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Aliases
Subgroups
5465 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 5 generators on 66 points:
(1,2);(3,4,11,18)(5,12,20,43)(6,24,26,47)(7,31,37,54)(8,38,33,16)(9,15,41,51)(10,42,40,17)(13,32,46,27)(14,25,49,35)(19,52,55,34)(21,28,56,39)(22,44,57,64)(23,60,50,45)(29,63,61,59)(30,53,62,58)(36,66,65,48);(3,5,11,20)(4,12,18,43)(6,19,26,55)(7,21,37,56)(8,13,33,46)(9,22,41,57)(10,23,40,50)(14,30,49,62)(15,44,51,64)(16,27,38,32)(17,45,42,60)(24,52,47,34)(25,53,35,58)(28,54,39,31)(29,48,61,66)(36,59,65,63);(3,6,25,60,9,29,36,64,40,62,52,43,8,39,7,32,11,26,35,45,41,61,65,44,10,30,34,12,33,28,37,27)(4,13,31,21,16,20,55,58,42,57,66,63,51,23,49,24,18,46,54,56,38,5,19,53,17,22,48,59,15,50,14,47);(5,20)(6,26)(12,43)(13,46)(21,56)(22,57)(23,50)(24,47)(27,32)(28,39)(29,61)(30,62)(44,64)(45,60)(53,58)(59,63)
Conjugacy classes & character table
184 conjugacy classes — view the full character table.
Relationships
GAP
Past the SmallGroups library coverage — no SmallGroups id. Construct it from a minimal faithful permutation representation:
gap> G := Group((1,2), (3,4,11,18)(5,12,20,43)(6,24,26,47)(7,31,37,54)(8,38,33,16)(9,15,41,51)(10,42,40,17)(13,32,46,27)(14,25,49,35)(19,52,55,34)(21,28,56,39)(22,44,57,64)(23,60,50,45)(29,63,61,59)(30,53,62,58)(36,66,65,48), (3,5,11,20)(4,12,18,43)(6,19,26,55)(7,21,37,56)(8,13,33,46)(9,22,41,57)(10,23,40,50)(14,30,49,62)(15,44,51,64)(16,27,38,32)(17,45,42,60)(24,52,47,34)(25,53,35,58)(28,54,39,31)(29,48,61,66)(36,59,65,63), (3,6,25,60,9,29,36,64,40,62,52,43,8,39,7,32,11,26,35,45,41,61,65,44,10,30,34,12,33,28,37,27)(4,13,31,21,16,20,55,58,42,57,66,63,51,23,49,24,18,46,54,56,38,5,19,53,17,22,48,59,15,50,14,47), (5,20)(6,26)(12,43)(13,46)(21,56)(22,57)(23,50)(24,47)(27,32)(28,39)(29,61)(30,62)(44,64)(45,60)(53,58)(59,63));
Finite Group Databasebeta