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Aliases
Subgroups
2566 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 4 generators on 66 points:
(3,4)(5,16,19,44,21,46,48,41)(6,23)(7,26,29,35)(8,31)(9,33)(10,15)(11,20,36,57,37,58,64,28)(12,32)(13,30,42,18)(14,24)(17,47,50,66,22,43,55,45)(25,38)(27,61,49,62)(34,53,60,59,39,56,63,51)(40,54,65,52);(5,17,48,55,21,22,19,50)(6,8)(7,27,29,49)(11,34,64,63,37,39,36,60)(12,38)(13,40,42,65)(16,43,41,66,46,47,44,45)(18,52,30,54)(20,56,28,59,58,53,57,51)(23,31)(25,32)(26,61,35,62);(1,2);(3,5,18,53,25,55,29,57,24,48,52,59,6,22,27,58,10,21,30,56,32,50,7,28,9,19,54,51,8,17,49,20)(4,11,35,43,23,60,42,44,33,64,62,45,38,34,40,46,15,37,26,47,31,63,13,41,14,36,61,66,12,39,65,16)
Conjugacy classes & character table
140 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)(5,16,19,44,21,46,48,41)(6,23)(7,26,29,35)(8,31)(9,33)(10,15)(11,20,36,57,37,58,64,28)(12,32)(13,30,42,18)(14,24)(17,47,50,66,22,43,55,45)(25,38)(27,61,49,62)(34,53,60,59,39,56,63,51)(40,54,65,52), (5,17,48,55,21,22,19,50)(6,8)(7,27,29,49)(11,34,64,63,37,39,36,60)(12,38)(13,40,42,65)(16,43,41,66,46,47,44,45)(18,52,30,54)(20,56,28,59,58,53,57,51)(23,31)(25,32)(26,61,35,62), (1,2), (3,5,18,53,25,55,29,57,24,48,52,59,6,22,27,58,10,21,30,56,32,50,7,28,9,19,54,51,8,17,49,20)(4,11,35,43,23,60,42,44,33,64,62,45,38,34,40,46,15,37,26,47,31,63,13,41,14,36,61,66,12,39,65,16));
Finite Group Databasebeta