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Aliases
Subgroups
3127 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 5 generators on 66 points:
(4,10,13,29,12,30,34,32)(6,20,22,49)(7,24)(8,27)(11,28,35,36,37,59,65,61)(14,41,40,31,39,63,62,64)(15,43,38,66,44,60,42,51)(17,33,45,58)(18,47)(19,46)(21,48,52,53)(23,55,54,50)(25,56)(26,57);(3,4,6,10,7,14,20,31,8,13,23,32,24,40,50,41,9,12,22,30,26,39,49,64,27,34,54,29,57,62,55,63)(5,15,17,43,18,11,33,36,19,38,21,51,47,35,53,28,16,44,45,60,25,37,58,61,46,42,52,66,56,65,48,59);(1,2);(3,5)(4,11,34,65,12,37,13,35)(6,21,22,52)(7,25)(8,19)(9,16)(10,28,32,61,30,59,29,36)(14,42,62,44,39,38,40,15)(17,23,45,54)(18,26)(20,48,49,53)(24,56)(27,46)(31,43,41,51,64,60,63,66)(33,55,58,50)(47,57);(4,12)(5,16)(6,22)(13,34)(14,39)(18,25)(19,46)(20,49)(23,54)(28,59)(36,61)(40,62)(43,60)(47,56)(50,55)(51,66)
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((4,10,13,29,12,30,34,32)(6,20,22,49)(7,24)(8,27)(11,28,35,36,37,59,65,61)(14,41,40,31,39,63,62,64)(15,43,38,66,44,60,42,51)(17,33,45,58)(18,47)(19,46)(21,48,52,53)(23,55,54,50)(25,56)(26,57), (3,4,6,10,7,14,20,31,8,13,23,32,24,40,50,41,9,12,22,30,26,39,49,64,27,34,54,29,57,62,55,63)(5,15,17,43,18,11,33,36,19,38,21,51,47,35,53,28,16,44,45,60,25,37,58,61,46,42,52,66,56,65,48,59), (1,2), (3,5)(4,11,34,65,12,37,13,35)(6,21,22,52)(7,25)(8,19)(9,16)(10,28,32,61,30,59,29,36)(14,42,62,44,39,38,40,15)(17,23,45,54)(18,26)(20,48,49,53)(24,56)(27,46)(31,43,41,51,64,60,63,66)(33,55,58,50)(47,57), (4,12)(5,16)(6,22)(13,34)(14,39)(18,25)(19,46)(20,49)(23,54)(28,59)(36,61)(40,62)(43,60)(47,56)(50,55)(51,66));
Finite Group Databasebeta