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Aliases
Subgroups
3788 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 5 generators on 50 points:
(3,4)(5,9)(6,10)(7,8)(11,16)(12,14)(13,15)(17,18)(19,20)(21,32)(22,27)(23,30)(24,41)(25,26)(28,35)(29,36)(31,40)(33,48)(34,44)(37,46)(38,45)(39,42)(43,49)(47,50);(4,8)(9,14)(10,15)(16,18)(20,26)(27,42)(28,32)(29,43)(30,31)(41,48)(44,46)(45,47);(20,27)(21,33)(22,36)(23,40)(24,35)(26,42)(28,29)(30,47)(31,45)(32,43)(34,38)(37,50)(39,49)(41,46)(44,48);(3,5,6,11,7,12,13,17)(4,9,10,16,8,14,15,18)(19,21,23,24,25,35,40,33)(20,28,30,48,26,32,31,41)(22,37,38,49,39,34,50,36)(27,44,45,29,42,46,47,43);(1,2)(19,22,35,37,23,38,33,49,25,39,21,34,40,50,24,36)(20,29,41,47,31,44,32,42,26,43,48,45,30,46,28,27)
Conjugacy classes & character table
200 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)(5,9)(6,10)(7,8)(11,16)(12,14)(13,15)(17,18)(19,20)(21,32)(22,27)(23,30)(24,41)(25,26)(28,35)(29,36)(31,40)(33,48)(34,44)(37,46)(38,45)(39,42)(43,49)(47,50), (4,8)(9,14)(10,15)(16,18)(20,26)(27,42)(28,32)(29,43)(30,31)(41,48)(44,46)(45,47), (20,27)(21,33)(22,36)(23,40)(24,35)(26,42)(28,29)(30,47)(31,45)(32,43)(34,38)(37,50)(39,49)(41,46)(44,48), (3,5,6,11,7,12,13,17)(4,9,10,16,8,14,15,18)(19,21,23,24,25,35,40,33)(20,28,30,48,26,32,31,41)(22,37,38,49,39,34,50,36)(27,44,45,29,42,46,47,43), (1,2)(19,22,35,37,23,38,33,49,25,39,21,34,40,50,24,36)(20,29,41,47,31,44,32,42,26,43,48,45,30,46,28,27));
Finite Group Databasebeta