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D6740 #72212367
Aliases
Splittings
Subgroups
32 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 2 generators on 346 points:
(1,2,3,4)(5,6,7,8,9)(10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,172,173,174,175,176,177,178,179,180,181,182,183,184,185,186,187,188,189,190,191,192,193,194,195,196,197,198,199,200,201,202,203,204,205,206,207,208,209,210,211,212,213,214,215,216,217,218,219,220,221,222,223,224,225,226,227,228,229,230,231,232,233,234,235,236,237,238,239,240,241,242,243,244,245,246,247,248,249,250,251,252,253,254,255,256,257,258,259,260,261,262,263,264,265,266,267,268,269,270,271,272,273,274,275,276,277,278,279,280,281,282,283,284,285,286,287,288,289,290,291,292,293,294,295,296,297,298,299,300,301,302,303,304,305,306,307,308,309,310,311,312,313,314,315,316,317,318,319,320,321,322,323,324,325,326,327,328,329,330,331,332,333,334,335,336,337,338,339,340,341,342,343,344,345,346);(2,4)(6,9)(7,8)(11,346)(12,345)(13,344)(14,343)(15,342)(16,341)(17,340)(18,339)(19,338)(20,337)(21,336)(22,335)(23,334)(24,333)(25,332)(26,331)(27,330)(28,329)(29,328)(30,327)(31,326)(32,325)(33,324)(34,323)(35,322)(36,321)(37,320)(38,319)(39,318)(40,317)(41,316)(42,315)(43,314)(44,313)(45,312)(46,311)(47,310)(48,309)(49,308)(50,307)(51,306)(52,305)(53,304)(54,303)(55,302)(56,301)(57,300)(58,299)(59,298)(60,297)(61,296)(62,295)(63,294)(64,293)(65,292)(66,291)(67,290)(68,289)(69,288)(70,287)(71,286)(72,285)(73,284)(74,283)(75,282)(76,281)(77,280)(78,279)(79,278)(80,277)(81,276)(82,275)(83,274)(84,273)(85,272)(86,271)(87,270)(88,269)(89,268)(90,267)(91,266)(92,265)(93,264)(94,263)(95,262)(96,261)(97,260)(98,259)(99,258)(100,257)(101,256)(102,255)(103,254)(104,253)(105,252)(106,251)(107,250)(108,249)(109,248)(110,247)(111,246)(112,245)(113,244)(114,243)(115,242)(116,241)(117,240)(118,239)(119,238)(120,237)(121,236)(122,235)(123,234)(124,233)(125,232)(126,231)(127,230)(128,229)(129,228)(130,227)(131,226)(132,225)(133,224)(134,223)(135,222)(136,221)(137,220)(138,219)(139,218)(140,217)(141,216)(142,215)(143,214)(144,213)(145,212)(146,211)(147,210)(148,209)(149,208)(150,207)(151,206)(152,205)(153,204)(154,203)(155,202)(156,201)(157,200)(158,199)(159,198)(160,197)(161,196)(162,195)(163,194)(164,193)(165,192)(166,191)(167,190)(168,189)(169,188)(170,187)(171,186)(172,185)(173,184)(174,183)(175,182)(176,181)(177,180)(178,179)
Polycyclic presentation:
2^3,5,337|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, 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