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Aliases
Subgroups
3032 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 4 generators on 66 points:
(4,11,13,16,15,34,33,46)(5,17,19,47,21,28,49,22)(6,23,18,26)(7,27)(8,30)(12,35,37,41)(14,43,44,57,36,45,42,32)(20,54,55,56,50,66,53,48)(24,25,51,52)(31,40,39,61)(38,60)(59,64);(1,2);(3,4,6,14,8,16,25,45,9,13,26,42,27,34,51,57,10,15,18,36,30,46,52,43,29,33,23,44,7,11,24,32)(5,12,20,38,22,40,54,63,19,41,53,64,17,39,48,62,21,37,50,60,47,61,66,65,49,35,55,59,28,31,56,58);(3,5,18,50,8,22,52,66,9,19,23,55,27,17,24,56,10,21,6,20,30,47,25,54,29,49,26,53,7,28,51,48)(4,12,36,60,16,40,43,65,13,41,44,59,34,39,32,58,15,37,14,38,46,61,45,63,33,35,42,64,11,31,57,62)
Conjugacy classes & character table
260 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((4,11,13,16,15,34,33,46)(5,17,19,47,21,28,49,22)(6,23,18,26)(7,27)(8,30)(12,35,37,41)(14,43,44,57,36,45,42,32)(20,54,55,56,50,66,53,48)(24,25,51,52)(31,40,39,61)(38,60)(59,64), (1,2), (3,4,6,14,8,16,25,45,9,13,26,42,27,34,51,57,10,15,18,36,30,46,52,43,29,33,23,44,7,11,24,32)(5,12,20,38,22,40,54,63,19,41,53,64,17,39,48,62,21,37,50,60,47,61,66,65,49,35,55,59,28,31,56,58), (3,5,18,50,8,22,52,66,9,19,23,55,27,17,24,56,10,21,6,20,30,47,25,54,29,49,26,53,7,28,51,48)(4,12,36,60,16,40,43,65,13,41,44,59,34,39,32,58,15,37,14,38,46,61,45,63,33,35,42,64,11,31,57,62));
Finite Group Databasebeta