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Aliases
Splittings
Subgroups
142 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 3 generators on 117 points:
(2,8)(3,14)(4,15)(5,20)(6,24)(9,10)(11,36)(12,38)(13,30)(16,46)(17,49)(18,42)(19,27)(21,55)(22,45)(23,28)(25,53)(26,29)(31,51)(32,50)(33,35)(34,57)(37,61)(39,40)(41,47)(43,44)(48,64)(52,59)(54,58)(56,60)(62,63)(65,66,68,70,72,74,76,78,80,82,84,86,88,90,92,94,96,98,100,102,104,106,108,110,112,114,116,117,115,113,111,109,107,105,103,101,99,97,95,93,91,89,87,85,83,81,79,77,75,73,71,69,67);(1,2)(3,8)(4,19)(5,23)(6,26)(7,13)(9,14)(10,15)(11,20)(12,24)(16,36)(17,38)(18,30)(21,54)(22,52)(25,56)(27,40)(28,39)(29,47)(31,46)(32,49)(33,42)(34,55)(35,45)(37,53)(41,57)(43,51)(44,50)(48,61)(58,64)(59,63)(60,62);(66,67)(68,69)(70,71)(72,73)(74,75)(76,77)(78,79)(80,81)(82,83)(84,85)(86,87)(88,89)(90,91)(92,93)(94,95)(96,97)(98,99)(100,101)(102,103)(104,105)(106,107)(108,109)(110,111)(112,113)(114,115)(116,117)
Conjugacy classes & character table
980 conjugacy classes. The character table is too large to display.
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 90609);
Finite Group Databasebeta