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Aliases
Subgroups
2232 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 4 generators on 66 points:
(3,4,6,10,7,13,22,30,8,12,25,32,17,41,51,43,9,14,24,31,26,44,56,61,27,42,60,29,52,64,58,65)(5,15,19,45,16,38,47,63,21,37,54,66,49,35,55,28,18,46,53,34,20,11,33,36,48,39,23,57,50,40,59,62);(1,2);(4,10,12,29,14,31,42,32)(5,16,18,20)(6,22,24,56)(7,17)(8,27)(11,34,35,57,38,45,40,66)(13,43,41,30,44,65,64,61)(15,36,39,62,46,63,37,28)(19,54)(21,50,48,49)(23,53)(25,58,60,51)(26,52)(33,47);(3,5,17,50,27,48,7,20,9,18,52,49,8,21,26,16)(4,11,13,37,12,40,41,46,14,38,44,39,42,35,64,15)(6,23,58,47,60,53,56,59,24,54,51,33,25,19,22,55)(10,28,61,34,32,36,65,57,31,62,30,45,29,63,43,66)
Conjugacy classes & character table
164 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((3,4,6,10,7,13,22,30,8,12,25,32,17,41,51,43,9,14,24,31,26,44,56,61,27,42,60,29,52,64,58,65)(5,15,19,45,16,38,47,63,21,37,54,66,49,35,55,28,18,46,53,34,20,11,33,36,48,39,23,57,50,40,59,62), (1,2), (4,10,12,29,14,31,42,32)(5,16,18,20)(6,22,24,56)(7,17)(8,27)(11,34,35,57,38,45,40,66)(13,43,41,30,44,65,64,61)(15,36,39,62,46,63,37,28)(19,54)(21,50,48,49)(23,53)(25,58,60,51)(26,52)(33,47), (3,5,17,50,27,48,7,20,9,18,52,49,8,21,26,16)(4,11,13,37,12,40,41,46,14,38,44,39,42,35,64,15)(6,23,58,47,60,53,56,59,24,54,51,33,25,19,22,55)(10,28,61,34,32,36,65,57,31,62,30,45,29,63,43,66));
Finite Group Databasebeta