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第 24869 題：有限群共軛類

本頁導覽
  1. 原題與已知條件
  2. 定義與適用範圍
  3. 逐步推導
  4. 逐步反向核對
  5. 結論
  6. 本題覆核與來源綁定

返回所在分頁 125

← 逐題詳解目錄 · 原題批次

R0048-24869 · q-20261015-advance-20261114-r03-finite-group-conjugacy-class-0069

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":[[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41],[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 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":[[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41],[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 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。

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, 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]], 0]

操作後

derived = [42, [[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], [34, 34, 34, 34], [35, 35, 35, 35], [36, 36, 36, 36], [37, 37, 37, 37], [38, 38, 38, 38], [39, 39, 39, 39], [40, 40, 40, 40], [41, 41, 41, 41]], 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, 42, 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, 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是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是], [是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是], [是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是], [是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是], [是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是], [是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是], [是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是], [是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是], [是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是], [是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是], [是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是], [是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是], [是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是], [是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是], [是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是], [是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是], [是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是], [是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是], [是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是], [是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是], [是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是], [是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是], [是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是], [是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是], [是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是], [是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是], [是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是]], 74088, 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, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41], [[0, 0, 0, 0], [1, 20, 0, 0], [2, 19, 0, 0], [3, 18, 0, 0], [4, 17, 0, 0], [5, 16, 0, 0], [6, 15, 0, 0], [7, 14, 0, 0], [8, 13, 0, 0], [9, 12, 0, 0], [10, 11, 0, 0], [11, 10, 0, 0], [12, 9, 0, 0], [13, 8, 0, 0], [14, 7, 0, 0], [15, 6, 0, 0], [16, 5, 0, 0], [17, 4, 0, 0], [18, 3, 0, 0], [19, 2, 0, 0], [20, 1, 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], [34, 34, 0, 0], [35, 35, 0, 0], [36, 36, 0, 0], [37, 37, 0, 0], [38, 38, 0, 0], [39, 39, 0, 0], [40, 40, 0, 0], [41, 41, 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, 34, 35, 36, 37, 38, 39, 40, 41]]

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, 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]]

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, 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, 34, 35, 36, 37, 38, 39, 40, 41]]

操作後

derived = [[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], [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]]

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, 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, 34, 35, 36, 37, 38, 39, 40, 41]]

操作後

derived = [[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], [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]]

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, 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, 34, 35, 36, 37, 38, 39, 40, 41]]

操作後

derived = [[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], [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]]

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, 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, 34, 35, 36, 37, 38, 39, 40, 41]]

操作後

derived = [[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], [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]]

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, 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, 34, 35, 36, 37, 38, 39, 40, 41]]

操作後

derived = [[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], [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]]

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, 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, 34, 35, 36, 37, 38, 39, 40, 41]]

操作後

derived = [[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], [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]]

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, 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, 34, 35, 36, 37, 38, 39, 40, 41]]

操作後

derived = [[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], [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]]

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, 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, 34, 35, 36, 37, 38, 39, 40, 41]]

操作後

derived = [[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], [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]]

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, 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, 34, 35, 36, 37, 38, 39, 40, 41]]

操作後

derived = [[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], [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]]

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, 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, 34, 35, 36, 37, 38, 39, 40, 41]]

操作後

derived = [[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], [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]]

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, 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, 34, 35, 36, 37, 38, 39, 40, 41]]

操作後

derived = [[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], [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]]

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, 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, 34, 35, 36, 37, 38, 39, 40, 41]]

操作後

derived = [[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], [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]]

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, 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, 34, 35, 36, 37, 38, 39, 40, 41]]

操作後

derived = [[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], [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]]

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, 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, 34, 35, 36, 37, 38, 39, 40, 41]]

操作後

derived = [[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], [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]]

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, 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, 34, 35, 36, 37, 38, 39, 40, 41]]

操作後

derived = [[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], [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]]

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, 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, 34, 35, 36, 37, 38, 39, 40, 41]]

操作後

derived = [[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], [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]]

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, 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, 34, 35, 36, 37, 38, 39, 40, 41]]

操作後

derived = [[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], [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]]

