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Aliases
Subgroups
2652 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 4 generators on 66 points:
(5,17)(6,7)(8,27)(9,35)(11,37)(12,44)(13,46)(14,47)(15,50)(18,41)(19,57)(20,53)(21,38)(22,54)(23,58)(24,28)(25,59)(26,30)(29,34)(31,32)(33,63)(36,52)(39,62)(40,65)(42,61)(43,48)(45,66)(49,55)(51,56)(60,64);(3,4)(5,18,20,43,22,56,59,49)(6,24,26,39)(7,28,30,62)(8,33)(9,15)(10,16)(11,38,40,34,42,64,66,23)(12,19,46,31)(13,32,44,57)(14,36)(17,51,53,55,54,41,25,48)(21,45,29,37,60,65,58,61)(27,63)(35,50)(47,52);(1,2);(3,5,19,54,27,64,30,58,9,20,26,53,36,23,57,60,10,22,31,17,52,38,7,29,35,59,6,25,8,34,32,21)(4,11,39,37,47,18,44,55,15,40,12,45,33,43,62,51,16,42,24,61,63,56,13,48,50,66,46,65,14,49,28,41)
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)(6,7)(8,27)(9,35)(11,37)(12,44)(13,46)(14,47)(15,50)(18,41)(19,57)(20,53)(21,38)(22,54)(23,58)(24,28)(25,59)(26,30)(29,34)(31,32)(33,63)(36,52)(39,62)(40,65)(42,61)(43,48)(45,66)(49,55)(51,56)(60,64), (3,4)(5,18,20,43,22,56,59,49)(6,24,26,39)(7,28,30,62)(8,33)(9,15)(10,16)(11,38,40,34,42,64,66,23)(12,19,46,31)(13,32,44,57)(14,36)(17,51,53,55,54,41,25,48)(21,45,29,37,60,65,58,61)(27,63)(35,50)(47,52), (1,2), (3,5,19,54,27,64,30,58,9,20,26,53,36,23,57,60,10,22,31,17,52,38,7,29,35,59,6,25,8,34,32,21)(4,11,39,37,47,18,44,55,15,40,12,45,33,43,62,51,16,42,24,61,63,56,13,48,50,66,46,65,14,49,28,41));
Finite Group Databasebeta