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Aliases
Subgroups
3032 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 4 generators on 66 points:
(4,10,13,32,15,24,16,34)(6,23)(7,27,29,58)(11,35,38,25)(12,39,41,62,17,31,43,60)(14,45,28,36,46,57,44,33)(18,20)(19,51,53,66)(26,56)(37,48,40,54)(42,64,59,61,47,65,52,63)(50,55);(1,2);(3,4,11,36,26,32,27,46,30,13,35,45,6,24,7,28,9,15,38,33,56,34,58,14,8,16,25,57,23,10,29,44)(5,17,37,61,55,62,51,42,49,43,48,64,20,31,19,52,22,12,40,63,50,60,66,47,21,41,54,65,18,39,53,59);(3,5)(4,12)(6,20)(7,19)(8,21)(9,22)(10,31)(11,37)(13,41)(14,42)(15,17)(16,43)(18,23)(24,39)(25,54)(26,55)(27,51)(28,59)(29,53)(30,49)(32,60)(33,61)(34,62)(35,48)(36,63)(38,40)(44,52)(45,65)(46,47)(50,56)(57,64)(58,66)
Conjugacy classes & character table
260 conjugacy classes. The character table is too large to display.
Relationships
GAP
Past the SmallGroups library coverage — no SmallGroups id. Construct it from a minimal faithful permutation representation:
gap> G := Group((4,10,13,32,15,24,16,34)(6,23)(7,27,29,58)(11,35,38,25)(12,39,41,62,17,31,43,60)(14,45,28,36,46,57,44,33)(18,20)(19,51,53,66)(26,56)(37,48,40,54)(42,64,59,61,47,65,52,63)(50,55), (1,2), (3,4,11,36,26,32,27,46,30,13,35,45,6,24,7,28,9,15,38,33,56,34,58,14,8,16,25,57,23,10,29,44)(5,17,37,61,55,62,51,42,49,43,48,64,20,31,19,52,22,12,40,63,50,60,66,47,21,41,54,65,18,39,53,59), (3,5)(4,12)(6,20)(7,19)(8,21)(9,22)(10,31)(11,37)(13,41)(14,42)(15,17)(16,43)(18,23)(24,39)(25,54)(26,55)(27,51)(28,59)(29,53)(30,49)(32,60)(33,61)(34,62)(35,48)(36,63)(38,40)(44,52)(45,65)(46,47)(50,56)(57,64)(58,66));
Finite Group Databasebeta