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Aliases
Splittings
Subgroups
4521 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 4 generators on 56 points:
(2,13,16,5,6,15)(3,8)(4,12)(7,26,19,18,17,24)(9,10)(11,22)(14,20,25,21,23,27)(30,35)(33,41)(36,46)(37,45)(39,47)(42,52)(43,51)(48,54)(49,53);(1,11,22,4,9,8,12,3,10)(2,17,27,6,19,21,16,7,20)(5,25,26,15,23,18,13,14,24)(28,34,50,31,44,32,38,29,40)(30,43,48,37,42,39,36,33,49)(35,51,54,45,52,47,46,41,53)(55,56);(30,36,37)(33,42,43)(35,45,46)(39,48,49)(41,51,52)(47,53,54);(1,2,5)(3,7,14)(4,6,15)(8,21,18)(9,19,23)(10,20,24)(11,17,25)(12,16,13)(22,27,26)(28,30,35)(29,33,41)(31,37,45)(32,39,47)(34,43,51)(36,46,38)(40,49,53)(42,52,44)(48,54,50)
Conjugacy classes & character table
396 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((2,13,16,5,6,15)(3,8)(4,12)(7,26,19,18,17,24)(9,10)(11,22)(14,20,25,21,23,27)(30,35)(33,41)(36,46)(37,45)(39,47)(42,52)(43,51)(48,54)(49,53), (1,11,22,4,9,8,12,3,10)(2,17,27,6,19,21,16,7,20)(5,25,26,15,23,18,13,14,24)(28,34,50,31,44,32,38,29,40)(30,43,48,37,42,39,36,33,49)(35,51,54,45,52,47,46,41,53)(55,56), (30,36,37)(33,42,43)(35,45,46)(39,48,49)(41,51,52)(47,53,54), (1,2,5)(3,7,14)(4,6,15)(8,21,18)(9,19,23)(10,20,24)(11,17,25)(12,16,13)(22,27,26)(28,30,35)(29,33,41)(31,37,45)(32,39,47)(34,43,51)(36,46,38)(40,49,53)(42,52,44)(48,54,50));
Finite Group Databasebeta