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Aliases
Subgroups
4370 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 4 generators on 66 points:
(3,4,7,13)(5,18,20,11)(6,23,24,34,26,47,59,64)(8,14,29,44)(9,16,31,45)(10,17,30,46)(12,37,39,19,41,53,66,54)(15,50,51,33)(21,49,57,35)(22,48,56,36)(25,40,55,63,32,42,61,43)(27,58,28,38,60,52,62,65);(1,2);(3,5,9,21,10,22,33,8)(4,11,16,35,17,36,15,44)(6,19,27,25,26,54,60,32)(7,20,31,57,30,56,50,29)(12,38,42,64,41,65,40,34)(13,18,45,49,46,48,51,14)(23,39,58,43,47,66,52,63)(24,37,28,61,59,53,62,55);(3,6)(4,12,15,40,17,41,16,42)(5,19)(7,28,30,62)(8,32)(9,27)(10,26)(11,34,35,38,36,64,44,65)(13,43,45,66,46,63,51,39)(14,47,48,58,49,23,18,52)(20,55,56,61)(21,25)(22,54)(24,31,59,50)(29,53,57,37)(33,60)
Conjugacy classes & character table
152 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((3,4,7,13)(5,18,20,11)(6,23,24,34,26,47,59,64)(8,14,29,44)(9,16,31,45)(10,17,30,46)(12,37,39,19,41,53,66,54)(15,50,51,33)(21,49,57,35)(22,48,56,36)(25,40,55,63,32,42,61,43)(27,58,28,38,60,52,62,65), (1,2), (3,5,9,21,10,22,33,8)(4,11,16,35,17,36,15,44)(6,19,27,25,26,54,60,32)(7,20,31,57,30,56,50,29)(12,38,42,64,41,65,40,34)(13,18,45,49,46,48,51,14)(23,39,58,43,47,66,52,63)(24,37,28,61,59,53,62,55), (3,6)(4,12,15,40,17,41,16,42)(5,19)(7,28,30,62)(8,32)(9,27)(10,26)(11,34,35,38,36,64,44,65)(13,43,45,66,46,63,51,39)(14,47,48,58,49,23,18,52)(20,55,56,61)(21,25)(22,54)(24,31,59,50)(29,53,57,37)(33,60));
Finite Group Databasebeta