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Aliases
Subgroups
436 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 3 generators on 67 points:
(1,2,3,8,4,9,13,26,5,10,14,28,17,34,40,23,6,11,15,29,18,32,41,52,20,30,43,24,47,54,37,53,7,12,16,27,19,33,39,59,21,35,44,56,46,31,62,51,22,36,42,25,48,57,38,58,49,60,64,55,45,61,63,50)(65,66,67);(2,8,10,24,11,25,30,28,12,27,35,55,36,29,60,56)(3,13,15,38,16,39,42,41)(4,17,19,46)(5,20)(6,22)(9,23,31,26,32,50,61,58,33,51,34,59,57,53,54,52)(14,37,43,40,44,63,64,62)(18,45,48,47)(21,49);(2,9,30,61,36,57,10,31,12,33,60,54,11,32,35,34)(3,14,42,64,16,44,15,43)(4,18,19,48)(5,21)(8,23,28,58,29,53,24,26,27,51,56,52,25,50,55,59)(13,37,41,62,39,63,38,40)(17,45,46,47)(20,49)
Conjugacy classes & character table
285 conjugacy classes. The character table is too large to display.
Relationships
GAP
Past the SmallGroups library coverage — no SmallGroups id. Construct it from a minimal faithful permutation representation:
gap> G := Group((1,2,3,8,4,9,13,26,5,10,14,28,17,34,40,23,6,11,15,29,18,32,41,52,20,30,43,24,47,54,37,53,7,12,16,27,19,33,39,59,21,35,44,56,46,31,62,51,22,36,42,25,48,57,38,58,49,60,64,55,45,61,63,50)(65,66,67), (2,8,10,24,11,25,30,28,12,27,35,55,36,29,60,56)(3,13,15,38,16,39,42,41)(4,17,19,46)(5,20)(6,22)(9,23,31,26,32,50,61,58,33,51,34,59,57,53,54,52)(14,37,43,40,44,63,64,62)(18,45,48,47)(21,49), (2,9,30,61,36,57,10,31,12,33,60,54,11,32,35,34)(3,14,42,64,16,44,15,43)(4,18,19,48)(5,21)(8,23,28,58,29,53,24,26,27,51,56,52,25,50,55,59)(13,37,41,62,39,63,38,40)(17,45,46,47)(20,49));
Finite Group Databasebeta