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D₂₀₁₀₄ #72274289

• metacyclic
• supersolvable
• metabelian
• solvable
• monomial
• stem

Aliases

Splittings

Subgroups

44 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 2 generators on 374 points:

(1,2,3,4,5,6,7,8)(9,10,11,12,13,14,15)(16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,172,173,174,175,176,177,178,179,180,181,182,183,184,185,186,187,188,189,190,191,192,193,194,195,196,197,198,199,200,201,202,203,204,205,206,207,208,209,210,211,212,213,214,215,216,217,218,219,220,221,222,223,224,225,226,227,228,229,230,231,232,233,234,235,236,237,238,239,240,241,242,243,244,245,246,247,248,249,250,251,252,253,254,255,256,257,258,259,260,261,262,263,264,265,266,267,268,269,270,271,272,273,274,275,276,277,278,279,280,281,282,283,284,285,286,287,288,289,290,291,292,293,294,295,296,297,298,299,300,301,302,303,304,305,306,307,308,309,310,311,312,313,314,315,316,317,318,319,320,321,322,323,324,325,326,327,328,329,330,331,332,333,334,335,336,337,338,339,340,341,342,343,344,345,346,347,348,349,350,351,352,353,354,355,356,357,358,359,360,361,362,363,364,365,366,367,368,369,370,371,372,373,374);(2,8)(3,7)(4,6)(10,15)(11,14)(12,13)(17,374)(18,373)(19,372)(20,371)(21,370)(22,369)(23,368)(24,367)(25,366)(26,365)(27,364)(28,363)(29,362)(30,361)(31,360)(32,359)(33,358)(34,357)(35,356)(36,355)(37,354)(38,353)(39,352)(40,351)(41,350)(42,349)(43,348)(44,347)(45,346)(46,345)(47,344)(48,343)(49,342)(50,341)(51,340)(52,339)(53,338)(54,337)(55,336)(56,335)(57,334)(58,333)(59,332)(60,331)(61,330)(62,329)(63,328)(64,327)(65,326)(66,325)(67,324)(68,323)(69,322)(70,321)(71,320)(72,319)(73,318)(74,317)(75,316)(76,315)(77,314)(78,313)(79,312)(80,311)(81,310)(82,309)(83,308)(84,307)(85,306)(86,305)(87,304)(88,303)(89,302)(90,301)(91,300)(92,299)(93,298)(94,297)(95,296)(96,295)(97,294)(98,293)(99,292)(100,291)(101,290)(102,289)(103,288)(104,287)(105,286)(106,285)(107,284)(108,283)(109,282)(110,281)(111,280)(112,279)(113,278)(114,277)(115,276)(116,275)(117,274)(118,273)(119,272)(120,271)(121,270)(122,269)(123,268)(124,267)(125,266)(126,265)(127,264)(128,263)(129,262)(130,261)(131,260)(132,259)(133,258)(134,257)(135,256)(136,255)(137,254)(138,253)(139,252)(140,251)(141,250)(142,249)(143,248)(144,247)(145,246)(146,245)(147,244)(148,243)(149,242)(150,241)(151,240)(152,239)(153,238)(154,237)(155,236)(156,235)(157,234)(158,233)(159,232)(160,231)(161,230)(162,229)(163,228)(164,227)(165,226)(166,225)(167,224)(168,223)(169,222)(170,221)(171,220)(172,219)(173,218)(174,217)(175,216)(176,215)(177,214)(178,213)(179,212)(180,211)(181,210)(182,209)(183,208)(184,207)(185,206)(186,205)(187,204)(188,203)(189,202)(190,201)(191,200)(192,199)(193,198)(194,197)(195,196)

Polycyclic presentation:

2^4,7,359|b^2=cd,c^2=d,b^a=bc,c^a=cd,e^a=e^6,f^a=f^358

Conjugacy classes & character table

10055 conjugacy classes. The character table is too large to display.

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, 7, 359]);;
gap> SetPower(coll, 2, F.3*F.4);;
gap> SetPower(coll, 3, F.4);;
gap> SetConjugate(coll, 2, 1, F.2*F.3);;
gap> SetConjugate(coll, 3, 1, F.3*F.4);;
gap> SetConjugate(coll, 5, 1, F.5^6);;
gap> SetConjugate(coll, 6, 1, F.6^358);;
gap> UpdatePolycyclicCollector(coll);;
gap> G := GroupByRws(coll);