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Dic₁₄₇₉₄ #72291985

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

Aliases

Splittings

Subgroups

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 2 generators on 590 points:

(1,2,3,4)(5,8,7,6)(9,10,11,12,13,14,15,16,17,18,19,20,21)(22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,172,173,174,175,176,177,178,179,180,181,182,183,184,185,186,187,188,189,190,191,192,193,194,195,196,197,198,199,200,201,202,203,204,205,206,207,208,209,210,211,212,213,214,215,216,217,218,219,220,221,222,223,224,225,226,227,228,229,230,231,232,233,234,235,236,237,238,239,240,241,242,243,244,245,246,247,248,249,250,251,252,253,254,255,256,257,258,259,260,261,262,263,264,265,266,267,268,269,270,271,272,273,274,275,276,277,278,279,280,281,282,283,284,285,286,287,288,289,290,291,292,293,294,295,296,297,298,299,300,301,302,303,304,305,306,307,308,309,310,311,312,313,314,315,316,317,318,319,320,321,322,323,324,325,326,327,328,329,330,331,332,333,334,335,336,337,338,339,340,341,342,343,344,345,346,347,348,349,350,351,352,353,354,355,356,357,358,359,360,361,362,363,364,365,366,367,368,369,370,371,372,373,374,375,376,377,378,379,380,381,382,383,384,385,386,387,388,389,390,391,392,393,394,395,396,397,398,399,400,401,402,403,404,405,406,407,408,409,410,411,412,413,414,415,416,417,418,419,420,421,422,423,424,425,426,427,428,429,430,431,432,433,434,435,436,437,438,439,440,441,442,443,444,445,446,447,448,449,450,451,452,453,454,455,456,457,458,459,460,461,462,463,464,465,466,467,468,469,470,471,472,473,474,475,476,477,478,479,480,481,482,483,484,485,486,487,488,489,490,491,492,493,494,495,496,497,498,499,500,501,502,503,504,505,506,507,508,509,510,511,512,513,514,515,516,517,518,519,520,521,522,523,524,525,526,527,528,529,530,531,532,533,534,535,536,537,538,539,540,541,542,543,544,545,546,547,548,549,550,551,552,553,554,555,556,557,558,559,560,561,562,563,564,565,566,567,568,569,570,571,572,573,574,575,576,577,578,579,580,581,582,583,584,585,586,587,588,589,590);(1,5,3,7)(2,6,4,8)(10,21)(11,20)(12,19)(13,18)(14,17)(15,16)(23,590)(24,589)(25,588)(26,587)(27,586)(28,585)(29,584)(30,583)(31,582)(32,581)(33,580)(34,579)(35,578)(36,577)(37,576)(38,575)(39,574)(40,573)(41,572)(42,571)(43,570)(44,569)(45,568)(46,567)(47,566)(48,565)(49,564)(50,563)(51,562)(52,561)(53,560)(54,559)(55,558)(56,557)(57,556)(58,555)(59,554)(60,553)(61,552)(62,551)(63,550)(64,549)(65,548)(66,547)(67,546)(68,545)(69,544)(70,543)(71,542)(72,541)(73,540)(74,539)(75,538)(76,537)(77,536)(78,535)(79,534)(80,533)(81,532)(82,531)(83,530)(84,529)(85,528)(86,527)(87,526)(88,525)(89,524)(90,523)(91,522)(92,521)(93,520)(94,519)(95,518)(96,517)(97,516)(98,515)(99,514)(100,513)(101,512)(102,511)(103,510)(104,509)(105,508)(106,507)(107,506)(108,505)(109,504)(110,503)(111,502)(112,501)(113,500)(114,499)(115,498)(116,497)(117,496)(118,495)(119,494)(120,493)(121,492)(122,491)(123,490)(124,489)(125,488)(126,487)(127,486)(128,485)(129,484)(130,483)(131,482)(132,481)(133,480)(134,479)(135,478)(136,477)(137,476)(138,475)(139,474)(140,473)(141,472)(142,471)(143,470)(144,469)(145,468)(146,467)(147,466)(148,465)(149,464)(150,463)(151,462)(152,461)(153,460)(154,459)(155,458)(156,457)(157,456)(158,455)(159,454)(160,453)(161,452)(162,451)(163,450)(164,449)(165,448)(166,447)(167,446)(168,445)(169,444)(170,443)(171,442)(172,441)(173,440)(174,439)(175,438)(176,437)(177,436)(178,435)(179,434)(180,433)(181,432)(182,431)(183,430)(184,429)(185,428)(186,427)(187,426)(188,425)(189,424)(190,423)(191,422)(192,421)(193,420)(194,419)(195,418)(196,417)(197,416)(198,415)(199,414)(200,413)(201,412)(202,411)(203,410)(204,409)(205,408)(206,407)(207,406)(208,405)(209,404)(210,403)(211,402)(212,401)(213,400)(214,399)(215,398)(216,397)(217,396)(218,395)(219,394)(220,393)(221,392)(222,391)(223,390)(224,389)(225,388)(226,387)(227,386)(228,385)(229,384)(230,383)(231,382)(232,381)(233,380)(234,379)(235,378)(236,377)(237,376)(238,375)(239,374)(240,373)(241,372)(242,371)(243,370)(244,369)(245,368)(246,367)(247,366)(248,365)(249,364)(250,363)(251,362)(252,361)(253,360)(254,359)(255,358)(256,357)(257,356)(258,355)(259,354)(260,353)(261,352)(262,351)(263,350)(264,349)(265,348)(266,347)(267,346)(268,345)(269,344)(270,343)(271,342)(272,341)(273,340)(274,339)(275,338)(276,337)(277,336)(278,335)(279,334)(280,333)(281,332)(282,331)(283,330)(284,329)(285,328)(286,327)(287,326)(288,325)(289,324)(290,323)(291,322)(292,321)(293,320)(294,319)(295,318)(296,317)(297,316)(298,315)(299,314)(300,313)(301,312)(302,311)(303,310)(304,309)(305,308)(306,307)

Polycyclic presentation:

2^3,13,569|a^2=c,b^2=c,b^a=bc,d^a=d^12,e^a=e^568

Conjugacy classes & character table

14797 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");;
gap> coll := SingleCollector(F, [2, 2, 2, 13, 569]);;
gap> SetPower(coll, 1, F.3);;
gap> SetPower(coll, 2, F.3);;
gap> SetConjugate(coll, 2, 1, F.2*F.3);;
gap> SetConjugate(coll, 4, 1, F.4^12);;
gap> SetConjugate(coll, 5, 1, F.5^568);;
gap> UpdatePolycyclicCollector(coll);;
gap> G := GroupByRws(coll);