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D1444 #72210208
Aliases
Splittings
Subgroups
24 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 2 generators on 365 points:
(1,2,3,4)(5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,172,173,174,175,176,177,178,179,180,181,182,183,184,185,186,187,188,189,190,191,192,193,194,195,196,197,198,199,200,201,202,203,204,205,206,207,208,209,210,211,212,213,214,215,216,217,218,219,220,221,222,223,224,225,226,227,228,229,230,231,232,233,234,235,236,237,238,239,240,241,242,243,244,245,246,247,248,249,250,251,252,253,254,255,256,257,258,259,260,261,262,263,264,265,266,267,268,269,270,271,272,273,274,275,276,277,278,279,280,281,282,283,284,285,286,287,288,289,290,291,292,293,294,295,296,297,298,299,300,301,302,303,304,305,306,307,308,309,310,311,312,313,314,315,316,317,318,319,320,321,322,323,324,325,326,327,328,329,330,331,332,333,334,335,336,337,338,339,340,341,342,343,344,345,346,347,348,349,350,351,352,353,354,355,356,357,358,359,360,361,362,363,364,365);(2,4)(6,365)(7,364)(8,363)(9,362)(10,361)(11,360)(12,359)(13,358)(14,357)(15,356)(16,355)(17,354)(18,353)(19,352)(20,351)(21,350)(22,349)(23,348)(24,347)(25,346)(26,345)(27,344)(28,343)(29,342)(30,341)(31,340)(32,339)(33,338)(34,337)(35,336)(36,335)(37,334)(38,333)(39,332)(40,331)(41,330)(42,329)(43,328)(44,327)(45,326)(46,325)(47,324)(48,323)(49,322)(50,321)(51,320)(52,319)(53,318)(54,317)(55,316)(56,315)(57,314)(58,313)(59,312)(60,311)(61,310)(62,309)(63,308)(64,307)(65,306)(66,305)(67,304)(68,303)(69,302)(70,301)(71,300)(72,299)(73,298)(74,297)(75,296)(76,295)(77,294)(78,293)(79,292)(80,291)(81,290)(82,289)(83,288)(84,287)(85,286)(86,285)(87,284)(88,283)(89,282)(90,281)(91,280)(92,279)(93,278)(94,277)(95,276)(96,275)(97,274)(98,273)(99,272)(100,271)(101,270)(102,269)(103,268)(104,267)(105,266)(106,265)(107,264)(108,263)(109,262)(110,261)(111,260)(112,259)(113,258)(114,257)(115,256)(116,255)(117,254)(118,253)(119,252)(120,251)(121,250)(122,249)(123,248)(124,247)(125,246)(126,245)(127,244)(128,243)(129,242)(130,241)(131,240)(132,239)(133,238)(134,237)(135,236)(136,235)(137,234)(138,233)(139,232)(140,231)(141,230)(142,229)(143,228)(144,227)(145,226)(146,225)(147,224)(148,223)(149,222)(150,221)(151,220)(152,219)(153,218)(154,217)(155,216)(156,215)(157,214)(158,213)(159,212)(160,211)(161,210)(162,209)(163,208)(164,207)(165,206)(166,205)(167,204)(168,203)(169,202)(170,201)(171,200)(172,199)(173,198)(174,197)(175,196)(176,195)(177,194)(178,193)(179,192)(180,191)(181,190)(182,189)(183,188)(184,187)(185,186)
Polycyclic presentation:
2^3,19^2|b^2=c,d^19=e,b^a=bc,d^a=d^18e^18,e^a=e^18
Conjugacy classes & character table
725 conjugacy classes — view the full character table.
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, 19, 19]);;
gap> SetPower(coll, 2, F.3);;
gap> SetPower(coll, 4, F.5);;
gap> SetConjugate(coll, 2, 1, F.2*F.3);;
gap> SetConjugate(coll, 4, 1, F.4^18*F.5^18);;
gap> SetConjugate(coll, 5, 1, F.5^18);;
gap> UpdatePolycyclicCollector(coll);;
gap> G := GroupByRws(coll);
Finite Group Databasebeta