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Aliases
Subgroups
3654 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 5 generators on 66 points:
(1,2);(5,16,19,40,6,21,23,42)(7,25,18,45)(8,28)(9,31)(11,32,33,65,34,66,50,60)(12,35,36,53)(13,37)(14,38)(17,39,43,44,22,51,54,55)(20,49,48,41,24,57,56,52)(26,58,46,61)(27,62,47,59)(29,63)(30,64);(3,4)(5,17,23,54,6,22,19,43)(7,26,18,46)(8,29)(9,14)(10,15)(11,20,50,56,34,24,33,48)(12,27,36,47)(13,30)(16,39,42,55,21,51,40,44)(25,58,45,61)(28,63)(31,38)(32,49,60,52,66,57,65,41)(35,62,53,59)(37,64);(3,5,7,16,8,20,25,41,9,19,27,42,28,48,59,49,10,6,18,21,30,24,45,52,31,23,47,40,64,56,62,57)(4,11,12,32,13,17,35,44,14,33,26,60,37,43,61,39,15,34,36,66,29,22,53,55,38,50,46,65,63,54,58,51);(3,6,7,21,8,24,25,52,9,23,27,40,28,56,59,57,10,5,18,16,30,20,45,41,31,19,47,42,64,48,62,49)(4,11,12,32,13,17,35,44,14,33,26,60,37,43,61,39,15,34,36,66,29,22,53,55,38,50,46,65,63,54,58,51)
Conjugacy classes & character table
188 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), (5,16,19,40,6,21,23,42)(7,25,18,45)(8,28)(9,31)(11,32,33,65,34,66,50,60)(12,35,36,53)(13,37)(14,38)(17,39,43,44,22,51,54,55)(20,49,48,41,24,57,56,52)(26,58,46,61)(27,62,47,59)(29,63)(30,64), (3,4)(5,17,23,54,6,22,19,43)(7,26,18,46)(8,29)(9,14)(10,15)(11,20,50,56,34,24,33,48)(12,27,36,47)(13,30)(16,39,42,55,21,51,40,44)(25,58,45,61)(28,63)(31,38)(32,49,60,52,66,57,65,41)(35,62,53,59)(37,64), (3,5,7,16,8,20,25,41,9,19,27,42,28,48,59,49,10,6,18,21,30,24,45,52,31,23,47,40,64,56,62,57)(4,11,12,32,13,17,35,44,14,33,26,60,37,43,61,39,15,34,36,66,29,22,53,55,38,50,46,65,63,54,58,51), (3,6,7,21,8,24,25,52,9,23,27,40,28,56,59,57,10,5,18,16,30,20,45,41,31,19,47,42,64,48,62,49)(4,11,12,32,13,17,35,44,14,33,26,60,37,43,61,39,15,34,36,66,29,22,53,55,38,50,46,65,63,54,58,51));
Finite Group Databasebeta