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Aliases
Subgroups
3284 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 4 generators on 66 points:
(5,15,18,42,19,43,49,22)(6,21,23,17)(7,25)(8,28)(10,29,31,53,16,41,45,37)(12,36,33,30)(13,39)(14,35)(20,46,50,44,26,51,54,56)(24,48,47,52)(27,55)(32,58,61,57,40,63,65,66)(34,62)(38,60,59,64);(3,4)(5,16,19,10)(6,12)(7,13)(8,14)(9,11)(15,41,43,29)(17,30)(18,45,49,31)(20,40,26,32)(21,36)(22,53,42,37)(23,33)(24,38)(25,39)(27,34)(28,35)(44,66,56,57)(46,63,51,58)(47,59)(48,60)(50,65,54,61)(52,64)(55,62);(1,2);(3,5,17,46,55,50,23,42,28,49,52,44,27,20,24,43,9,19,21,51,25,54,6,22,8,18,48,56,7,26,47,15)(4,10,30,58,62,61,33,53,35,45,64,57,34,32,38,41,11,16,36,63,39,65,12,37,14,31,60,66,13,40,59,29)
Conjugacy classes & character table
188 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((5,15,18,42,19,43,49,22)(6,21,23,17)(7,25)(8,28)(10,29,31,53,16,41,45,37)(12,36,33,30)(13,39)(14,35)(20,46,50,44,26,51,54,56)(24,48,47,52)(27,55)(32,58,61,57,40,63,65,66)(34,62)(38,60,59,64), (3,4)(5,16,19,10)(6,12)(7,13)(8,14)(9,11)(15,41,43,29)(17,30)(18,45,49,31)(20,40,26,32)(21,36)(22,53,42,37)(23,33)(24,38)(25,39)(27,34)(28,35)(44,66,56,57)(46,63,51,58)(47,59)(48,60)(50,65,54,61)(52,64)(55,62), (1,2), (3,5,17,46,55,50,23,42,28,49,52,44,27,20,24,43,9,19,21,51,25,54,6,22,8,18,48,56,7,26,47,15)(4,10,30,58,62,61,33,53,35,45,64,57,34,32,38,41,11,16,36,63,39,65,12,37,14,31,60,66,13,40,59,29));
Finite Group Databasebeta