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Aliases
Subgroups
1729 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 4 generators on 66 points:
(3,4,7,14,9,17,32,42,10,6,8,15,31,28,34,44,11,16,13,26,33,43,40,58,35,27,25,30,39,57,56,60)(5,18,20,41,22,46,51,64,23,47,48,37,54,61,66,63,24,12,29,36,52,38,59,62,55,19,21,45,50,49,53,65);(1,2);(3,5)(4,12)(6,19)(7,29)(8,21)(9,22)(10,23)(11,24)(13,20)(14,41)(15,37)(16,18)(17,38)(25,48)(26,36)(27,47)(28,49)(30,45)(31,54)(32,59)(33,52)(34,53)(35,55)(39,50)(40,51)(42,64)(43,46)(44,63)(56,66)(57,61)(58,62)(60,65);(3,6,25,26,33,57,34,42,10,16,7,30,39,17,40,44,11,27,8,14,9,28,56,58,35,4,13,15,31,43,32,60)(5,19,48,36,52,61,53,64,23,18,29,45,50,38,51,63,24,47,21,41,22,49,66,62,55,12,20,37,54,46,59,65)
Conjugacy classes & character table
232 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((3,4,7,14,9,17,32,42,10,6,8,15,31,28,34,44,11,16,13,26,33,43,40,58,35,27,25,30,39,57,56,60)(5,18,20,41,22,46,51,64,23,47,48,37,54,61,66,63,24,12,29,36,52,38,59,62,55,19,21,45,50,49,53,65), (1,2), (3,5)(4,12)(6,19)(7,29)(8,21)(9,22)(10,23)(11,24)(13,20)(14,41)(15,37)(16,18)(17,38)(25,48)(26,36)(27,47)(28,49)(30,45)(31,54)(32,59)(33,52)(34,53)(35,55)(39,50)(40,51)(42,64)(43,46)(44,63)(56,66)(57,61)(58,62)(60,65), (3,6,25,26,33,57,34,42,10,16,7,30,39,17,40,44,11,27,8,14,9,28,56,58,35,4,13,15,31,43,32,60)(5,19,48,36,52,61,53,64,23,18,29,45,50,38,51,63,24,47,21,41,22,49,66,62,55,12,20,37,54,46,59,65));
Finite Group Databasebeta