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Aliases
Subgroups
3319 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 5 generators on 66 points:
(3,4,9,12)(5,15,17,40)(6,20,24,50)(7,25,28,59)(8,29,26,14)(10,30,31,19)(11,34,37,22)(13,39,36,27)(16,43,21,53)(18,47,46,33)(23,58,56,52)(32,61,35,64)(38,57,51,63)(41,54,65,44)(42,60,66,48)(45,62,55,49);(10,31)(15,40)(32,35)(33,47)(41,65)(42,66)(43,53)(49,62);(1,2);(3,5)(4,10,12,31)(6,21)(7,18)(8,19)(9,17)(11,35,37,32)(13,33,36,47)(14,15,29,40)(16,24)(20,49,50,62)(22,54)(23,55)(25,42,59,66)(26,30)(27,48)(28,46)(34,44)(38,65,51,41)(39,60)(43,52,53,58)(45,56)(57,61)(63,64);(3,6,7,22,26,56,39,63,9,24,28,34,8,23,27,57)(4,11,36,50,29,51,25,52,12,37,13,20,14,38,59,58)(5,16,18,44,30,55,60,61,17,21,46,54,19,45,48,64)(10,32,47,49,40,65,42,43,31,35,33,62,15,41,66,53)
Conjugacy classes & character table
148 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((3,4,9,12)(5,15,17,40)(6,20,24,50)(7,25,28,59)(8,29,26,14)(10,30,31,19)(11,34,37,22)(13,39,36,27)(16,43,21,53)(18,47,46,33)(23,58,56,52)(32,61,35,64)(38,57,51,63)(41,54,65,44)(42,60,66,48)(45,62,55,49), (10,31)(15,40)(32,35)(33,47)(41,65)(42,66)(43,53)(49,62), (1,2), (3,5)(4,10,12,31)(6,21)(7,18)(8,19)(9,17)(11,35,37,32)(13,33,36,47)(14,15,29,40)(16,24)(20,49,50,62)(22,54)(23,55)(25,42,59,66)(26,30)(27,48)(28,46)(34,44)(38,65,51,41)(39,60)(43,52,53,58)(45,56)(57,61)(63,64), (3,6,7,22,26,56,39,63,9,24,28,34,8,23,27,57)(4,11,36,50,29,51,25,52,12,37,13,20,14,38,59,58)(5,16,18,44,30,55,60,61,17,21,46,54,19,45,48,64)(10,32,47,49,40,65,42,43,31,35,33,62,15,41,66,53));
Finite Group Databasebeta