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Aliases
Subgroups
2290 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 4 generators on 66 points:
(3,4)(5,17,19,49,22,54,24,64)(6,25,28,13)(7,32,35,12)(8,38)(9,42)(10,16)(11,20,44,27,46,59,48,58)(14,41)(15,30)(18,21,47,60,56,61,53,34)(23,50,43,45,40,65,63,55)(26,57,52,37)(29,51)(31,33,62,66)(36,39);(3,4)(5,18,19,47,22,56,24,53)(6,26,28,52)(7,33,35,66)(8,39)(9,15)(10,16)(11,43,44,40,46,63,48,23)(12,31,32,62)(13,37,25,57)(14,29)(17,21,49,60,54,61,64,34)(20,45,27,65,59,55,58,50)(30,42)(36,38)(41,51);(1,2);(3,5,7,34,41,43,28,58,30,19,57,61,8,40,31,59,10,22,35,60,36,63,6,27,9,24,37,21,29,23,62,20)(4,11,13,50,38,56,12,49,42,44,66,55,14,53,52,17,16,46,25,65,51,18,32,64,15,48,33,45,39,47,26,54)
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((3,4)(5,17,19,49,22,54,24,64)(6,25,28,13)(7,32,35,12)(8,38)(9,42)(10,16)(11,20,44,27,46,59,48,58)(14,41)(15,30)(18,21,47,60,56,61,53,34)(23,50,43,45,40,65,63,55)(26,57,52,37)(29,51)(31,33,62,66)(36,39), (3,4)(5,18,19,47,22,56,24,53)(6,26,28,52)(7,33,35,66)(8,39)(9,15)(10,16)(11,43,44,40,46,63,48,23)(12,31,32,62)(13,37,25,57)(14,29)(17,21,49,60,54,61,64,34)(20,45,27,65,59,55,58,50)(30,42)(36,38)(41,51), (1,2), (3,5,7,34,41,43,28,58,30,19,57,61,8,40,31,59,10,22,35,60,36,63,6,27,9,24,37,21,29,23,62,20)(4,11,13,50,38,56,12,49,42,44,66,55,14,53,52,17,16,46,25,65,51,18,32,64,15,48,33,45,39,47,26,54));
Finite Group Databasebeta