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Aliases
Splittings
Subgroups
2998 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 3 generators on 83 points:
(2,23,31,6,8,25)(3,13)(4,17)(5,21)(7,51,58,22,27,52)(9,53,60,24,30,54)(10,57,32,28,36,63)(11,67,62,39,33,73)(12,69,61,41,34,55)(14,42)(15,46)(16,44)(18,19)(20,50)(26,72,79,38,56,66)(29,71,80,37,59,65)(35,68,64,40,70,81)(43,49)(45,76)(47,75)(48,78)(74,77);(1,11,24,20,29,22,17,2,38,5,40,41,18,28,10,19,12,35,21,26,6,4,7,37,50,9,39)(3,56,55,48,27,32,49,30,64,16,33,25,45,59,65,47,8,73,14,68,54,15,57,52,77,34,66)(13,81,23,74,63,71,46,61,67,42,79,53,75,58,51,76,60,72,44,62,69,43,80,36,78,31,70)(82,83);(2,28,11,9,29,26,12,7,40)(4,18,20)(6,10,39,24,37,38,41,22,35)(8,57,33,30,59,56,34,27,68)(15,45,48)(17,19,50)(23,36,67,53,71,72,69,51,70)(25,32,73,54,65,66,55,52,64)(31,63,62,60,80,79,61,58,81)(43,75,74)(46,76,78)(47,77,49)
Conjugacy classes & character table
324 conjugacy classes. The character table is too large to display.
Relationships
GAP
Past the SmallGroups library coverage — no SmallGroups id. Construct it from a minimal faithful permutation representation:
gap> G := Group((2,23,31,6,8,25)(3,13)(4,17)(5,21)(7,51,58,22,27,52)(9,53,60,24,30,54)(10,57,32,28,36,63)(11,67,62,39,33,73)(12,69,61,41,34,55)(14,42)(15,46)(16,44)(18,19)(20,50)(26,72,79,38,56,66)(29,71,80,37,59,65)(35,68,64,40,70,81)(43,49)(45,76)(47,75)(48,78)(74,77), (1,11,24,20,29,22,17,2,38,5,40,41,18,28,10,19,12,35,21,26,6,4,7,37,50,9,39)(3,56,55,48,27,32,49,30,64,16,33,25,45,59,65,47,8,73,14,68,54,15,57,52,77,34,66)(13,81,23,74,63,71,46,61,67,42,79,53,75,58,51,76,60,72,44,62,69,43,80,36,78,31,70)(82,83), (2,28,11,9,29,26,12,7,40)(4,18,20)(6,10,39,24,37,38,41,22,35)(8,57,33,30,59,56,34,27,68)(15,45,48)(17,19,50)(23,36,67,53,71,72,69,51,70)(25,32,73,54,65,66,55,52,64)(31,63,62,60,80,79,61,58,81)(43,75,74)(46,76,78)(47,77,49));
Finite Group Databasebeta