# 第 24865 題：有限群共軛類

[返回所在分頁 125](https://ocme.evemisslab.com/zh-Hant/questions/page/125/)

[← 逐題詳解目錄](https://ocme.evemisslab.com/zh-Hant/questions/) · [原題批次](https://ocme.evemisslab.com/zh-Hant/practice/batch-20261015-advance-20261114-r03-finite-group-conjugacy-class-foundations/#q-20261015-advance-20261114-r03-finite-group-conjugacy-class-0065)

本頁是已完成第二對話 AI 數理與中英語義覆核的教學詳解，只支持本題明示的模型與前提。沒有人工審查或新 Lean 證明，也不提升原題或 MKO 的 Canonical 真值狀態。

R0048-24865 · q-20261015-advance-20261114-r03-finite-group-conjugacy-class-0065



## 原題與已知條件

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 exact_ordered_tuple_declared_by_interface 欄序回答。


- G001 — 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 exact_ordered_tuple_declared_by_interface 欄序回答。





## 定義與適用範圍

沿用原題明示的論域、假設與來源 MKO 定義。本題已完成第二對話數理與中英語義覆核，並由原始參數逐題獨立重算模型、答案與每個算術步驟；原題仍為 candidate。


- [mko-finite-group-conjugacy-class](https://ocme.evemisslab.com/zh-Hant/mko/mko-finite-group-conjugacy-class/)





## 逐步推導

S001 · implies操作前

source roles = [conjugacy-partition-audit]

操作後

derived = [[classes, partition_certificate, covered_element_count, group_order, certificate]]

條件：無

直接列來源完整欄序，不需JavaScript；原題、布林旗標、數學物件與非聲稱保持分層。

步驟識別與依賴規則：source_ordered_fields_without_JS · 依賴：G001





S002 · implies操作前

source roles = [Conjugacy ORIGINAL group, 64, [[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]], 0]

操作後

derived = [34, [[0, 0, 0, 0], [1, 1, 1, 1], [2, 2, 2, 2], [3, 3, 3, 3], [4, 4, 4, 4], [5, 5, 5, 5], [6, 6, 6, 6], [7, 7, 7, 7], [8, 8, 8, 8], [9, 9, 9, 9], [10, 10, 10, 10], [11, 11, 11, 11], [12, 12, 12, 12], [13, 13, 13, 13], [14, 14, 14, 14], [15, 15, 15, 15], [16, 16, 16, 16], [17, 17, 17, 17], [18, 18, 18, 18], [19, 19, 19, 19], [20, 20, 20, 20], [21, 21, 21, 21], [22, 22, 22, 22], [23, 23, 23, 23], [24, 24, 24, 24], [25, 25, 25, 25], [26, 26, 26, 26], [27, 27, 27, 27], [28, 28, 28, 28], [29, 29, 29, 29], [30, 30, 30, 30], [31, 31, 31, 31], [32, 32, 32, 32], [33, 33, 33, 33]], 是]

條件：無

先驗完整n×n閉合表與實際identity標籤，非預設0。mod44上限32，mod45上限64；同一carrier不能混入另一表。

步驟識別與依賴規則：Group_complete_Cayley_signature_actual_identity · 依賴：G001, S001





S003 · implies操作前

source roles = [Conjugacy ORIGINAL group, 34, FOR EVERY x,y,z in0..n-1]

操作後

derived = [[[是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是], [是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是], [是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是], [是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是], [是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是], [是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是], [是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是], [是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是], [是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是], [是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是], [是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是], [是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是], [是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是], [是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是], [是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是], [是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是], [是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是], [是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是], [是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是], [是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是], [是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是], [是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是], [是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是], [是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是], [是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是], [是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是], [是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是], [是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是], [是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是], [是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是], [是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是], [是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是], [是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是], [是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是]], 39304, 是]

條件：無

矩陣(x,y)逐全部z核(xy)z=x(yz)，故涵蓋全部n³三元組，不是抽樣。表已在前步完整列出，不重印數百萬同義查表項。

步驟識別與依賴規則：Group_ALL_associativity_triples_compact_complete_pair_matrix · 依賴：G001, S002





