← Prev (#72320750) Next (#72320752) →
Aliases
Subgroups
1063 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 4 generators on 66 points:
(4,11,14,39)(5,17,22,49)(6,24)(7,9)(8,32)(12,41)(13,40,16,38)(15,48,47,62)(18,43)(19,30)(20,31,26,21)(23,59,58,54)(25,37,42,33)(27,34)(28,55)(29,35)(36,53)(44,64)(45,51)(46,63)(50,56,65,57)(52,66);(1,2);(3,4,7,16,10,14,9,13)(5,18,21,36,22,53,31,43)(6,25,28,48,30,42,29,62)(8,33,27,47,34,37,32,15)(11,35,40,19,39,55,38,24)(12,26,46,49,45,20,44,17)(23,60,57,52,58,61,56,66)(41,65,64,54,51,50,63,59);(3,5,19,54,34,58,28,17,7,31,55,65,32,57,30,20,10,22,24,59,8,23,29,49,9,21,35,50,27,56,6,26)(4,12,42,60,47,51,38,53,13,46,48,52,33,63,39,43,14,45,25,61,15,41,40,18,16,44,62,66,37,64,11,36)
Conjugacy classes & character table
112 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((4,11,14,39)(5,17,22,49)(6,24)(7,9)(8,32)(12,41)(13,40,16,38)(15,48,47,62)(18,43)(19,30)(20,31,26,21)(23,59,58,54)(25,37,42,33)(27,34)(28,55)(29,35)(36,53)(44,64)(45,51)(46,63)(50,56,65,57)(52,66), (1,2), (3,4,7,16,10,14,9,13)(5,18,21,36,22,53,31,43)(6,25,28,48,30,42,29,62)(8,33,27,47,34,37,32,15)(11,35,40,19,39,55,38,24)(12,26,46,49,45,20,44,17)(23,60,57,52,58,61,56,66)(41,65,64,54,51,50,63,59), (3,5,19,54,34,58,28,17,7,31,55,65,32,57,30,20,10,22,24,59,8,23,29,49,9,21,35,50,27,56,6,26)(4,12,42,60,47,51,38,53,13,46,48,52,33,63,39,43,14,45,25,61,15,41,40,18,16,44,62,66,37,64,11,36));
Finite Group Databasebeta