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D₂₉₀₇₉ #72292664

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

Aliases

Splittings

Subgroups

20 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 2 generators on 440 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)(82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,172,173,174,175,176,177,178,179,180,181,182,183,184,185,186,187,188,189,190,191,192,193,194,195,196,197,198,199,200,201,202,203,204,205,206,207,208,209,210,211,212,213,214,215,216,217,218,219,220,221,222,223,224,225,226,227,228,229,230,231,232,233,234,235,236,237,238,239,240,241,242,243,244,245,246,247,248,249,250,251,252,253,254,255,256,257,258,259,260,261,262,263,264,265,266,267,268,269,270,271,272,273,274,275,276,277,278,279,280,281,282,283,284,285,286,287,288,289,290,291,292,293,294,295,296,297,298,299,300,301,302,303,304,305,306,307,308,309,310,311,312,313,314,315,316,317,318,319,320,321,322,323,324,325,326,327,328,329,330,331,332,333,334,335,336,337,338,339,340,341,342,343,344,345,346,347,348,349,350,351,352,353,354,355,356,357,358,359,360,361,362,363,364,365,366,367,368,369,370,371,372,373,374,375,376,377,378,379,380,381,382,383,384,385,386,387,388,389,390,391,392,393,394,395,396,397,398,399,400,401,402,403,404,405,406,407,408,409,410,411,412,413,414,415,416,417,418,419,420,421,422,423,424,425,426,427,428,429,430,431,432,433,434,435,436,437,438,439,440);(2,81)(3,80)(4,79)(5,78)(6,77)(7,76)(8,75)(9,74)(10,73)(11,72)(12,71)(13,70)(14,69)(15,68)(16,67)(17,66)(18,65)(19,64)(20,63)(21,62)(22,61)(23,60)(24,59)(25,58)(26,57)(27,56)(28,55)(29,54)(30,53)(31,52)(32,51)(33,50)(34,49)(35,48)(36,47)(37,46)(38,45)(39,44)(40,43)(41,42)(83,440)(84,439)(85,438)(86,437)(87,436)(88,435)(89,434)(90,433)(91,432)(92,431)(93,430)(94,429)(95,428)(96,427)(97,426)(98,425)(99,424)(100,423)(101,422)(102,421)(103,420)(104,419)(105,418)(106,417)(107,416)(108,415)(109,414)(110,413)(111,412)(112,411)(113,410)(114,409)(115,408)(116,407)(117,406)(118,405)(119,404)(120,403)(121,402)(122,401)(123,400)(124,399)(125,398)(126,397)(127,396)(128,395)(129,394)(130,393)(131,392)(132,391)(133,390)(134,389)(135,388)(136,387)(137,386)(138,385)(139,384)(140,383)(141,382)(142,381)(143,380)(144,379)(145,378)(146,377)(147,376)(148,375)(149,374)(150,373)(151,372)(152,371)(153,370)(154,369)(155,368)(156,367)(157,366)(158,365)(159,364)(160,363)(161,362)(162,361)(163,360)(164,359)(165,358)(166,357)(167,356)(168,355)(169,354)(170,353)(171,352)(172,351)(173,350)(174,349)(175,348)(176,347)(177,346)(178,345)(179,344)(180,343)(181,342)(182,341)(183,340)(184,339)(185,338)(186,337)(187,336)(188,335)(189,334)(190,333)(191,332)(192,331)(193,330)(194,329)(195,328)(196,327)(197,326)(198,325)(199,324)(200,323)(201,322)(202,321)(203,320)(204,319)(205,318)(206,317)(207,316)(208,315)(209,314)(210,313)(211,312)(212,311)(213,310)(214,309)(215,308)(216,307)(217,306)(218,305)(219,304)(220,303)(221,302)(222,301)(223,300)(224,299)(225,298)(226,297)(227,296)(228,295)(229,294)(230,293)(231,292)(232,291)(233,290)(234,289)(235,288)(236,287)(237,286)(238,285)(239,284)(240,283)(241,282)(242,281)(243,280)(244,279)(245,278)(246,277)(247,276)(248,275)(249,274)(250,273)(251,272)(252,271)(253,270)(254,269)(255,268)(256,267)(257,266)(258,265)(259,264)(260,263)(261,262)

Polycyclic presentation:

2,3,359,3^3|b^3=d,d^3=e,e^3=f,b^a=b^2d^2e^2f^2,c^a=c^358,d^a=d^2e^2f^2,e^a=e^2f^2,f^a=f^2

Conjugacy classes & character table

14541 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, 3, 359, 3, 3, 3]);;
gap> SetPower(coll, 2, F.4);;
gap> SetPower(coll, 4, F.5);;
gap> SetPower(coll, 5, F.6);;
gap> SetConjugate(coll, 2, 1, F.2^2*F.4^2*F.5^2*F.6^2);;
gap> SetConjugate(coll, 3, 1, F.3^358);;
gap> SetConjugate(coll, 4, 1, F.4^2*F.5^2*F.6^2);;
gap> SetConjugate(coll, 5, 1, F.5^2*F.6^2);;
gap> SetConjugate(coll, 6, 1, F.6^2);;
gap> UpdatePolycyclicCollector(coll);;
gap> G := GroupByRws(coll);