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Aliases
Subgroups
3516 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 5 generators on 66 points:
(4,10)(5,16)(6,11)(7,25)(9,24)(12,39)(13,44)(14,47)(15,35)(17,50)(18,19)(20,56)(22,37)(23,59)(26,51)(27,62)(28,33)(29,60)(30,38)(31,36)(34,43)(40,41)(42,65)(45,53)(46,61)(48,57)(49,55)(52,66)(54,63)(58,64);(1,2);(3,4,11,14,8,15,6,22)(5,17,16,45,18,52,19,42)(7,26,28,61,29,36,23,44)(9,31,38,46,30,51,24,13)(10,33,37,25,35,59,47,60)(12,21,43,49,40,32,58,55)(20,39,48,64,54,41,27,34)(50,57,65,56,66,62,53,63);(3,5,6,19,8,18,11,16)(4,12)(7,27,28,20,29,48,23,54)(9,32,24,49,30,21,38,55)(10,34,35,64)(13,45)(14,43)(15,40)(17,51)(22,58)(25,56,59,62,60,63,33,57)(26,53,36,65)(31,52)(37,39,47,41)(42,46)(44,66,61,50);(5,18)(12,40)(16,19)(17,52)(20,54)(21,32)(27,48)(34,64)(39,41)(42,45)(43,58)(49,55)(50,66)(53,65)(56,63)(57,62)
Conjugacy classes & character table
164 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((4,10)(5,16)(6,11)(7,25)(9,24)(12,39)(13,44)(14,47)(15,35)(17,50)(18,19)(20,56)(22,37)(23,59)(26,51)(27,62)(28,33)(29,60)(30,38)(31,36)(34,43)(40,41)(42,65)(45,53)(46,61)(48,57)(49,55)(52,66)(54,63)(58,64), (1,2), (3,4,11,14,8,15,6,22)(5,17,16,45,18,52,19,42)(7,26,28,61,29,36,23,44)(9,31,38,46,30,51,24,13)(10,33,37,25,35,59,47,60)(12,21,43,49,40,32,58,55)(20,39,48,64,54,41,27,34)(50,57,65,56,66,62,53,63), (3,5,6,19,8,18,11,16)(4,12)(7,27,28,20,29,48,23,54)(9,32,24,49,30,21,38,55)(10,34,35,64)(13,45)(14,43)(15,40)(17,51)(22,58)(25,56,59,62,60,63,33,57)(26,53,36,65)(31,52)(37,39,47,41)(42,46)(44,66,61,50), (5,18)(12,40)(16,19)(17,52)(20,54)(21,32)(27,48)(34,64)(39,41)(42,45)(43,58)(49,55)(50,66)(53,65)(56,63)(57,62));
Finite Group Databasebeta