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Aliases
Subgroups
2965 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 5 generators on 66 points:
(1,2);(3,4,7,14,9,16,31,43,11,17,32,15,10,34,8,33)(5,12,20,37,22,39,46,62,18,35,45,38,23,54,21,53)(6,24,25,40,27,55,26,41,29,42,30,58,28,57,56,13)(19,47,48,60,50,64,49,59,44,61,52,66,51,65,63,36);(3,5)(4,12)(6,19)(7,20)(8,21)(9,22)(10,23)(11,18)(13,36)(14,37)(15,38)(16,39)(17,35)(24,47)(25,48)(26,49)(27,50)(28,51)(29,44)(30,52)(31,46)(32,45)(33,53)(34,54)(40,60)(41,59)(42,61)(43,62)(55,64)(56,63)(57,65)(58,66);(5,18)(12,35)(19,44)(20,45)(21,46)(22,23)(36,59)(37,38)(39,54)(47,61)(48,52)(49,63)(50,51)(53,62)(60,66)(64,65);(3,6,8,26,10,28,32,25,11,29,31,56,9,27,7,30)(4,13,15,24,16,40,33,55,17,41,14,42,34,58,43,57)(5,19,21,49,23,51,45,48,18,44,46,63,22,50,20,52)(12,36,38,47,39,60,53,64,35,59,37,61,54,66,62,65)
Conjugacy classes & character table
232 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), (3,4,7,14,9,16,31,43,11,17,32,15,10,34,8,33)(5,12,20,37,22,39,46,62,18,35,45,38,23,54,21,53)(6,24,25,40,27,55,26,41,29,42,30,58,28,57,56,13)(19,47,48,60,50,64,49,59,44,61,52,66,51,65,63,36), (3,5)(4,12)(6,19)(7,20)(8,21)(9,22)(10,23)(11,18)(13,36)(14,37)(15,38)(16,39)(17,35)(24,47)(25,48)(26,49)(27,50)(28,51)(29,44)(30,52)(31,46)(32,45)(33,53)(34,54)(40,60)(41,59)(42,61)(43,62)(55,64)(56,63)(57,65)(58,66), (5,18)(12,35)(19,44)(20,45)(21,46)(22,23)(36,59)(37,38)(39,54)(47,61)(48,52)(49,63)(50,51)(53,62)(60,66)(64,65), (3,6,8,26,10,28,32,25,11,29,31,56,9,27,7,30)(4,13,15,24,16,40,33,55,17,41,14,42,34,58,43,57)(5,19,21,49,23,51,45,48,18,44,46,63,22,50,20,52)(12,36,38,47,39,60,53,64,35,59,37,61,54,66,62,65));
Finite Group Databasebeta