S004 · implies操作前

source roles = [Conjugacy ORIGINAL group, 0]

操作後

derived = [[0, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33], [[0, 0, 0, 0], [1, 16, 0, 0], [2, 15, 0, 0], [3, 14, 0, 0], [4, 13, 0, 0], [5, 12, 0, 0], [6, 11, 0, 0], [7, 10, 0, 0], [8, 9, 0, 0], [9, 8, 0, 0], [10, 7, 0, 0], [11, 6, 0, 0], [12, 5, 0, 0], [13, 4, 0, 0], [14, 3, 0, 0], [15, 2, 0, 0], [16, 1, 0, 0], [17, 17, 0, 0], [18, 18, 0, 0], [19, 19, 0, 0], [20, 20, 0, 0], [21, 21, 0, 0], [22, 22, 0, 0], [23, 23, 0, 0], [24, 24, 0, 0], [25, 25, 0, 0], [26, 26, 0, 0], [27, 27, 0, 0], [28, 28, 0, 0], [29, 29, 0, 0], [30, 30, 0, 0], [31, 31, 0, 0], [32, 32, 0, 0], [33, 33, 0, 0]], 是]

條件：無

每個元素的左、右逆都要回到同一實際identity；結合律使兩側逆唯一。這才完成群前提。

步驟識別與依賴規則：Group_ALL_two_sided_inverses · 依賴：G001, S003





S005 · implies操作前

source roles = [0, 0, [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]]

操作後

derived = [[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, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33]]

條件：無

對每個原元素x先算gx再乘g^-1，形成完整acting row；這是element action，不是conjugate subgroup。

步驟識別與依賴規則：Conjugacy_EVERY_g_EVERY_element_exact_action_row · 依賴：G001, S004





S006 · implies操作前

source roles = [1, 16, [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]]

操作後

derived = [[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], [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]]

條件：無

對每個原元素x先算gx再乘g^-1，形成完整acting row；這是element action，不是conjugate subgroup。

步驟識別與依賴規則：Conjugacy_EVERY_g_EVERY_element_exact_action_row · 依賴：G001, S005





S007 · implies操作前

source roles = [2, 15, [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]]

操作後

derived = [[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], [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]]

條件：無

對每個原元素x先算gx再乘g^-1，形成完整acting row；這是element action，不是conjugate subgroup。

步驟識別與依賴規則：Conjugacy_EVERY_g_EVERY_element_exact_action_row · 依賴：G001, S006





S008 · implies操作前

source roles = [3, 14, [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]]

操作後

derived = [[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], [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]]

條件：無

對每個原元素x先算gx再乘g^-1，形成完整acting row；這是element action，不是conjugate subgroup。

步驟識別與依賴規則：Conjugacy_EVERY_g_EVERY_element_exact_action_row · 依賴：G001, S007





S009 · implies操作前

source roles = [4, 13, [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]]

操作後

derived = [[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], [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]]

條件：無

對每個原元素x先算gx再乘g^-1，形成完整acting row；這是element action，不是conjugate subgroup。

步驟識別與依賴規則：Conjugacy_EVERY_g_EVERY_element_exact_action_row · 依賴：G001, S008





S010 · implies操作前

source roles = [5, 12, [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]]

操作後

derived = [[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], [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]]

條件：無

對每個原元素x先算gx再乘g^-1，形成完整acting row；這是element action，不是conjugate subgroup。

步驟識別與依賴規則：Conjugacy_EVERY_g_EVERY_element_exact_action_row · 依賴：G001, S009





S011 · implies操作前

source roles = [6, 11, [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]]

操作後

derived = [[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], [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]]

條件：無

對每個原元素x先算gx再乘g^-1，形成完整acting row；這是element action，不是conjugate subgroup。

步驟識別與依賴規則：Conjugacy_EVERY_g_EVERY_element_exact_action_row · 依賴：G001, S010





S012 · implies操作前

source roles = [7, 10, [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]]

操作後

derived = [[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], [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]]

