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Aliases
Subgroups
1207 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 4 generators on 66 points:
(3,4,7,14,8,15,33,49,11,17,9,35,10,16,34,50)(5,18,20,52,23,12,36,38,24,40,32,39,21,41,22,47)(6,25,27,60,30,46,62,48,31,45,29,63,28,13,42,44)(19,37,53,64,54,65,58,43,55,66,56,59,57,51,26,61);(1,2);(3,5)(4,12)(6,26)(7,32)(8,23)(9,20)(10,21)(11,24)(13,43)(14,47)(15,40)(16,18)(17,41)(19,29)(22,33)(25,59)(27,55)(28,56)(30,53)(31,58)(34,36)(35,38)(37,44)(39,50)(42,54)(45,64)(46,61)(48,66)(49,52)(51,63)(57,62)(60,65);(3,6,10,28,11,31,8,30)(4,13,15,25,17,46,16,45)(5,19,24,55)(7,29,34,62,9,27,33,42)(12,37)(14,48,49,63,35,44,50,60)(18,51)(20,56,32,53)(21,57,23,54)(22,58,36,26)(38,59)(39,61)(40,65)(41,66)(43,52)(47,64)
Conjugacy classes & character table
136 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((3,4,7,14,8,15,33,49,11,17,9,35,10,16,34,50)(5,18,20,52,23,12,36,38,24,40,32,39,21,41,22,47)(6,25,27,60,30,46,62,48,31,45,29,63,28,13,42,44)(19,37,53,64,54,65,58,43,55,66,56,59,57,51,26,61), (1,2), (3,5)(4,12)(6,26)(7,32)(8,23)(9,20)(10,21)(11,24)(13,43)(14,47)(15,40)(16,18)(17,41)(19,29)(22,33)(25,59)(27,55)(28,56)(30,53)(31,58)(34,36)(35,38)(37,44)(39,50)(42,54)(45,64)(46,61)(48,66)(49,52)(51,63)(57,62)(60,65), (3,6,10,28,11,31,8,30)(4,13,15,25,17,46,16,45)(5,19,24,55)(7,29,34,62,9,27,33,42)(12,37)(14,48,49,63,35,44,50,60)(18,51)(20,56,32,53)(21,57,23,54)(22,58,36,26)(38,59)(39,61)(40,65)(41,66)(43,52)(47,64));
Finite Group Databasebeta