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Aliases
Subgroups
2834 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 4 generators on 66 points:
(3,4,6,14,9,16,31,40,8,17,7,33,21,52,34,12,11,18,32,41,10,38,29,42,37,15,36,50,30,46,35,43)(5,19,22,45,25,53,58,39,27,49,23,60,20,54,55,63,28,51,59,66,26,62,56,64,24,13,44,47,57,48,61,65);(1,2);(4,12,15,42,18,43,17,40)(5,20,28,57)(6,29,32,31)(7,34,36,35)(8,37)(9,21)(10,30)(13,45,19,47,49,66,51,60)(14,38,33,52,41,16,50,46)(23,44)(24,26,27,25)(39,54,65,62,64,48,63,53)(55,58)(56,61);(3,5,21,20,37,24,9,25,11,28,30,57,8,27,10,26)(4,13,46,62,15,51,38,54,18,49,52,53,17,19,16,48)(6,22,34,55,36,44,31,58,32,59,35,61,7,23,29,56)(12,39,33,45,40,65,14,47,43,64,50,66,42,63,41,60)
Conjugacy classes & character table
188 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((3,4,6,14,9,16,31,40,8,17,7,33,21,52,34,12,11,18,32,41,10,38,29,42,37,15,36,50,30,46,35,43)(5,19,22,45,25,53,58,39,27,49,23,60,20,54,55,63,28,51,59,66,26,62,56,64,24,13,44,47,57,48,61,65), (1,2), (4,12,15,42,18,43,17,40)(5,20,28,57)(6,29,32,31)(7,34,36,35)(8,37)(9,21)(10,30)(13,45,19,47,49,66,51,60)(14,38,33,52,41,16,50,46)(23,44)(24,26,27,25)(39,54,65,62,64,48,63,53)(55,58)(56,61), (3,5,21,20,37,24,9,25,11,28,30,57,8,27,10,26)(4,13,46,62,15,51,38,54,18,49,52,53,17,19,16,48)(6,22,34,55,36,44,31,58,32,59,35,61,7,23,29,56)(12,39,33,45,40,65,14,47,43,64,50,66,42,63,41,60));
Finite Group Databasebeta