條件：無

對每個原元素x先算gx再乘g^-1，形成完整acting row；這是element action，不是conjugate subgroup。

步驟識別與依賴規則：Conjugacy_EVERY_g_EVERY_element_exact_action_row · 依賴：G001, S011





S013 · implies操作前

source roles = [8, 9, [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]]

操作後

derived = [[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], [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]]

條件：無

對每個原元素x先算gx再乘g^-1，形成完整acting row；這是element action，不是conjugate subgroup。

步驟識別與依賴規則：Conjugacy_EVERY_g_EVERY_element_exact_action_row · 依賴：G001, S012





S014 · implies操作前

source roles = [9, 8, [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]]

操作後

derived = [[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], [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]]

條件：無

對每個原元素x先算gx再乘g^-1，形成完整acting row；這是element action，不是conjugate subgroup。

步驟識別與依賴規則：Conjugacy_EVERY_g_EVERY_element_exact_action_row · 依賴：G001, S013





S015 · implies操作前

source roles = [10, 7, [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]]

操作後

derived = [[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], [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]]

條件：無

對每個原元素x先算gx再乘g^-1，形成完整acting row；這是element action，不是conjugate subgroup。

步驟識別與依賴規則：Conjugacy_EVERY_g_EVERY_element_exact_action_row · 依賴：G001, S014





S016 · implies操作前

source roles = [11, 6, [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]]

操作後

derived = [[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], [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]]

條件：無

對每個原元素x先算gx再乘g^-1，形成完整acting row；這是element action，不是conjugate subgroup。

步驟識別與依賴規則：Conjugacy_EVERY_g_EVERY_element_exact_action_row · 依賴：G001, S015





S017 · implies操作前

source roles = [12, 5, [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]]

操作後

derived = [[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], [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]]

條件：無

對每個原元素x先算gx再乘g^-1，形成完整acting row；這是element action，不是conjugate subgroup。

步驟識別與依賴規則：Conjugacy_EVERY_g_EVERY_element_exact_action_row · 依賴：G001, S016





S018 · implies操作前

source roles = [13, 4, [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]]

操作後

derived = [[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], [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]]

條件：無

對每個原元素x先算gx再乘g^-1，形成完整acting row；這是element action，不是conjugate subgroup。

步驟識別與依賴規則：Conjugacy_EVERY_g_EVERY_element_exact_action_row · 依賴：G001, S017





S019 · implies操作前

source roles = [14, 3, [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]]

操作後

derived = [[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], [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]]

條件：無

對每個原元素x先算gx再乘g^-1，形成完整acting row；這是element action，不是conjugate subgroup。

步驟識別與依賴規則：Conjugacy_EVERY_g_EVERY_element_exact_action_row · 依賴：G001, S018





S020 · implies操作前

source roles = [15, 2, [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]]

操作後

derived = [[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], [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]]

條件：無

對每個原元素x先算gx再乘g^-1，形成完整acting row；這是element action，不是conjugate subgroup。

步驟識別與依賴規則：Conjugacy_EVERY_g_EVERY_element_exact_action_row · 依賴：G001, S019





S021 · implies操作前

source roles = [16, 1, [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]]

操作後

derived = [[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], [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]]

條件：無

對每個原元素x先算gx再乘g^-1，形成完整acting row；這是element action，不是conjugate subgroup。

步驟識別與依賴規則：Conjugacy_EVERY_g_EVERY_element_exact_action_row · 依賴：G001, S020





S022 · implies操作前

source roles = [17, 17, [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]]

操作後

derived = [[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], [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]]

條件：無

對每個原元素x先算gx再乘g^-1，形成完整acting row；這是element action，不是conjugate subgroup。

步驟識別與依賴規則：Conjugacy_EVERY_g_EVERY_element_exact_action_row · 依賴：G001, S021





S023 · implies操作前

source roles = [18, 18, [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]]

操作後

derived = [[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], [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]]

條件：無

對每個原元素x先算gx再乘g^-1，形成完整acting row；這是element action，不是conjugate subgroup。

步驟識別與依賴規則：Conjugacy_EVERY_g_EVERY_element_exact_action_row · 依賴：G001, S022





S024 · implies操作前

source roles = [19, 19, [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]]

