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Dic3370 #72213891
Aliases
Splittings
Subgroups
24 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 2 generators on 350 points:
(1,2,3,4)(5,8,7,6)(9,10,11,12,13)(14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,172,173,174,175,176,177,178,179,180,181,182,183,184,185,186,187,188,189,190,191,192,193,194,195,196,197,198,199,200,201,202,203,204,205,206,207,208,209,210,211,212,213,214,215,216,217,218,219,220,221,222,223,224,225,226,227,228,229,230,231,232,233,234,235,236,237,238,239,240,241,242,243,244,245,246,247,248,249,250,251,252,253,254,255,256,257,258,259,260,261,262,263,264,265,266,267,268,269,270,271,272,273,274,275,276,277,278,279,280,281,282,283,284,285,286,287,288,289,290,291,292,293,294,295,296,297,298,299,300,301,302,303,304,305,306,307,308,309,310,311,312,313,314,315,316,317,318,319,320,321,322,323,324,325,326,327,328,329,330,331,332,333,334,335,336,337,338,339,340,341,342,343,344,345,346,347,348,349,350);(1,5,3,7)(2,6,4,8)(10,13)(11,12)(15,350)(16,349)(17,348)(18,347)(19,346)(20,345)(21,344)(22,343)(23,342)(24,341)(25,340)(26,339)(27,338)(28,337)(29,336)(30,335)(31,334)(32,333)(33,332)(34,331)(35,330)(36,329)(37,328)(38,327)(39,326)(40,325)(41,324)(42,323)(43,322)(44,321)(45,320)(46,319)(47,318)(48,317)(49,316)(50,315)(51,314)(52,313)(53,312)(54,311)(55,310)(56,309)(57,308)(58,307)(59,306)(60,305)(61,304)(62,303)(63,302)(64,301)(65,300)(66,299)(67,298)(68,297)(69,296)(70,295)(71,294)(72,293)(73,292)(74,291)(75,290)(76,289)(77,288)(78,287)(79,286)(80,285)(81,284)(82,283)(83,282)(84,281)(85,280)(86,279)(87,278)(88,277)(89,276)(90,275)(91,274)(92,273)(93,272)(94,271)(95,270)(96,269)(97,268)(98,267)(99,266)(100,265)(101,264)(102,263)(103,262)(104,261)(105,260)(106,259)(107,258)(108,257)(109,256)(110,255)(111,254)(112,253)(113,252)(114,251)(115,250)(116,249)(117,248)(118,247)(119,246)(120,245)(121,244)(122,243)(123,242)(124,241)(125,240)(126,239)(127,238)(128,237)(129,236)(130,235)(131,234)(132,233)(133,232)(134,231)(135,230)(136,229)(137,228)(138,227)(139,226)(140,225)(141,224)(142,223)(143,222)(144,221)(145,220)(146,219)(147,218)(148,217)(149,216)(150,215)(151,214)(152,213)(153,212)(154,211)(155,210)(156,209)(157,208)(158,207)(159,206)(160,205)(161,204)(162,203)(163,202)(164,201)(165,200)(166,199)(167,198)(168,197)(169,196)(170,195)(171,194)(172,193)(173,192)(174,191)(175,190)(176,189)(177,188)(178,187)(179,186)(180,185)(181,184)(182,183)
Polycyclic presentation:
2^3,5,337|a^2=c,b^2=c,b^a=bc,d^a=d^4,e^a=e^336
Conjugacy classes & character table
3373 conjugacy classes. The character table is too large to display.
Relationships
GAP
Past the SmallGroups library coverage — no SmallGroups id. Construct it from its polycyclic presentation:
gap> F := FreeGroup(IsSyllableWordsFamily, "a", "b", "c", "d", "e");;
gap> coll := SingleCollector(F, [2, 2, 2, 5, 337]);;
gap> SetPower(coll, 1, F.3);;
gap> SetPower(coll, 2, F.3);;
gap> SetConjugate(coll, 2, 1, F.2*F.3);;
gap> SetConjugate(coll, 4, 1, F.4^4);;
gap> SetConjugate(coll, 5, 1, F.5^336);;
gap> UpdatePolycyclicCollector(coll);;
gap> G := GroupByRws(coll);
Finite Group Databasebeta