← Prev (#72320319) Next (#72320321) →
Aliases
Subgroups
1771 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 4 generators on 66 points:
(3,4)(5,17)(6,23)(7,28)(8,16)(9,35)(10,36)(11,19)(12,14)(13,31)(15,34)(18,48)(20,54)(21,57)(22,40)(24,58)(25,44)(26,32)(27,43)(29,42)(30,62)(33,63)(37,39)(38,49)(41,46)(45,55)(47,53)(50,56)(51,61)(52,65)(59,66)(60,64);(3,5,8,19)(4,11)(6,24)(7,20,30,51)(9,21,33,52)(10,22,34,53)(12,41,42,37)(13,38)(14,39)(15,40)(16,17)(18,27)(23,48,43,58)(25,49,31,55)(26,59)(28,61)(29,46)(32,56,64,66)(35,65)(36,47)(44,45)(50,60)(54,62)(57,63);(1,2);(3,6,25,36,9,26,32,63,34,44,23,16,42,62,7,29,8,27,31,15,33,60,64,35,10,13,43,4,12,28,30,14)(5,18,49,40,21,50,56,65,53,38,48,11,37,61,20,39,19,24,55,47,52,59,66,57,22,45,58,17,41,54,51,46)
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)(6,23)(7,28)(8,16)(9,35)(10,36)(11,19)(12,14)(13,31)(15,34)(18,48)(20,54)(21,57)(22,40)(24,58)(25,44)(26,32)(27,43)(29,42)(30,62)(33,63)(37,39)(38,49)(41,46)(45,55)(47,53)(50,56)(51,61)(52,65)(59,66)(60,64), (3,5,8,19)(4,11)(6,24)(7,20,30,51)(9,21,33,52)(10,22,34,53)(12,41,42,37)(13,38)(14,39)(15,40)(16,17)(18,27)(23,48,43,58)(25,49,31,55)(26,59)(28,61)(29,46)(32,56,64,66)(35,65)(36,47)(44,45)(50,60)(54,62)(57,63), (1,2), (3,6,25,36,9,26,32,63,34,44,23,16,42,62,7,29,8,27,31,15,33,60,64,35,10,13,43,4,12,28,30,14)(5,18,49,40,21,50,56,65,53,38,48,11,37,61,20,39,19,24,55,47,52,59,66,57,22,45,58,17,41,54,51,46));
Finite Group Databasebeta