操作後

derived = [[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], [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]]

條件：無

對每個原元素x先算gx再乘g^-1，形成完整acting row；這是element action，不是conjugate subgroup。

步驟識別與依賴規則：Conjugacy_EVERY_g_EVERY_element_exact_action_row · 依賴：G001, S023





S025 · implies操作前

source roles = [20, 20, [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]]

操作後

derived = [[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], [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]]

條件：無

對每個原元素x先算gx再乘g^-1，形成完整acting row；這是element action，不是conjugate subgroup。

步驟識別與依賴規則：Conjugacy_EVERY_g_EVERY_element_exact_action_row · 依賴：G001, S024





S026 · implies操作前

source roles = [21, 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, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33]]

操作後

derived = [[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], [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]]

條件：無

對每個原元素x先算gx再乘g^-1，形成完整acting row；這是element action，不是conjugate subgroup。

步驟識別與依賴規則：Conjugacy_EVERY_g_EVERY_element_exact_action_row · 依賴：G001, S025





S027 · implies操作前

source roles = [22, 22, [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]]

操作後

derived = [[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], [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]]

條件：無

對每個原元素x先算gx再乘g^-1，形成完整acting row；這是element action，不是conjugate subgroup。

步驟識別與依賴規則：Conjugacy_EVERY_g_EVERY_element_exact_action_row · 依賴：G001, S026





S028 · implies操作前

source roles = [23, 23, [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]]

操作後

derived = [[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], [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]]

條件：無

對每個原元素x先算gx再乘g^-1，形成完整acting row；這是element action，不是conjugate subgroup。

步驟識別與依賴規則：Conjugacy_EVERY_g_EVERY_element_exact_action_row · 依賴：G001, S027





S029 · implies操作前

source roles = [24, 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, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33]]

操作後

derived = [[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], [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]]

條件：無

對每個原元素x先算gx再乘g^-1，形成完整acting row；這是element action，不是conjugate subgroup。

步驟識別與依賴規則：Conjugacy_EVERY_g_EVERY_element_exact_action_row · 依賴：G001, S028





S030 · implies操作前

source roles = [25, 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, 28, 29, 30, 31, 32, 33]]

操作後

derived = [[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], [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]]

條件：無

對每個原元素x先算gx再乘g^-1，形成完整acting row；這是element action，不是conjugate subgroup。

步驟識別與依賴規則：Conjugacy_EVERY_g_EVERY_element_exact_action_row · 依賴：G001, S029





S031 · implies操作前

source roles = [26, 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, 26, 27, 28, 29, 30, 31, 32, 33]]

操作後

derived = [[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], [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]]

條件：無

對每個原元素x先算gx再乘g^-1，形成完整acting row；這是element action，不是conjugate subgroup。

步驟識別與依賴規則：Conjugacy_EVERY_g_EVERY_element_exact_action_row · 依賴：G001, S030





S032 · implies操作前

source roles = [27, 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, 26, 27, 28, 29, 30, 31, 32, 33]]

操作後

derived = [[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], [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]]

條件：無

對每個原元素x先算gx再乘g^-1，形成完整acting row；這是element action，不是conjugate subgroup。

步驟識別與依賴規則：Conjugacy_EVERY_g_EVERY_element_exact_action_row · 依賴：G001, S031





S033 · implies操作前

source roles = [28, 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, 27, 28, 29, 30, 31, 32, 33]]

操作後

derived = [[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], [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]]

條件：無

對每個原元素x先算gx再乘g^-1，形成完整acting row；這是element action，不是conjugate subgroup。

步驟識別與依賴規則：Conjugacy_EVERY_g_EVERY_element_exact_action_row · 依賴：G001, S032





S034 · implies操作前

source roles = [29, 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, 32, 33]]

操作後

derived = [[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], [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]]

條件：無

對每個原元素x先算gx再乘g^-1，形成完整acting row；這是element action，不是conjugate subgroup。

步驟識別與依賴規則：Conjugacy_EVERY_g_EVERY_element_exact_action_row · 依賴：G001, S033





S035 · implies操作前

source roles = [30, 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, 27, 28, 29, 30, 31, 32, 33]]

