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Dic3341 #27211359
Aliases
Splittings
Subgroups
12 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 2 generators on 274 points:
(1,2)(3,4)(5,6,7,8,9,10,11,12,13,14,15,16,17)(18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,172,173,174,175,176,177,178,179,180,181,182,183,184,185,186,187,188,189,190,191,192,193,194,195,196,197,198,199,200,201,202,203,204,205,206,207,208,209,210,211,212,213,214,215,216,217,218,219,220,221,222,223,224,225,226,227,228,229,230,231,232,233,234,235,236,237,238,239,240,241,242,243,244,245,246,247,248,249,250,251,252,253,254,255,256,257,258,259,260,261,262,263,264,265,266,267,268,269,270,271,272,273,274);(1,3,2,4)(6,17)(7,16)(8,15)(9,14)(10,13)(11,12)(19,274)(20,273)(21,272)(22,271)(23,270)(24,269)(25,268)(26,267)(27,266)(28,265)(29,264)(30,263)(31,262)(32,261)(33,260)(34,259)(35,258)(36,257)(37,256)(38,255)(39,254)(40,253)(41,252)(42,251)(43,250)(44,249)(45,248)(46,247)(47,246)(48,245)(49,244)(50,243)(51,242)(52,241)(53,240)(54,239)(55,238)(56,237)(57,236)(58,235)(59,234)(60,233)(61,232)(62,231)(63,230)(64,229)(65,228)(66,227)(67,226)(68,225)(69,224)(70,223)(71,222)(72,221)(73,220)(74,219)(75,218)(76,217)(77,216)(78,215)(79,214)(80,213)(81,212)(82,211)(83,210)(84,209)(85,208)(86,207)(87,206)(88,205)(89,204)(90,203)(91,202)(92,201)(93,200)(94,199)(95,198)(96,197)(97,196)(98,195)(99,194)(100,193)(101,192)(102,191)(103,190)(104,189)(105,188)(106,187)(107,186)(108,185)(109,184)(110,183)(111,182)(112,181)(113,180)(114,179)(115,178)(116,177)(117,176)(118,175)(119,174)(120,173)(121,172)(122,171)(123,170)(124,169)(125,168)(126,167)(127,166)(128,165)(129,164)(130,163)(131,162)(132,161)(133,160)(134,159)(135,158)(136,157)(137,156)(138,155)(139,154)(140,153)(141,152)(142,151)(143,150)(144,149)(145,148)(146,147)
Polycyclic presentation:
2,13,257,2|a^2=d,b^a=b^12,c^a=c^256
Conjugacy classes & character table
3344 conjugacy classes. The character table is too large to display.
Relationships
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13364, 4);
Finite Group Databasebeta