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Aliases
Subgroups
2495 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 5 generators on 50 points:
(1,2);(3,4)(5,13)(6,16)(7,12)(8,10)(9,15)(11,14)(17,18)(19,20)(21,31)(22,35)(23,29)(24,30)(25,28)(26,34)(27,39)(32,42)(33,43)(36,44)(37,45)(38,47)(40,46)(41,48)(49,50);(3,5,7,14,8,15,17,6)(4,9,12,16,10,13,18,11)(19,21,23,24,25,34,41,33)(20,26,29,43,28,31,48,30)(22,36,38,50,39,37,40,32)(27,44,46,49,35,45,47,42);(4,10)(9,13)(11,16)(12,18)(19,22,24,37,23,40,34,50,25,39,33,36,41,38,21,32)(20,27,30,44,29,47,26,42,28,35,43,45,48,46,31,49);(3,6,17,15,8,14,7,5)(4,11,18,13,10,16,12,9)(20,28)(21,33)(22,37,39,36)(23,41)(24,34)(26,43)(27,45,35,44)(30,31)(32,38,50,40)(42,46,49,47)
Conjugacy classes & character table
124 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)(5,13)(6,16)(7,12)(8,10)(9,15)(11,14)(17,18)(19,20)(21,31)(22,35)(23,29)(24,30)(25,28)(26,34)(27,39)(32,42)(33,43)(36,44)(37,45)(38,47)(40,46)(41,48)(49,50), (3,5,7,14,8,15,17,6)(4,9,12,16,10,13,18,11)(19,21,23,24,25,34,41,33)(20,26,29,43,28,31,48,30)(22,36,38,50,39,37,40,32)(27,44,46,49,35,45,47,42), (4,10)(9,13)(11,16)(12,18)(19,22,24,37,23,40,34,50,25,39,33,36,41,38,21,32)(20,27,30,44,29,47,26,42,28,35,43,45,48,46,31,49), (3,6,17,15,8,14,7,5)(4,11,18,13,10,16,12,9)(20,28)(21,33)(22,37,39,36)(23,41)(24,34)(26,43)(27,45,35,44)(30,31)(32,38,50,40)(42,46,49,47));
Finite Group Databasebeta