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Aliases
Subgroups
2182 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 4 generators on 66 points:
(4,12)(5,18)(6,28)(7,31)(8,36)(9,30)(10,39)(13,19)(14,43)(15,42)(16,34)(17,45)(20,33)(21,60)(22,26)(23,61)(24,46)(25,57)(27,29)(32,35)(37,65)(38,56)(40,66)(41,63)(44,54)(47,48)(49,51)(50,52)(53,59)(58,62);(1,2);(3,4,6,12,9,15,31,43,39,54,7,34,8,37,28,63,11,17,33,45,36,41,35,65,10,16,32,44,30,14,20,42)(5,19,21,58,24,13,46,47,60,49,18,55,23,59,57,48,27,50,22,62,38,52,56,66,26,53,29,64,25,51,61,40);(3,5,20,46,8,25,7,21,10,26,35,61,9,38,6,29,11,27,28,56,30,23,32,22,39,60,31,57,36,24,33,18)(4,13,43,62,14,50,12,40,16,51,42,55,41,49,44,66,17,52,65,58,37,19,45,48,54,59,63,64,15,53,34,47)
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((4,12)(5,18)(6,28)(7,31)(8,36)(9,30)(10,39)(13,19)(14,43)(15,42)(16,34)(17,45)(20,33)(21,60)(22,26)(23,61)(24,46)(25,57)(27,29)(32,35)(37,65)(38,56)(40,66)(41,63)(44,54)(47,48)(49,51)(50,52)(53,59)(58,62), (1,2), (3,4,6,12,9,15,31,43,39,54,7,34,8,37,28,63,11,17,33,45,36,41,35,65,10,16,32,44,30,14,20,42)(5,19,21,58,24,13,46,47,60,49,18,55,23,59,57,48,27,50,22,62,38,52,56,66,26,53,29,64,25,51,61,40), (3,5,20,46,8,25,7,21,10,26,35,61,9,38,6,29,11,27,28,56,30,23,32,22,39,60,31,57,36,24,33,18)(4,13,43,62,14,50,12,40,16,51,42,55,41,49,44,66,17,52,65,58,37,19,45,48,54,59,63,64,15,53,34,47));
Finite Group Databasebeta