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Aliases
Subgroups
613 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 4 generators on 66 points:
(1,2);(3,4,7,14,9,16,33,47,11,17,34,48,38,51,20,54,12,18,30,49,37,15,6,28,10,39,31,61,8,35,32,41)(5,19,22,42,24,53,57,63,26,13,40,43,23,44,55,66,27,45,59,64,60,65,29,62,25,46,58,52,36,50,21,56);(3,5,20,55,8,36,34,40,10,25,33,57,37,60,7,22,12,27,32,21,38,23,31,58,11,26,6,29,9,24,30,59)(4,13,41,63,35,53,61,42,39,19,28,56,15,50,49,52,18,46,54,62,51,65,48,64,17,45,47,66,16,44,14,43);(3,6,8,30,10,20,37,34,12,33,38,7,11,32,9,31)(4,14,15,28,17,48,35,41,18,49,16,47,39,61,51,54)(5,21,23,40,25,29,24,22,27,55,36,58,26,57,60,59)(13,42,44,63,45,43,65,66,46,64,50,62,19,52,53,56)
Conjugacy classes & character table
184 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((1,2), (3,4,7,14,9,16,33,47,11,17,34,48,38,51,20,54,12,18,30,49,37,15,6,28,10,39,31,61,8,35,32,41)(5,19,22,42,24,53,57,63,26,13,40,43,23,44,55,66,27,45,59,64,60,65,29,62,25,46,58,52,36,50,21,56), (3,5,20,55,8,36,34,40,10,25,33,57,37,60,7,22,12,27,32,21,38,23,31,58,11,26,6,29,9,24,30,59)(4,13,41,63,35,53,61,42,39,19,28,56,15,50,49,52,18,46,54,62,51,65,48,64,17,45,47,66,16,44,14,43), (3,6,8,30,10,20,37,34,12,33,38,7,11,32,9,31)(4,14,15,28,17,48,35,41,18,49,16,47,39,61,51,54)(5,21,23,40,25,29,24,22,27,55,36,58,26,57,60,59)(13,42,44,63,45,43,65,66,46,64,50,62,19,52,53,56));
Finite Group Databasebeta