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Aliases
Subgroups
973 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 4 generators on 66 points:
(3,4,7,14,10,17,34,16,11,18,20,39,8,15,9,36)(5,19,22,53,23,43,37,42,24,50,32,51,35,12,38,41)(6,25,27,47,28,13,29,45,31,46,33,63,30,48,62,49)(21,40,54,44,56,52,60,66,57,65,26,59,55,64,61,58);(1,2);(3,5,20,22,10,23,9,37,11,24,7,32,8,35,34,38)(4,12,39,41,17,19,36,53,18,43,14,42,15,50,16,51)(6,26,33,55,28,61,62,21,31,54,27,56,30,60,29,57)(13,44,49,52,46,66,47,65,48,59,45,64,25,58,63,40);(3,6,20,27,10,28,9,29,11,31,7,33,8,30,34,62)(4,13,14,49,17,46,16,47,18,48,39,45,15,25,36,63)(5,21,38,60,35,55,32,54,24,57,37,61,23,56,22,26)(12,40,53,58,50,64,41,59,43,65,51,66,19,52,42,44)
Conjugacy classes & character table
136 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((3,4,7,14,10,17,34,16,11,18,20,39,8,15,9,36)(5,19,22,53,23,43,37,42,24,50,32,51,35,12,38,41)(6,25,27,47,28,13,29,45,31,46,33,63,30,48,62,49)(21,40,54,44,56,52,60,66,57,65,26,59,55,64,61,58), (1,2), (3,5,20,22,10,23,9,37,11,24,7,32,8,35,34,38)(4,12,39,41,17,19,36,53,18,43,14,42,15,50,16,51)(6,26,33,55,28,61,62,21,31,54,27,56,30,60,29,57)(13,44,49,52,46,66,47,65,48,59,45,64,25,58,63,40), (3,6,20,27,10,28,9,29,11,31,7,33,8,30,34,62)(4,13,14,49,17,46,16,47,18,48,39,45,15,25,36,63)(5,21,38,60,35,55,32,54,24,57,37,61,23,56,22,26)(12,40,53,58,50,64,41,59,43,65,51,66,19,52,42,44));
Finite Group Databasebeta