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Aliases
Subgroups
2006 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 4 generators on 66 points:
(4,10,13,35,14,36,32,37)(5,16,19,48,21,41,23,58)(6,24,18,40)(8,29)(9,28)(11,38)(15,46,30,25,45,60,39,53)(17,49,51,66)(20,55,54,31,56,50,26,22)(27,61,33,59)(34,57,52,63)(42,65)(43,64)(47,62);(1,2);(3,4,11,39,9,32,38,45,7,14,8,30,28,13,29,15)(5,17,50,49,19,52,22,57,21,51,55,66,23,34,31,63)(6,25,24,36,27,60,59,37,18,53,40,10,33,46,61,35)(12,41,47,20,43,48,62,26,44,16,42,56,64,58,65,54);(3,5,18,54,11,22,24,58,9,23,33,56,38,50,59,16,7,21,6,26,8,31,40,48,28,19,27,20,29,55,61,41)(4,12,37,17,15,47,46,66,13,43,36,52,30,62,53,63,14,44,35,51,45,42,60,49,32,64,10,34,39,65,25,57)
Conjugacy classes & character table
140 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((4,10,13,35,14,36,32,37)(5,16,19,48,21,41,23,58)(6,24,18,40)(8,29)(9,28)(11,38)(15,46,30,25,45,60,39,53)(17,49,51,66)(20,55,54,31,56,50,26,22)(27,61,33,59)(34,57,52,63)(42,65)(43,64)(47,62), (1,2), (3,4,11,39,9,32,38,45,7,14,8,30,28,13,29,15)(5,17,50,49,19,52,22,57,21,51,55,66,23,34,31,63)(6,25,24,36,27,60,59,37,18,53,40,10,33,46,61,35)(12,41,47,20,43,48,62,26,44,16,42,56,64,58,65,54), (3,5,18,54,11,22,24,58,9,23,33,56,38,50,59,16,7,21,6,26,8,31,40,48,28,19,27,20,29,55,61,41)(4,12,37,17,15,47,46,66,13,43,36,52,30,62,53,63,14,44,35,51,45,42,60,49,32,64,10,34,39,65,25,57));
Finite Group Databasebeta