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D2888 #72210715
Aliases
Splittings
Subgroups
33 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 2 generators on 369 points:
(1,2,3,4,5,6,7,8)(9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,172,173,174,175,176,177,178,179,180,181,182,183,184,185,186,187,188,189,190,191,192,193,194,195,196,197,198,199,200,201,202,203,204,205,206,207,208,209,210,211,212,213,214,215,216,217,218,219,220,221,222,223,224,225,226,227,228,229,230,231,232,233,234,235,236,237,238,239,240,241,242,243,244,245,246,247,248,249,250,251,252,253,254,255,256,257,258,259,260,261,262,263,264,265,266,267,268,269,270,271,272,273,274,275,276,277,278,279,280,281,282,283,284,285,286,287,288,289,290,291,292,293,294,295,296,297,298,299,300,301,302,303,304,305,306,307,308,309,310,311,312,313,314,315,316,317,318,319,320,321,322,323,324,325,326,327,328,329,330,331,332,333,334,335,336,337,338,339,340,341,342,343,344,345,346,347,348,349,350,351,352,353,354,355,356,357,358,359,360,361,362,363,364,365,366,367,368,369);(2,8)(3,7)(4,6)(10,369)(11,368)(12,367)(13,366)(14,365)(15,364)(16,363)(17,362)(18,361)(19,360)(20,359)(21,358)(22,357)(23,356)(24,355)(25,354)(26,353)(27,352)(28,351)(29,350)(30,349)(31,348)(32,347)(33,346)(34,345)(35,344)(36,343)(37,342)(38,341)(39,340)(40,339)(41,338)(42,337)(43,336)(44,335)(45,334)(46,333)(47,332)(48,331)(49,330)(50,329)(51,328)(52,327)(53,326)(54,325)(55,324)(56,323)(57,322)(58,321)(59,320)(60,319)(61,318)(62,317)(63,316)(64,315)(65,314)(66,313)(67,312)(68,311)(69,310)(70,309)(71,308)(72,307)(73,306)(74,305)(75,304)(76,303)(77,302)(78,301)(79,300)(80,299)(81,298)(82,297)(83,296)(84,295)(85,294)(86,293)(87,292)(88,291)(89,290)(90,289)(91,288)(92,287)(93,286)(94,285)(95,284)(96,283)(97,282)(98,281)(99,280)(100,279)(101,278)(102,277)(103,276)(104,275)(105,274)(106,273)(107,272)(108,271)(109,270)(110,269)(111,268)(112,267)(113,266)(114,265)(115,264)(116,263)(117,262)(118,261)(119,260)(120,259)(121,258)(122,257)(123,256)(124,255)(125,254)(126,253)(127,252)(128,251)(129,250)(130,249)(131,248)(132,247)(133,246)(134,245)(135,244)(136,243)(137,242)(138,241)(139,240)(140,239)(141,238)(142,237)(143,236)(144,235)(145,234)(146,233)(147,232)(148,231)(149,230)(150,229)(151,228)(152,227)(153,226)(154,225)(155,224)(156,223)(157,222)(158,221)(159,220)(160,219)(161,218)(162,217)(163,216)(164,215)(165,214)(166,213)(167,212)(168,211)(169,210)(170,209)(171,208)(172,207)(173,206)(174,205)(175,204)(176,203)(177,202)(178,201)(179,200)(180,199)(181,198)(182,197)(183,196)(184,195)(185,194)(186,193)(187,192)(188,191)(189,190)
Polycyclic presentation:
2^4,19^2|b^2=cd,c^2=d,e^19=f,b^a=bc,c^a=cd,e^a=e^18f^18,f^a=f^18
Conjugacy classes & character table
1447 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", "f");;
gap> coll := SingleCollector(F, [2, 2, 2, 2, 19, 19]);;
gap> SetPower(coll, 2, F.3*F.4);;
gap> SetPower(coll, 3, F.4);;
gap> SetPower(coll, 5, F.6);;
gap> SetConjugate(coll, 2, 1, F.2*F.3);;
gap> SetConjugate(coll, 3, 1, F.3*F.4);;
gap> SetConjugate(coll, 5, 1, F.5^18*F.6^18);;
gap> SetConjugate(coll, 6, 1, F.6^18);;
gap> UpdatePolycyclicCollector(coll);;
gap> G := GroupByRws(coll);
Finite Group Databasebeta