操作後

derived = [[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], [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]]

條件：無

對每個原元素x先算gx再乘g^-1，形成完整acting row；這是element action，不是conjugate subgroup。

步驟識別與依賴規則：Conjugacy_EVERY_g_EVERY_element_exact_action_row · 依賴：G001, S034





S036 · implies操作前

source roles = [31, 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, 26, 27, 28, 29, 30, 31, 32, 33]]

操作後

derived = [[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], [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]]

條件：無

對每個原元素x先算gx再乘g^-1，形成完整acting row；這是element action，不是conjugate subgroup。

步驟識別與依賴規則：Conjugacy_EVERY_g_EVERY_element_exact_action_row · 依賴：G001, S035





S037 · implies操作前

source roles = [32, 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, 27, 28, 29, 30, 31, 32, 33]]

操作後

derived = [[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], [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]]

條件：無

對每個原元素x先算gx再乘g^-1，形成完整acting row；這是element action，不是conjugate subgroup。

步驟識別與依賴規則：Conjugacy_EVERY_g_EVERY_element_exact_action_row · 依賴：G001, S036





S038 · implies操作前

source roles = [33, 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]]

操作後

derived = [[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], [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]]

條件：無

對每個原元素x先算gx再乘g^-1，形成完整acting row；這是element action，不是conjugate subgroup。

步驟識別與依賴規則：Conjugacy_EVERY_g_EVERY_element_exact_action_row · 依賴：G001, S037





S039 · implies操作前

source roles = [0, 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, 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]]]

操作後

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條件：無

逐全部g,h,x核composition，亦由(gh)^-1=h^-1g^-1及結合律推同一公式；identity另驗。不是僅列出一個action表就假定axioms。

步驟識別與依賴規則：Conjugacy_ALL_action_axioms_and_GENERAL_algebra · 依賴：G001, S038





S040 · implies操作前

source roles = [[[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]]]

操作後

derived = [[[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]], 34, 34, 是]

條件：無

e給自反、g^-1給反向、群乘積給傳遞；故所有完整orbits相等或不交並覆蓋G。按來源coset-like列表排序不代表它們是cosets；不引centralizer/class-size或類方程。

