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Aliases
Subgroups
3114 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 4 generators on 66 points:
(4,10,12,34,13,36,28,35)(5,15,18,19,21,49,20,51)(6,23,25,17)(7,27)(8,29)(11,38,39,47)(14,45,43,37,44,24,30,64)(16,40)(22,60,48,50,31,57,59,62)(26,33,56,58)(32,46)(41,52,42,66)(54,55)(61,63);(1,2);(3,4)(5,16)(6,24)(7,28)(8,30)(9,13)(10,33)(11,15)(12,27)(14,46)(17,35)(18,40)(19,42)(20,54)(21,55)(22,61)(23,34)(25,45)(26,64)(29,44)(31,63)(32,43)(36,58)(37,56)(38,57)(39,49)(41,51)(47,60)(48,65)(50,66)(52,62)(53,59);(3,5,17,50,46,48,25,49,27,20,58,57,32,22,26,51,9,21,23,62,29,59,6,15,7,18,33,60,8,31,56,19)(4,11,24,63,43,66,35,54,28,41,64,53,14,47,10,16,13,39,45,61,30,52,34,40,12,42,37,65,44,38,36,55)
Conjugacy classes & character table
164 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((4,10,12,34,13,36,28,35)(5,15,18,19,21,49,20,51)(6,23,25,17)(7,27)(8,29)(11,38,39,47)(14,45,43,37,44,24,30,64)(16,40)(22,60,48,50,31,57,59,62)(26,33,56,58)(32,46)(41,52,42,66)(54,55)(61,63), (1,2), (3,4)(5,16)(6,24)(7,28)(8,30)(9,13)(10,33)(11,15)(12,27)(14,46)(17,35)(18,40)(19,42)(20,54)(21,55)(22,61)(23,34)(25,45)(26,64)(29,44)(31,63)(32,43)(36,58)(37,56)(38,57)(39,49)(41,51)(47,60)(48,65)(50,66)(52,62)(53,59), (3,5,17,50,46,48,25,49,27,20,58,57,32,22,26,51,9,21,23,62,29,59,6,15,7,18,33,60,8,31,56,19)(4,11,24,63,43,66,35,54,28,41,64,53,14,47,10,16,13,39,45,61,30,52,34,40,12,42,37,65,44,38,36,55));
Finite Group Databasebeta