← Prev (#72245286) Next (#72245288) →
Aliases
Subgroups
617 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 4 generators on 66 points:
(1,2);(3,4,9,17,11,18,10,40)(5,19,25,43,27,48,26,63)(6,28,20,13,32,50,31,14)(7,33,35,49,30,42,36,51)(8,37,38,53,39,15,34,16)(12,41,46,60,47,56,65,22)(21,52,57,45,58,44,29,64)(23,61,59,55,24,54,62,66);(3,5,20,21,8,24,36,56,9,25,32,57,38,62,7,22,11,27,31,58,39,23,35,41,10,26,6,29,34,59,30,60)(4,12,42,66,16,45,28,43,40,65,49,54,15,52,14,19,18,47,33,55,53,64,50,63,17,46,51,61,37,44,13,48);(3,6,8,30,9,20,38,36,11,32,39,7,10,31,34,35)(4,13,15,49,17,50,16,42,18,14,37,51,40,28,53,33)(5,21,23,41,25,57,59,60,27,58,24,56,26,29,62,22)(12,43,44,66,46,48,64,61,47,63,52,55,65,19,45,54)
Conjugacy classes & character table
136 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((1,2), (3,4,9,17,11,18,10,40)(5,19,25,43,27,48,26,63)(6,28,20,13,32,50,31,14)(7,33,35,49,30,42,36,51)(8,37,38,53,39,15,34,16)(12,41,46,60,47,56,65,22)(21,52,57,45,58,44,29,64)(23,61,59,55,24,54,62,66), (3,5,20,21,8,24,36,56,9,25,32,57,38,62,7,22,11,27,31,58,39,23,35,41,10,26,6,29,34,59,30,60)(4,12,42,66,16,45,28,43,40,65,49,54,15,52,14,19,18,47,33,55,53,64,50,63,17,46,51,61,37,44,13,48), (3,6,8,30,9,20,38,36,11,32,39,7,10,31,34,35)(4,13,15,49,17,50,16,42,18,14,37,51,40,28,53,33)(5,21,23,41,25,57,59,60,27,58,24,56,26,29,62,22)(12,43,44,66,46,48,64,61,47,63,52,55,65,19,45,54));
Finite Group Databasebeta