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Aliases
Subgroups
2714 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 4 generators on 66 points:
(5,16,19,42,21,44,53,26)(6,22)(7,18,27,50)(8,29)(10,30,32,64,33,59,47,38)(11,35)(12,31,39,36)(13,40)(14,37)(17,41,45,46,34,66,65,62)(20,54,52,43,23,49,56,58)(24,57)(25,48,60,61)(28,63,55,51);(3,4)(5,17,19,45,21,34,53,65)(6,11)(7,25,27,60)(8,14)(9,15)(10,20,32,52,33,23,47,56)(12,28,39,55)(13,24)(16,41,42,46,44,66,26,62)(18,48,50,61)(22,35)(29,37)(30,54,64,43,59,49,38,58)(31,63,36,51)(40,57);(1,2);(3,5,18,49,57,52,7,26,29,53,63,58,24,20,55,16,9,21,50,54,22,56,27,42,8,19,51,43,6,23,28,44)(4,10,31,41,35,65,12,38,37,47,48,46,11,34,60,30,15,33,36,66,40,45,39,64,14,32,61,62,13,17,25,59)
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((5,16,19,42,21,44,53,26)(6,22)(7,18,27,50)(8,29)(10,30,32,64,33,59,47,38)(11,35)(12,31,39,36)(13,40)(14,37)(17,41,45,46,34,66,65,62)(20,54,52,43,23,49,56,58)(24,57)(25,48,60,61)(28,63,55,51), (3,4)(5,17,19,45,21,34,53,65)(6,11)(7,25,27,60)(8,14)(9,15)(10,20,32,52,33,23,47,56)(12,28,39,55)(13,24)(16,41,42,46,44,66,26,62)(18,48,50,61)(22,35)(29,37)(30,54,64,43,59,49,38,58)(31,63,36,51)(40,57), (1,2), (3,5,18,49,57,52,7,26,29,53,63,58,24,20,55,16,9,21,50,54,22,56,27,42,8,19,51,43,6,23,28,44)(4,10,31,41,35,65,12,38,37,47,48,46,11,34,60,30,15,33,36,66,40,45,39,64,14,32,61,62,13,17,25,59));
Finite Group Databasebeta