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Aliases
Subgroups
5024 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 5 generators on 66 points:
(3,4,7,13,9,15,26,46,10,17,8,32,31,16,33,14)(5,18,21,11,23,35,51,37,19,47,22,36,50,45,55,38)(6,24,27,43,28,56,62,12,29,40,30,42,58,41,60,44)(20,34,52,63,53,39,61,48,49,64,54,65,25,57,59,66);(5,19)(20,49)(21,22)(23,50)(25,53)(51,55)(52,54)(59,61);(1,2);(3,5,9,23,10,19,31,50)(4,11)(6,25,58,49,29,53,28,20)(7,22,26,55,8,21,33,51)(12,39,44,57)(13,45)(14,47)(15,37)(16,38)(17,36)(18,46)(24,48,40,66)(27,61,60,52,30,59,62,54)(32,35)(34,42,64,43)(41,63,56,65);(3,6,26,60,31,58,7,30,10,29,33,62,9,28,8,27)(4,12,13,24,15,42,46,56,17,44,32,40,16,43,14,41)(5,20,51,59,50,25,21,54,19,49,55,61,23,53,22,52)(11,34,35,65,37,39,47,66,36,64,45,63,38,57,18,48)
Conjugacy classes & character table
200 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((3,4,7,13,9,15,26,46,10,17,8,32,31,16,33,14)(5,18,21,11,23,35,51,37,19,47,22,36,50,45,55,38)(6,24,27,43,28,56,62,12,29,40,30,42,58,41,60,44)(20,34,52,63,53,39,61,48,49,64,54,65,25,57,59,66), (5,19)(20,49)(21,22)(23,50)(25,53)(51,55)(52,54)(59,61), (1,2), (3,5,9,23,10,19,31,50)(4,11)(6,25,58,49,29,53,28,20)(7,22,26,55,8,21,33,51)(12,39,44,57)(13,45)(14,47)(15,37)(16,38)(17,36)(18,46)(24,48,40,66)(27,61,60,52,30,59,62,54)(32,35)(34,42,64,43)(41,63,56,65), (3,6,26,60,31,58,7,30,10,29,33,62,9,28,8,27)(4,12,13,24,15,42,46,56,17,44,32,40,16,43,14,41)(5,20,51,59,50,25,21,54,19,49,55,61,23,53,22,52)(11,34,35,65,37,39,47,66,36,64,45,63,38,57,18,48));
Finite Group Databasebeta