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Aliases
Subgroups
1729 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 4 generators on 66 points:
(5,17,19,48)(6,22)(7,28)(8,31)(9,25)(11,33,35,45)(12,38)(13,40)(14,42)(15,43)(18,51,52,20)(21,55,47,50)(23,56)(24,32)(26,30)(27,29)(34,36,61,62)(37,65,63,60)(39,44)(41,57)(46,53,54,49)(58,66,64,59);(1,2);(3,4)(5,11)(6,23)(7,13)(8,14)(9,15)(10,16)(12,27)(17,45)(18,34)(19,35)(20,36)(21,37)(22,56)(24,39)(25,43)(26,57)(28,40)(29,38)(30,41)(31,42)(32,44)(33,48)(46,58)(47,63)(49,66)(50,65)(51,62)(52,61)(53,59)(54,64)(55,60);(3,5,7,18,8,20,6,17,25,47,22,49,24,46,28,55,10,19,30,52,32,51,27,48,9,21,29,53,31,54,26,50)(4,11,13,34,14,36,23,45,43,63,56,66,39,58,40,60,16,35,41,61,44,62,12,33,15,37,38,59,42,64,57,65)
Conjugacy classes & character table
160 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((5,17,19,48)(6,22)(7,28)(8,31)(9,25)(11,33,35,45)(12,38)(13,40)(14,42)(15,43)(18,51,52,20)(21,55,47,50)(23,56)(24,32)(26,30)(27,29)(34,36,61,62)(37,65,63,60)(39,44)(41,57)(46,53,54,49)(58,66,64,59), (1,2), (3,4)(5,11)(6,23)(7,13)(8,14)(9,15)(10,16)(12,27)(17,45)(18,34)(19,35)(20,36)(21,37)(22,56)(24,39)(25,43)(26,57)(28,40)(29,38)(30,41)(31,42)(32,44)(33,48)(46,58)(47,63)(49,66)(50,65)(51,62)(52,61)(53,59)(54,64)(55,60), (3,5,7,18,8,20,6,17,25,47,22,49,24,46,28,55,10,19,30,52,32,51,27,48,9,21,29,53,31,54,26,50)(4,11,13,34,14,36,23,45,43,63,56,66,39,58,40,60,16,35,41,61,44,62,12,33,15,37,38,59,42,64,57,65));
Finite Group Databasebeta