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Aliases
Subgroups
2555 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 5 generators on 50 points:
(1,2);(3,4,8,10)(5,12,6,9)(7,11,13,17)(14,18,15,16)(19,20)(21,30)(22,28)(23,29)(24,27)(25,26)(31,45)(32,44)(33,43)(34,39)(35,38)(36,40)(37,41)(42,48)(46,49)(47,50);(3,5,7,14,8,6,13,15)(4,9,11,16,10,12,17,18)(20,26)(21,24)(22,33,35,48)(23,37)(28,42,38,43)(29,44)(31,46,36,47)(32,34)(39,41)(40,49,45,50);(3,6,7,15,8,5,13,14)(4,9,11,16,10,12,17,18)(19,21,25,24)(20,27,26,30)(23,37,34,32)(28,38)(29,44,39,41)(33,48)(40,45)(46,47);(4,10)(9,12)(11,17)(16,18)(19,22,34,48,24,36,32,47,25,35,23,33,21,31,37,46)(20,28,39,42,27,40,44,50,26,38,29,43,30,45,41,49)
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), (3,4,8,10)(5,12,6,9)(7,11,13,17)(14,18,15,16)(19,20)(21,30)(22,28)(23,29)(24,27)(25,26)(31,45)(32,44)(33,43)(34,39)(35,38)(36,40)(37,41)(42,48)(46,49)(47,50), (3,5,7,14,8,6,13,15)(4,9,11,16,10,12,17,18)(20,26)(21,24)(22,33,35,48)(23,37)(28,42,38,43)(29,44)(31,46,36,47)(32,34)(39,41)(40,49,45,50), (3,6,7,15,8,5,13,14)(4,9,11,16,10,12,17,18)(19,21,25,24)(20,27,26,30)(23,37,34,32)(28,38)(29,44,39,41)(33,48)(40,45)(46,47), (4,10)(9,12)(11,17)(16,18)(19,22,34,48,24,36,32,47,25,35,23,33,21,31,37,46)(20,28,39,42,27,40,44,50,26,38,29,43,30,45,41,49));
Finite Group Databasebeta