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Dic317 #11929637
Aliases
Splittings
Subgroups
6 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 2 generators on 321 points:
(1,2)(3,4)(5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,172,173,174,175,176,177,178,179,180,181,182,183,184,185,186,187,188,189,190,191,192,193,194,195,196,197,198,199,200,201,202,203,204,205,206,207,208,209,210,211,212,213,214,215,216,217,218,219,220,221,222,223,224,225,226,227,228,229,230,231,232,233,234,235,236,237,238,239,240,241,242,243,244,245,246,247,248,249,250,251,252,253,254,255,256,257,258,259,260,261,262,263,264,265,266,267,268,269,270,271,272,273,274,275,276,277,278,279,280,281,282,283,284,285,286,287,288,289,290,291,292,293,294,295,296,297,298,299,300,301,302,303,304,305,306,307,308,309,310,311,312,313,314,315,316,317,318,319,320,321);(1,3,2,4)(6,321)(7,320)(8,319)(9,318)(10,317)(11,316)(12,315)(13,314)(14,313)(15,312)(16,311)(17,310)(18,309)(19,308)(20,307)(21,306)(22,305)(23,304)(24,303)(25,302)(26,301)(27,300)(28,299)(29,298)(30,297)(31,296)(32,295)(33,294)(34,293)(35,292)(36,291)(37,290)(38,289)(39,288)(40,287)(41,286)(42,285)(43,284)(44,283)(45,282)(46,281)(47,280)(48,279)(49,278)(50,277)(51,276)(52,275)(53,274)(54,273)(55,272)(56,271)(57,270)(58,269)(59,268)(60,267)(61,266)(62,265)(63,264)(64,263)(65,262)(66,261)(67,260)(68,259)(69,258)(70,257)(71,256)(72,255)(73,254)(74,253)(75,252)(76,251)(77,250)(78,249)(79,248)(80,247)(81,246)(82,245)(83,244)(84,243)(85,242)(86,241)(87,240)(88,239)(89,238)(90,237)(91,236)(92,235)(93,234)(94,233)(95,232)(96,231)(97,230)(98,229)(99,228)(100,227)(101,226)(102,225)(103,224)(104,223)(105,222)(106,221)(107,220)(108,219)(109,218)(110,217)(111,216)(112,215)(113,214)(114,213)(115,212)(116,211)(117,210)(118,209)(119,208)(120,207)(121,206)(122,205)(123,204)(124,203)(125,202)(126,201)(127,200)(128,199)(129,198)(130,197)(131,196)(132,195)(133,194)(134,193)(135,192)(136,191)(137,190)(138,189)(139,188)(140,187)(141,186)(142,185)(143,184)(144,183)(145,182)(146,181)(147,180)(148,179)(149,178)(150,177)(151,176)(152,175)(153,174)(154,173)(155,172)(156,171)(157,170)(158,169)(159,168)(160,167)(161,166)(162,165)(163,164)
Polycyclic presentation:
2^2,317|a^2=b,c^a=c^316
Conjugacy classes & character table
320 conjugacy classes — view the full character table.
Relationships
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1268, 1);
Finite Group Databasebeta