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Aliases
Subgroups
2587 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 5 generators on 68 points:
(1,2,3,4);(5,6)(7,17)(8,23)(9,27)(10,30)(11,12)(13,20)(14,19)(15,24)(16,28)(18,37)(21,50)(22,51)(25,56)(26,52)(29,57)(31,42)(32,41)(33,55)(34,60)(35,61)(36,62)(38,45)(39,48)(40,44)(43,67)(46,54)(47,53)(49,58)(59,68)(63,65)(64,66);(7,18)(13,31)(17,37)(20,42)(21,43)(22,44)(34,59)(35,58)(38,63)(39,64)(40,51)(45,65)(48,66)(49,61)(50,67)(60,68);(6,12)(13,31)(14,32)(15,33)(16,30)(17,37)(23,52)(27,57)(34,59)(35,58)(36,53)(38,63)(39,64)(40,51)(50,67)(54,56);(5,7,19,45,9,21,46,61,28,44,62,68,55,66,26,42,11,18,41,65,29,43,25,49,10,22,47,60,24,48,8,20)(6,13,23,39,15,34,53,51,30,58,56,67,57,63,32,37,12,31,52,64,33,59,36,40,16,35,54,50,27,38,14,17)
Conjugacy classes & character table
208 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), (5,6)(7,17)(8,23)(9,27)(10,30)(11,12)(13,20)(14,19)(15,24)(16,28)(18,37)(21,50)(22,51)(25,56)(26,52)(29,57)(31,42)(32,41)(33,55)(34,60)(35,61)(36,62)(38,45)(39,48)(40,44)(43,67)(46,54)(47,53)(49,58)(59,68)(63,65)(64,66), (7,18)(13,31)(17,37)(20,42)(21,43)(22,44)(34,59)(35,58)(38,63)(39,64)(40,51)(45,65)(48,66)(49,61)(50,67)(60,68), (6,12)(13,31)(14,32)(15,33)(16,30)(17,37)(23,52)(27,57)(34,59)(35,58)(36,53)(38,63)(39,64)(40,51)(50,67)(54,56), (5,7,19,45,9,21,46,61,28,44,62,68,55,66,26,42,11,18,41,65,29,43,25,49,10,22,47,60,24,48,8,20)(6,13,23,39,15,34,53,51,30,58,56,67,57,63,32,37,12,31,52,64,33,59,36,40,16,35,54,50,27,38,14,17));
Finite Group Databasebeta