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Aliases
Subgroups
5125 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 5 generators on 66 points:
(1,2);(3,4)(5,17)(6,22,25,40)(7,28)(8,31)(9,34)(10,11)(12,21)(13,24,35,26)(14,30)(15,33)(16,29)(18,45,48,65)(19,50)(20,38)(23,53,49,66)(27,61,46,55)(32,62)(36,63,43,47)(37,56)(39,57,64,59)(41,60,54,58)(42,51)(44,52);(4,11)(12,17)(13,35)(14,15)(16,34)(22,40)(28,31)(36,43)(37,42)(38,44)(39,64)(41,54)(45,65)(50,62)(53,66)(55,61);(3,5)(4,12)(6,23,25,49)(7,19)(8,32)(9,20)(10,21)(11,17)(13,39,35,64)(14,37)(15,42)(16,38)(18,46,48,27)(22,53,40,66)(24,57,26,59)(28,62)(29,52)(30,51)(31,50)(33,56)(34,44)(36,54,43,41)(45,55,65,61)(47,60,63,58);(3,6,8,26,9,27,33,60,10,25,7,24,29,46,30,58)(4,13,15,40,16,41,31,61,11,35,14,22,34,54,28,55)(5,18,19,47,20,49,51,59,21,48,32,63,52,23,56,57)(12,36,37,65,38,64,62,66,17,43,42,45,44,39,50,53)
Conjugacy classes & character table
136 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((1,2), (3,4)(5,17)(6,22,25,40)(7,28)(8,31)(9,34)(10,11)(12,21)(13,24,35,26)(14,30)(15,33)(16,29)(18,45,48,65)(19,50)(20,38)(23,53,49,66)(27,61,46,55)(32,62)(36,63,43,47)(37,56)(39,57,64,59)(41,60,54,58)(42,51)(44,52), (4,11)(12,17)(13,35)(14,15)(16,34)(22,40)(28,31)(36,43)(37,42)(38,44)(39,64)(41,54)(45,65)(50,62)(53,66)(55,61), (3,5)(4,12)(6,23,25,49)(7,19)(8,32)(9,20)(10,21)(11,17)(13,39,35,64)(14,37)(15,42)(16,38)(18,46,48,27)(22,53,40,66)(24,57,26,59)(28,62)(29,52)(30,51)(31,50)(33,56)(34,44)(36,54,43,41)(45,55,65,61)(47,60,63,58), (3,6,8,26,9,27,33,60,10,25,7,24,29,46,30,58)(4,13,15,40,16,41,31,61,11,35,14,22,34,54,28,55)(5,18,19,47,20,49,51,59,21,48,32,63,52,23,56,57)(12,36,37,65,38,64,62,66,17,43,42,45,44,39,50,53));
Finite Group Databasebeta