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Aliases
Subgroups
2324 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 4 generators on 66 points:
(4,10,13,33,15,29,16,35)(5,17,20,48,23,22,24,50)(6,25,19,54)(7,28)(11,36,39,27)(12,40,43,45)(14,47,26,37,42,61,46,34)(18,51,32,55)(21,57,59,52,41,38,56,49)(30,62)(53,63)(58,65);(1,2);(3,4,11,37,30,33,25,42,31,13,36,47,7,29,6,26,9,15,39,34,62,35,54,14,8,16,27,61,28,10,19,46)(5,18,52,44,48,12,41,65,20,55,57,64,22,40,59,63,23,32,49,66,50,43,21,58,24,51,38,60,17,45,56,53);(3,5,19,41,7,17,36,52,8,24,54,56,30,50,11,38,9,23,6,21,28,22,27,49,31,20,25,59,62,48,39,57)(4,12,42,66,10,32,37,53,16,45,46,64,35,55,61,58,15,43,14,44,29,18,34,63,13,40,26,60,33,51,47,65)
Conjugacy classes & character table
212 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((4,10,13,33,15,29,16,35)(5,17,20,48,23,22,24,50)(6,25,19,54)(7,28)(11,36,39,27)(12,40,43,45)(14,47,26,37,42,61,46,34)(18,51,32,55)(21,57,59,52,41,38,56,49)(30,62)(53,63)(58,65), (1,2), (3,4,11,37,30,33,25,42,31,13,36,47,7,29,6,26,9,15,39,34,62,35,54,14,8,16,27,61,28,10,19,46)(5,18,52,44,48,12,41,65,20,55,57,64,22,40,59,63,23,32,49,66,50,43,21,58,24,51,38,60,17,45,56,53), (3,5,19,41,7,17,36,52,8,24,54,56,30,50,11,38,9,23,6,21,28,22,27,49,31,20,25,59,62,48,39,57)(4,12,42,66,10,32,37,53,16,45,46,64,35,55,61,58,15,43,14,44,29,18,34,63,13,40,26,60,33,51,47,65));
Finite Group Databasebeta