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Aliases
Subgroups
2463 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 5 generators on 66 points:
(1,2);(3,4,8,14)(5,15,17,32)(6,20)(7,25,26,35)(9,28,27,12)(10,19,31,49)(11,33)(13,38,39,21)(16,42)(18,30,48,62)(22,54)(23,36)(24,51)(29,59)(34,64)(37,53)(40,63)(41,65,57,43)(44,60)(45,61)(46,50)(47,66)(52,55)(56,58);(3,5)(4,10,14,31)(6,16)(7,18)(8,17)(9,19)(11,34,36,29)(12,32,28,15)(13,30,39,62)(20,50,51,60)(21,43)(22,46)(23,45)(24,47)(25,57,35,41)(26,48)(27,49)(33,63)(37,40,58,61)(38,65)(42,54,66,52)(44,55)(53,59)(56,64);(3,6,21,53,27,55,7,23,8,24,38,56,9,22,26,33)(4,11,35,54,28,58,39,51,14,36,25,52,12,37,13,20)(5,16,43,59,49,44,18,45,17,47,65,64,19,46,48,63)(10,29,41,42,15,40,62,50,31,34,57,66,32,61,30,60);(4,12,14,28)(5,17)(6,22,24,55)(7,26)(10,15,31,32)(13,35,39,25)(16,44,47,46)(19,49)(20,51)(21,38)(23,56,33,53)(29,34)(30,57,62,41)(40,61)(45,59,63,64)(52,54)
Conjugacy classes & character table
112 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), (3,4,8,14)(5,15,17,32)(6,20)(7,25,26,35)(9,28,27,12)(10,19,31,49)(11,33)(13,38,39,21)(16,42)(18,30,48,62)(22,54)(23,36)(24,51)(29,59)(34,64)(37,53)(40,63)(41,65,57,43)(44,60)(45,61)(46,50)(47,66)(52,55)(56,58), (3,5)(4,10,14,31)(6,16)(7,18)(8,17)(9,19)(11,34,36,29)(12,32,28,15)(13,30,39,62)(20,50,51,60)(21,43)(22,46)(23,45)(24,47)(25,57,35,41)(26,48)(27,49)(33,63)(37,40,58,61)(38,65)(42,54,66,52)(44,55)(53,59)(56,64), (3,6,21,53,27,55,7,23,8,24,38,56,9,22,26,33)(4,11,35,54,28,58,39,51,14,36,25,52,12,37,13,20)(5,16,43,59,49,44,18,45,17,47,65,64,19,46,48,63)(10,29,41,42,15,40,62,50,31,34,57,66,32,61,30,60), (4,12,14,28)(5,17)(6,22,24,55)(7,26)(10,15,31,32)(13,35,39,25)(16,44,47,46)(19,49)(20,51)(21,38)(23,56,33,53)(29,34)(30,57,62,41)(40,61)(45,59,63,64)(52,54));
Finite Group Databasebeta