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Aliases
Subgroups
342 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 3 generators on 67 points:
(1,2,4,13,6,15,29,11,8,16,20,14,7,37,5,32,10,17,31,53,35,39,33,41,9,38,30,54,36,52,34,44)(3,18,21,55,23,43,59,64,25,40,57,12,42,45,62,47,27,56,60,49,19,51,22,61,26,63,28,50,24,46,58,48)(65,66,67);(2,11,39,14,16,32,52,53,17,41,15,54,38,44,37,13)(3,19,26,42,27,23,25,24)(4,20,31,30)(5,29,34,33)(6,35)(7,36)(12,43,61,18,55,46,47,63,50,51,64,56,49,45,48,40)(21,58,57,59,60,62,28,22);(1,3,20,21,6,19,5,22,8,25,31,57,7,24,33,58,10,27,30,60,35,23,34,59,9,26,4,28,36,42,29,62)(2,12,44,18,37,64,14,46,38,55,41,63,15,48,13,51,17,50,32,56,52,61,54,45,16,49,11,40,39,47,53,43)
Conjugacy classes & character table
282 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((1,2,4,13,6,15,29,11,8,16,20,14,7,37,5,32,10,17,31,53,35,39,33,41,9,38,30,54,36,52,34,44)(3,18,21,55,23,43,59,64,25,40,57,12,42,45,62,47,27,56,60,49,19,51,22,61,26,63,28,50,24,46,58,48)(65,66,67), (2,11,39,14,16,32,52,53,17,41,15,54,38,44,37,13)(3,19,26,42,27,23,25,24)(4,20,31,30)(5,29,34,33)(6,35)(7,36)(12,43,61,18,55,46,47,63,50,51,64,56,49,45,48,40)(21,58,57,59,60,62,28,22), (1,3,20,21,6,19,5,22,8,25,31,57,7,24,33,58,10,27,30,60,35,23,34,59,9,26,4,28,36,42,29,62)(2,12,44,18,37,64,14,46,38,55,41,63,15,48,13,51,17,50,32,56,52,61,54,45,16,49,11,40,39,47,53,43));
Finite Group Databasebeta