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Aliases
Subgroups
1069 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 4 generators on 66 points:
(3,4)(5,15,18,10)(6,12)(7,13)(8,14)(9,11)(16,20,38,35)(17,36,42,28)(19,37,45,29)(21,24)(22,32)(23,33)(25,34)(26,30)(27,31)(39,44,41,53)(40,46,59,57)(43,58,62,54)(47,50)(48,51)(49,56)(52,55)(60,63,61,66)(64,65);(1,2);(3,4)(5,16,18,38)(6,21)(7,13)(8,14)(9,11)(10,20,15,35)(12,24)(17,41,42,39)(19,40,45,59)(22,47)(23,48)(25,34)(26,30)(27,31)(28,53,36,44)(29,46,37,57)(32,50)(33,51)(43,61,62,60)(49,64)(52,55)(54,66,58,63)(56,65);(3,5,6,17,7,19,22,43,8,20,23,44,25,46,49,63,9,18,24,42,26,45,50,62,27,35,51,53,52,57,65,66)(4,10,12,28,13,29,32,54,14,16,33,39,34,40,56,60,11,15,21,36,30,37,47,58,31,38,48,41,55,59,64,61)
Conjugacy classes & character table
184 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((3,4)(5,15,18,10)(6,12)(7,13)(8,14)(9,11)(16,20,38,35)(17,36,42,28)(19,37,45,29)(21,24)(22,32)(23,33)(25,34)(26,30)(27,31)(39,44,41,53)(40,46,59,57)(43,58,62,54)(47,50)(48,51)(49,56)(52,55)(60,63,61,66)(64,65), (1,2), (3,4)(5,16,18,38)(6,21)(7,13)(8,14)(9,11)(10,20,15,35)(12,24)(17,41,42,39)(19,40,45,59)(22,47)(23,48)(25,34)(26,30)(27,31)(28,53,36,44)(29,46,37,57)(32,50)(33,51)(43,61,62,60)(49,64)(52,55)(54,66,58,63)(56,65), (3,5,6,17,7,19,22,43,8,20,23,44,25,46,49,63,9,18,24,42,26,45,50,62,27,35,51,53,52,57,65,66)(4,10,12,28,13,29,32,54,14,16,33,39,34,40,56,60,11,15,21,36,30,37,47,58,31,38,48,41,55,59,64,61));
Finite Group Databasebeta