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Aliases
Subgroups
3136 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 5 generators on 66 points:
(4,10,12,27,13,28,35,30)(6,19,21,45)(7,23)(8,25)(11,31,33,55,32,26,51,52)(14,38,36,29,37,57,56,58)(16,41,20,44)(17,43)(18,40)(22,49,48,46)(24,50)(34,61,60,59,53,62,66,54)(39,63)(42,65,47,64);(3,4,6,10,7,14,19,29,8,12,22,30,23,36,46,38,9,13,21,28,24,37,45,58,25,35,48,27,50,56,49,57)(5,11,16,31,17,34,41,59,18,33,42,52,43,60,64,61,15,32,20,26,39,53,44,54,40,51,47,55,63,66,65,62);(1,2);(3,5)(4,11)(6,20)(7,17)(8,18)(9,15)(10,26)(12,33)(13,32)(14,34)(16,21)(19,44)(22,47)(23,43)(24,39)(25,40)(27,52)(28,31)(29,54)(30,55)(35,51)(36,60)(37,53)(38,62)(41,45)(42,48)(46,65)(49,64)(50,63)(56,66)(57,61)(58,59);(5,15)(11,32)(16,20)(17,39)(18,40)(26,31)(33,51)(34,53)(41,44)(42,47)(43,63)(52,55)(54,59)(60,66)(61,62)(64,65)
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((4,10,12,27,13,28,35,30)(6,19,21,45)(7,23)(8,25)(11,31,33,55,32,26,51,52)(14,38,36,29,37,57,56,58)(16,41,20,44)(17,43)(18,40)(22,49,48,46)(24,50)(34,61,60,59,53,62,66,54)(39,63)(42,65,47,64), (3,4,6,10,7,14,19,29,8,12,22,30,23,36,46,38,9,13,21,28,24,37,45,58,25,35,48,27,50,56,49,57)(5,11,16,31,17,34,41,59,18,33,42,52,43,60,64,61,15,32,20,26,39,53,44,54,40,51,47,55,63,66,65,62), (1,2), (3,5)(4,11)(6,20)(7,17)(8,18)(9,15)(10,26)(12,33)(13,32)(14,34)(16,21)(19,44)(22,47)(23,43)(24,39)(25,40)(27,52)(28,31)(29,54)(30,55)(35,51)(36,60)(37,53)(38,62)(41,45)(42,48)(46,65)(49,64)(50,63)(56,66)(57,61)(58,59), (5,15)(11,32)(16,20)(17,39)(18,40)(26,31)(33,51)(34,53)(41,44)(42,47)(43,63)(52,55)(54,59)(60,66)(61,62)(64,65));
Finite Group Databasebeta