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Aliases
Subgroups
3139 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 5 generators on 66 points:
(3,4)(5,16,18,42,20,43,21,41)(6,12)(7,24,26,56)(8,28)(9,31)(10,15)(11,19,34,50,35,51,33,48)(13,27,38,58)(14,30)(17,40,45,44,47,64,52,63)(22,53,25,55)(23,39)(29,60)(32,49,59,46,62,65,61,66)(36,54,37,57);(3,5,7,19,8,17,27,46,9,18,25,48,30,45,57,49,10,20,26,51,29,47,58,66,6,21,22,50,23,52,54,65)(4,11,13,16,14,32,24,44,12,34,36,41,28,59,53,40,15,35,38,43,39,62,56,63,31,33,37,42,60,61,55,64);(1,2);(5,17,21,52,20,47,18,45)(7,25,26,22)(8,29)(11,32,33,61,35,62,34,59)(13,36,38,37)(14,39)(16,40,41,63,43,64,42,44)(19,49,48,66,51,65,50,46)(23,30)(24,55,56,53)(27,54,58,57)(28,60);(3,6,10,9)(4,12,15,31)(5,18,20,21)(7,25,26,22)(8,23,29,30)(11,33,35,34)(13,37,38,36)(14,28,39,60)(16,41,43,42)(17,45,47,52)(19,50,51,48)(24,55,56,53)(27,57,58,54)(32,61,62,59)(40,63,64,44)(46,65,66,49)
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((3,4)(5,16,18,42,20,43,21,41)(6,12)(7,24,26,56)(8,28)(9,31)(10,15)(11,19,34,50,35,51,33,48)(13,27,38,58)(14,30)(17,40,45,44,47,64,52,63)(22,53,25,55)(23,39)(29,60)(32,49,59,46,62,65,61,66)(36,54,37,57), (3,5,7,19,8,17,27,46,9,18,25,48,30,45,57,49,10,20,26,51,29,47,58,66,6,21,22,50,23,52,54,65)(4,11,13,16,14,32,24,44,12,34,36,41,28,59,53,40,15,35,38,43,39,62,56,63,31,33,37,42,60,61,55,64), (1,2), (5,17,21,52,20,47,18,45)(7,25,26,22)(8,29)(11,32,33,61,35,62,34,59)(13,36,38,37)(14,39)(16,40,41,63,43,64,42,44)(19,49,48,66,51,65,50,46)(23,30)(24,55,56,53)(27,54,58,57)(28,60), (3,6,10,9)(4,12,15,31)(5,18,20,21)(7,25,26,22)(8,23,29,30)(11,33,35,34)(13,37,38,36)(14,28,39,60)(16,41,43,42)(17,45,47,52)(19,50,51,48)(24,55,56,53)(27,57,58,54)(32,61,62,59)(40,63,64,44)(46,65,66,49));
Finite Group Databasebeta