← Prev (#72320404) Next (#72320406) →
Aliases
Subgroups
2828 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 4 generators on 66 points:
(3,4)(5,17,19,48,22,50,24,62)(6,13,26,46)(7,12,28,40)(8,34)(9,37)(10,16)(11,20,41,56,43,58,45,53)(14,36)(15,38)(18,21,49,60,52,59,44,54)(23,61,55,66,57,51,39,42)(25,33,63,65)(27,47)(29,64,32,30)(31,35);(3,4)(5,18,19,49,22,52,24,44)(6,25,26,63)(7,30,28,64)(8,35)(9,15)(10,16)(11,39,41,23,43,55,45,57)(12,29,40,32)(13,33,46,65)(14,27)(17,21,48,60,50,59,62,54)(20,42,56,61,58,66,53,51)(31,34)(36,47)(37,38);(1,2);(3,5,6,20,27,57,7,21,9,24,29,56,31,55,33,60,10,22,26,58,8,23,28,59,38,19,32,53,36,39,65,54)(4,11,40,50,35,49,13,42,15,45,63,62,47,18,30,61,16,43,12,17,14,44,46,66,37,41,25,48,34,52,64,51)
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((3,4)(5,17,19,48,22,50,24,62)(6,13,26,46)(7,12,28,40)(8,34)(9,37)(10,16)(11,20,41,56,43,58,45,53)(14,36)(15,38)(18,21,49,60,52,59,44,54)(23,61,55,66,57,51,39,42)(25,33,63,65)(27,47)(29,64,32,30)(31,35), (3,4)(5,18,19,49,22,52,24,44)(6,25,26,63)(7,30,28,64)(8,35)(9,15)(10,16)(11,39,41,23,43,55,45,57)(12,29,40,32)(13,33,46,65)(14,27)(17,21,48,60,50,59,62,54)(20,42,56,61,58,66,53,51)(31,34)(36,47)(37,38), (1,2), (3,5,6,20,27,57,7,21,9,24,29,56,31,55,33,60,10,22,26,58,8,23,28,59,38,19,32,53,36,39,65,54)(4,11,40,50,35,49,13,42,15,45,63,62,47,18,30,61,16,43,12,17,14,44,46,66,37,41,25,48,34,52,64,51));
Finite Group Databasebeta