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Aliases
Subgroups
1429 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 4 generators on 66 points:
(3,4)(5,17,22,48)(6,25)(7,29)(8,34)(9,37)(10,16)(11,20,40,58)(12,27)(13,32)(14,31)(15,35)(18,45,52,21)(19,44)(23,63,62,64)(24,39,38,50)(26,43)(28,54)(30,56)(33,51)(36,42)(41,61,47,65)(46,55,53,59)(49,57,66,60);(3,4)(5,18)(6,12)(7,30)(8,14)(9,15)(10,16)(11,38)(13,33)(17,45)(19,54)(20,50)(21,48)(22,52)(23,53)(24,40)(25,27)(26,42)(28,44)(29,56)(31,34)(32,51)(35,37)(36,43)(39,58)(41,57)(46,62)(47,60)(49,65)(55,64)(59,63)(61,66);(1,2);(3,5,19,55,36,62,33,45,35,38,32,61,31,60,28,58,10,22,27,59,8,23,7,21,9,24,56,65,26,57,6,20)(4,11,25,49,43,47,30,50,37,52,29,64,34,53,12,17,16,40,54,66,14,41,13,39,15,18,51,63,42,46,44,48)
Conjugacy classes & character table
124 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)(5,17,22,48)(6,25)(7,29)(8,34)(9,37)(10,16)(11,20,40,58)(12,27)(13,32)(14,31)(15,35)(18,45,52,21)(19,44)(23,63,62,64)(24,39,38,50)(26,43)(28,54)(30,56)(33,51)(36,42)(41,61,47,65)(46,55,53,59)(49,57,66,60), (3,4)(5,18)(6,12)(7,30)(8,14)(9,15)(10,16)(11,38)(13,33)(17,45)(19,54)(20,50)(21,48)(22,52)(23,53)(24,40)(25,27)(26,42)(28,44)(29,56)(31,34)(32,51)(35,37)(36,43)(39,58)(41,57)(46,62)(47,60)(49,65)(55,64)(59,63)(61,66), (1,2), (3,5,19,55,36,62,33,45,35,38,32,61,31,60,28,58,10,22,27,59,8,23,7,21,9,24,56,65,26,57,6,20)(4,11,25,49,43,47,30,50,37,52,29,64,34,53,12,17,16,40,54,66,14,41,13,39,15,18,51,63,42,46,44,48));
Finite Group Databasebeta