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Aliases
Subgroups
2074 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 4 generators on 66 points:
(5,17,19,47,21,25,51,20)(6,23,26,59)(7,29,28,32)(8,33)(9,35)(11,36,37,38,39,41,57,60)(12,40,30,63)(13,43,24,44)(14,42)(15,45)(18,50,52,53,54,46,65,66)(22,56,48,49,55,64,62,58)(27,31)(34,61);(1,2);(3,4)(5,18,51,65,21,54,19,52)(6,24,26,13)(7,30,28,12)(8,34)(9,15)(10,16)(11,22,57,62,39,55,37,48)(14,31)(17,46,20,53,25,50,47,66)(23,44,59,43)(27,42)(29,63,32,40)(33,61)(35,45)(36,64,60,49,41,56,38,58);(3,5,7,20,31,55,29,64,9,19,6,25,27,62,59,49,10,21,28,47,8,22,32,56,35,51,26,17,33,48,23,58)(4,11,13,38,34,54,43,50,15,37,30,36,61,65,40,66,16,39,24,60,14,18,44,46,45,57,12,41,42,52,63,53)
Conjugacy classes & character table
140 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((5,17,19,47,21,25,51,20)(6,23,26,59)(7,29,28,32)(8,33)(9,35)(11,36,37,38,39,41,57,60)(12,40,30,63)(13,43,24,44)(14,42)(15,45)(18,50,52,53,54,46,65,66)(22,56,48,49,55,64,62,58)(27,31)(34,61), (1,2), (3,4)(5,18,51,65,21,54,19,52)(6,24,26,13)(7,30,28,12)(8,34)(9,15)(10,16)(11,22,57,62,39,55,37,48)(14,31)(17,46,20,53,25,50,47,66)(23,44,59,43)(27,42)(29,63,32,40)(33,61)(35,45)(36,64,60,49,41,56,38,58), (3,5,7,20,31,55,29,64,9,19,6,25,27,62,59,49,10,21,28,47,8,22,32,56,35,51,26,17,33,48,23,58)(4,11,13,38,34,54,43,50,15,37,30,36,61,65,40,66,16,39,24,60,14,18,44,46,45,57,12,41,42,52,63,53));
Finite Group Databasebeta