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Aliases
Subgroups
3112 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 4 generators on 66 points:
(4,10,13,23,14,31,44,33)(5,16,18,47)(6,22,24,37)(8,28)(9,27)(11,25,36,58)(12,38,40,62,41,64,43,61)(15,45,39,32,29,57,56,34)(17,26)(20,21,50,51)(30,55,59,46,60,42,52,65)(35,53)(48,63)(54,66);(1,2);(3,4,11,34,28,56,58,31,27,44,22,45,8,29,24,33,7,14,36,32,17,39,25,10,9,13,37,57,26,15,6,23)(5,12,35,62,47,65,66,60,51,40,53,38,20,55,49,59,18,41,48,61,16,46,54,30,21,43,63,64,50,42,19,52);(3,5,17,16,27,51,26,50,7,18,28,47,9,21,8,20)(4,12,39,46,44,40,15,42,14,41,56,65,13,43,29,55)(6,19,36,48,58,66,37,63,24,49,11,35,25,54,22,53)(10,30,45,38,23,52,32,61,31,60,57,64,33,59,34,62)
Conjugacy classes & character table
212 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((4,10,13,23,14,31,44,33)(5,16,18,47)(6,22,24,37)(8,28)(9,27)(11,25,36,58)(12,38,40,62,41,64,43,61)(15,45,39,32,29,57,56,34)(17,26)(20,21,50,51)(30,55,59,46,60,42,52,65)(35,53)(48,63)(54,66), (1,2), (3,4,11,34,28,56,58,31,27,44,22,45,8,29,24,33,7,14,36,32,17,39,25,10,9,13,37,57,26,15,6,23)(5,12,35,62,47,65,66,60,51,40,53,38,20,55,49,59,18,41,48,61,16,46,54,30,21,43,63,64,50,42,19,52), (3,5,17,16,27,51,26,50,7,18,28,47,9,21,8,20)(4,12,39,46,44,40,15,42,14,41,56,65,13,43,29,55)(6,19,36,48,58,66,37,63,24,49,11,35,25,54,22,53)(10,30,45,38,23,52,32,61,31,60,57,64,33,59,34,62));
Finite Group Databasebeta