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, 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, 34, 35, 36, 37, 38, 39, 40, 41]]

操作後

derived = [[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], [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]]

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, 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, 34, 35, 36, 37, 38, 39, 40, 41]]

操作後

derived = [[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], [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]]

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, 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, 34, 35, 36, 37, 38, 39, 40, 41]]

操作後

derived = [[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], [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]]

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, 34, 35, 36, 37, 38, 39, 40, 41]]

操作後

derived = [[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], [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]]

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, 34, 35, 36, 37, 38, 39, 40, 41]]

操作後

derived = [[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], [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]]

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, 34, 35, 36, 37, 38, 39, 40, 41]]

操作後

derived = [[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], [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]]

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, 34, 35, 36, 37, 38, 39, 40, 41]]

操作後

derived = [[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], [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]]

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, 34, 35, 36, 37, 38, 39, 40, 41]]

操作後

derived = [[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], [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]]

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, 34, 35, 36, 37, 38, 39, 40, 41]]

操作後

derived = [[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], [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]]

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, 34, 35, 36, 37, 38, 39, 40, 41]]

操作後

derived = [[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], [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]]

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, 34, 35, 36, 37, 38, 39, 40, 41]]

操作後

derived = [[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], [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]]

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, 34, 35, 36, 37, 38, 39, 40, 41]]

操作後

derived = [[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], [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]]

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, 34, 35, 36, 37, 38, 39, 40, 41]]

操作後

derived = [[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], [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]]

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, 34, 35, 36, 37, 38, 39, 40, 41]]

操作後

derived = [[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], [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]]

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, 34, 35, 36, 37, 38, 39, 40, 41]]

操作後

derived = [[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], [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]]

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, 34, 35, 36, 37, 38, 39, 40, 41]]

操作後

derived = [[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], [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]]

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 = [34, 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, 34, 35, 36, 37, 38, 39, 40, 41]]

操作後

derived = [[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], [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]]

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, S038

S040 · implies

操作前

source roles = [35, 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, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41]]

操作後

derived = [[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], [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]]

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, S039

S041 · implies

操作前

source roles = [36, 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, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41]]

操作後

derived = [[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], [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]]

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, S040

S042 · implies

操作前

source roles = [37, 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, 40, 41]]

操作後

derived = [[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], [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]]

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, S041

S043 · implies

操作前

source roles = [38, 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, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41]]

操作後

derived = [[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], [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]]

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, S042

S044 · implies

操作前

source roles = [39, 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, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41]]

操作後

derived = [[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], [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]]

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, S043

S045 · implies

操作前

source roles = [40, 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, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41]]

操作後

derived = [[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], [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]]

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, S044

S046 · implies

操作前

source roles = [41, 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]]

操作後

derived = [[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], [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]]

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, S045

S047 · implies

操作前

source roles = [0, 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, 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]]]

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, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是], [是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是], [是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是], [是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是], [是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是], [是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是], [是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是], [是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是], [是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是], [是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是], [是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是], [是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是], [是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是], [是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是], [是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是]], 是, (gh)x(gh)^-1=g(hxh^-1)g^-1]

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, S046

S048 · 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, 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]]]

操作後

derived = [[[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]], 42, 42, 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, S047

逐步反向核對

  • S048 · 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。
  • S047 · 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。
  • S046 · 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。
  • S045 · 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。
  • S044 · 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。
  • S043 · 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。
  • S042 · 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。
  • S041 · 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。
  • 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, 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: a108326ef28d581d0f3293d3b19e7656ad32a4eefa7d849be6a31d81c9c990e6
  • candidate record SHA-256: b18ad90bd1143f7cd5bba10c50336edc07ae16beb3b0a1c05c4e6d2db6083d3c
  • semantic review receipt SHA-256: 049a9e07e69fead88d93b34f0937b9470a06d71c1a8d097058fc83554529bdd0
  • question-first witness SHA-256: 0c71ebb418f3de347d232d159fc25e93036f4ab9166bcfb5ee5b4be86d5c55b9
  • Lean: NOT_RUN · human review: NOT_PERFORMED
同源完整 JSON