步驟識別與依賴規則：Conjugacy_complete_orbits_equal_or_disjoint_partition · 依賴：G001, S039









## 逐步反向核對


- S040 · premise_and_result_audit — 回到原始資料與本步條件核對，不把單向推論誤稱等價。
- S039 · premise_and_result_audit — 回到原始資料與本步條件核對，不把單向推論誤稱等價。
- S038 · premise_and_result_audit — 回到原始資料與本步條件核對，不把單向推論誤稱等價。
- S037 · premise_and_result_audit — 回到原始資料與本步條件核對，不把單向推論誤稱等價。
- S036 · premise_and_result_audit — 回到原始資料與本步條件核對，不把單向推論誤稱等價。
- S035 · premise_and_result_audit — 回到原始資料與本步條件核對，不把單向推論誤稱等價。
- S034 · premise_and_result_audit — 回到原始資料與本步條件核對，不把單向推論誤稱等價。
- S033 · premise_and_result_audit — 回到原始資料與本步條件核對，不把單向推論誤稱等價。
- S032 · premise_and_result_audit — 回到原始資料與本步條件核對，不把單向推論誤稱等價。
- S031 · premise_and_result_audit — 回到原始資料與本步條件核對，不把單向推論誤稱等價。
- S030 · premise_and_result_audit — 回到原始資料與本步條件核對，不把單向推論誤稱等價。
- S029 · premise_and_result_audit — 回到原始資料與本步條件核對，不把單向推論誤稱等價。
- S028 · premise_and_result_audit — 回到原始資料與本步條件核對，不把單向推論誤稱等價。
- S027 · premise_and_result_audit — 回到原始資料與本步條件核對，不把單向推論誤稱等價。
- S026 · premise_and_result_audit — 回到原始資料與本步條件核對，不把單向推論誤稱等價。
- S025 · premise_and_result_audit — 回到原始資料與本步條件核對，不把單向推論誤稱等價。
- S024 · premise_and_result_audit — 回到原始資料與本步條件核對，不把單向推論誤稱等價。
- S023 · premise_and_result_audit — 回到原始資料與本步條件核對，不把單向推論誤稱等價。
- S022 · premise_and_result_audit — 回到原始資料與本步條件核對，不把單向推論誤稱等價。
- S021 · premise_and_result_audit — 回到原始資料與本步條件核對，不把單向推論誤稱等價。
- S020 · premise_and_result_audit — 回到原始資料與本步條件核對，不把單向推論誤稱等價。
- S019 · premise_and_result_audit — 回到原始資料與本步條件核對，不把單向推論誤稱等價。
- S018 · premise_and_result_audit — 回到原始資料與本步條件核對，不把單向推論誤稱等價。
- S017 · premise_and_result_audit — 回到原始資料與本步條件核對，不把單向推論誤稱等價。
- S016 · premise_and_result_audit — 回到原始資料與本步條件核對，不把單向推論誤稱等價。
- S015 · premise_and_result_audit — 回到原始資料與本步條件核對，不把單向推論誤稱等價。
- S014 · premise_and_result_audit — 回到原始資料與本步條件核對，不把單向推論誤稱等價。
- S013 · premise_and_result_audit — 回到原始資料與本步條件核對，不把單向推論誤稱等價。
- S012 · premise_and_result_audit — 回到原始資料與本步條件核對，不把單向推論誤稱等價。
- S011 · premise_and_result_audit — 回到原始資料與本步條件核對，不把單向推論誤稱等價。
- S010 · premise_and_result_audit — 回到原始資料與本步條件核對，不把單向推論誤稱等價。
- S009 · premise_and_result_audit — 回到原始資料與本步條件核對，不把單向推論誤稱等價。
- S008 · premise_and_result_audit — 回到原始資料與本步條件核對，不把單向推論誤稱等價。
- S007 · premise_and_result_audit — 回到原始資料與本步條件核對，不把單向推論誤稱等價。
- S006 · premise_and_result_audit — 回到原始資料與本步條件核對，不把單向推論誤稱等價。
- S005 · premise_and_result_audit — 回到原始資料與本步條件核對，不把單向推論誤稱等價。
- S004 · premise_and_result_audit — 回到原始資料與本步條件核對，不把單向推論誤稱等價。
- S003 · premise_and_result_audit — 回到原始資料與本步條件核對，不把單向推論誤稱等價。
- S002 · premise_and_result_audit — 回到原始資料與本步條件核對，不把單向推論誤稱等價。
- S001 · premise_and_result_audit — 回到原始資料與本步條件核對，不把單向推論誤稱等價。





## 結論

([[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)

依上列完整代值及條件核對得到原題答案；原題編號、格式與狀態保持不變。





## 本題覆核與來源綁定

覆核日期：2026-10-26

原題、答案、步驟表達式、數值 AST 與既有歷史保持原樣；原來的候選狀態屬於來源歷史，不覆寫為形式化證明。

來源雜湊與覆核憑證
- input commit: 0f7be61e2c22317a4075561dc822c87d881a50db
- original question SHA-256: ba4ea46048243b4885b768dcf308b748c45104bb6eacca63ab5bf5808e342882
- candidate record SHA-256: 391933c5b580c5c2c8e10f00d42a6780369897e341f0e09483fa647d3e205ed8
- semantic review receipt SHA-256: 049a9e07e69fead88d93b34f0937b9470a06d71c1a8d097058fc83554529bdd0
- question-first witness SHA-256: 0c71ebb418f3de347d232d159fc25e93036f4ab9166bcfb5ee5b4be86d5c55b9
- Lean: NOT_RUN · human review: NOT_PERFORMED

[同源完整 JSON](https://ocme.evemisslab.com/data/question-derivations/questions/q-20261015-advance-20261114-r03-finite-group-conjugacy-class-0065.json)




