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Aliases
Subgroups
800 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 4 generators on 66 points:
(1,2);(3,4,6,15,8,17,31,13,10,18,22,16,9,39,7,34,12,19,33,55,37,41,35,43,11,40,32,56,38,54,36,46)(5,20,23,57,25,45,61,66,27,42,59,14,44,47,64,49,29,58,62,51,21,53,24,63,28,65,30,52,26,48,60,50);(4,13,41,16,18,34,54,55,19,43,17,56,40,46,39,15)(5,21,28,44,29,25,27,26)(6,22,33,32)(7,31,36,35)(8,37)(9,38)(14,45,63,20,57,48,49,65,52,53,66,58,51,47,50,42)(23,60,59,61,62,64,30,24);(3,5,22,23,8,21,7,24,10,27,33,59,9,26,35,60,12,29,32,62,37,25,36,61,11,28,6,30,38,44,31,64)(4,14,46,20,39,66,16,48,40,57,43,65,17,50,15,53,19,52,34,58,54,63,56,47,18,51,13,42,41,49,55,45)
Conjugacy classes & character table
188 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), (3,4,6,15,8,17,31,13,10,18,22,16,9,39,7,34,12,19,33,55,37,41,35,43,11,40,32,56,38,54,36,46)(5,20,23,57,25,45,61,66,27,42,59,14,44,47,64,49,29,58,62,51,21,53,24,63,28,65,30,52,26,48,60,50), (4,13,41,16,18,34,54,55,19,43,17,56,40,46,39,15)(5,21,28,44,29,25,27,26)(6,22,33,32)(7,31,36,35)(8,37)(9,38)(14,45,63,20,57,48,49,65,52,53,66,58,51,47,50,42)(23,60,59,61,62,64,30,24), (3,5,22,23,8,21,7,24,10,27,33,59,9,26,35,60,12,29,32,62,37,25,36,61,11,28,6,30,38,44,31,64)(4,14,46,20,39,66,16,48,40,57,43,65,17,50,15,53,19,52,34,58,54,63,56,47,18,51,13,42,41,49,55,45));
Finite Group Databasebeta