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Aliases
Subgroups
2346 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 4 generators on 66 points:
(3,4,7,14,27,49,30,39,8,16,31,36,25,50,61,40,10,17,32,52,6,24,26,37,33,15,53,38,9,13,28,11)(5,18,20,54,19,48,56,51,22,43,29,63,34,45,62,65,21,55,59,35,57,46,58,42,60,47,64,66,23,12,41,44);(1,2);(4,11)(5,19)(6,25)(7,28)(8,33)(9,27)(12,42)(13,14)(15,39)(16,37)(17,40)(18,35)(21,57)(22,23)(24,36)(26,31)(29,64)(30,53)(32,61)(34,60)(38,49)(41,56)(43,63)(44,46)(45,51)(47,66)(48,65)(50,52)(54,55)(58,62);(3,5,6,19,8,22,9,34,10,21,27,57,33,60,25,23)(4,12,13,43,15,46,24,18,17,45,50,47,16,48,49,55)(7,29,30,41,31,59,61,56,32,64,26,62,53,20,28,58)(11,35,36,65,37,63,14,51,40,54,38,44,39,66,52,42)
Conjugacy classes & character table
164 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((3,4,7,14,27,49,30,39,8,16,31,36,25,50,61,40,10,17,32,52,6,24,26,37,33,15,53,38,9,13,28,11)(5,18,20,54,19,48,56,51,22,43,29,63,34,45,62,65,21,55,59,35,57,46,58,42,60,47,64,66,23,12,41,44), (1,2), (4,11)(5,19)(6,25)(7,28)(8,33)(9,27)(12,42)(13,14)(15,39)(16,37)(17,40)(18,35)(21,57)(22,23)(24,36)(26,31)(29,64)(30,53)(32,61)(34,60)(38,49)(41,56)(43,63)(44,46)(45,51)(47,66)(48,65)(50,52)(54,55)(58,62), (3,5,6,19,8,22,9,34,10,21,27,57,33,60,25,23)(4,12,13,43,15,46,24,18,17,45,50,47,16,48,49,55)(7,29,30,41,31,59,61,56,32,64,26,62,53,20,28,58)(11,35,36,65,37,63,14,51,40,54,38,44,39,66,52,42));
Finite Group Databasebeta