,37,36,35,34,33,32,31,30,29,28,27,53,52,51,50,49,48,47,46,45,44,43,42,41,40,39,11,10,9,8,7,6,5,4,3,2,1,0,26,25,24,23,22,21,20,19,18,17,16,15,14,13,12],[39,38,37,36,35,34,33,32,31,30,29,28,27,53,52,51,50,49,48,47,46,45,44,43,42,41,40,12,11,10,9,8,7,6,5,4,3,2,1,0,26,25,24,23,22,21,20,19,18,17,16,15,14,13],[40,39,38,37,36,35,34,33,32,31,30,29,28,27,53,52,51,50,49,48,47,46,45,44,43,42,41,13,12,11,10,9,8,7,6,5,4,3,2,1,0,26,25,24,23,22,21,20,19,18,17,16,15,14],[41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,53,52,51,50,49,48,47,46,45,44,43,42,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0,26,25,24,23,22,21,20,19,18,17,16,15],[42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,53,52,51,50,49,48,47,46,45,44,43,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0,26,25,24,23,22,21,20,19,18,17,16],[43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,53,52,51,50,49,48,47,46,45,44,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0,26,25,24,23,22,21,20,19,18,17],[44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,53,52,51,50,49,48,47,46,45,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0,26,25,24,23,22,21,20,19,18],[45,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,53,52,51,50,49,48,47,46,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0,26,25,24,23,22,21,20,19],[46,45,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,53,52,51,50,49,48,47,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0,26,25,24,23,22,21,20],[47,46,45,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,53,52,51,50,49,48,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0,26,25,24,23,22,21],[48,47,46,45,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,53,52,51,50,49,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0,26,25,24,23,22],[49,48,47,46,45,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,53,52,51,50,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0,26,25,24,23],[50,49,48,47,46,45,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,53,52,51,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0,26,25,24],[51,50,49,48,47,46,45,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,53,52,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0,26,25],[52,51,50,49,48,47,46,45,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,53,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0,26],[53,52,51,50,49,48,47,46,45,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0]],"identity":0,"element":0,"other":27}。請依 [element, singleton_class, commutes_with_all, other, conjugate_to_other, nonconjugate_certificate, boundary] 欄序回答。

查看答案與解釋(0, [0], 是, 27, 否, 是, singleton_class_iff_commutes_with_every_g_and_other_outside_class_is_nonconjugate_without_class_size_formula)

Wave6第八層核對=(0, [0], 是, 27, 否, 是, singleton_class_iff_commutes_with_every_g_and_other_outside_class_is_nonconjugate_without_class_size_formula)；依完整明示資料獨立重算；共軛類是element orbit並形成完整partition；singleton以forall g commute核對；共軛類不是coset或conjugate subgroup；不使用centralizer、class-size公式或類方程。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r03-finite-group-conjugacy-class-0100/)

有限群共軛類 · qf-mod45-conjugacy-singleton-nonconjugate-boundary · candidate



[原始題目 JSONL](https://ocme.evemisslab.com/data/questions/batches/batch-20261015-advance-20261114-r03-finite-group-conjugacy-class-foundations/questions.jsonl) · [驗收報告](https://ocme.evemisslab.com/data/questions/batches/batch-20261015-advance-20261114-r03-finite-group-conjugacy-class-foundations/validation-report.json)