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Aliases
Subgroups
4016 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 4 generators on 66 points:
(3,4,7,13)(5,17,19,11)(6,22,23,54,25,56,59,32)(8,14,28,33)(9,15,30,43)(10,16,29,44)(12,36,38,49,40,57,66,18)(20,46,53,34)(21,48,52,35)(24,55,58,65,50,39,51,41)(26,47,27,37,60,64,61,63)(31,45,62,42);(1,2);(3,5,9,20,10,21,31,8)(4,11,15,34,16,35,45,33)(6,18,26,50,25,49,60,24)(7,19,30,53,29,52,62,28)(12,37,39,32,40,63,55,54)(13,17,43,46,44,48,42,14)(22,38,47,41,56,66,64,65)(23,57,27,58,59,36,61,51);(3,6)(4,12,15,39,16,40,45,55)(5,18)(7,27,29,61)(8,24)(9,26)(10,25)(11,32,33,37,35,54,34,63)(13,41,42,38,44,65,43,66)(14,22,17,47,46,56,48,64)(19,51,52,58)(20,50)(21,49)(23,30,59,62)(28,36,53,57)(31,60)
Conjugacy classes & character table
152 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((3,4,7,13)(5,17,19,11)(6,22,23,54,25,56,59,32)(8,14,28,33)(9,15,30,43)(10,16,29,44)(12,36,38,49,40,57,66,18)(20,46,53,34)(21,48,52,35)(24,55,58,65,50,39,51,41)(26,47,27,37,60,64,61,63)(31,45,62,42), (1,2), (3,5,9,20,10,21,31,8)(4,11,15,34,16,35,45,33)(6,18,26,50,25,49,60,24)(7,19,30,53,29,52,62,28)(12,37,39,32,40,63,55,54)(13,17,43,46,44,48,42,14)(22,38,47,41,56,66,64,65)(23,57,27,58,59,36,61,51), (3,6)(4,12,15,39,16,40,45,55)(5,18)(7,27,29,61)(8,24)(9,26)(10,25)(11,32,33,37,35,54,34,63)(13,41,42,38,44,65,43,66)(14,22,17,47,46,56,48,64)(19,51,52,58)(20,50)(21,49)(23,30,59,62)(28,36,53,57)(31,60));
Finite Group Databasebeta