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Dic₁₄₂₉₇ #72290886

• metacyclic
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Splittings

Subgroups

18 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 2 generators on 862 points:

(1,2)(3,4)(5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21)(22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,172,173,174,175,176,177,178,179,180,181,182,183,184,185,186,187,188,189,190,191,192,193,194,195,196,197,198,199,200,201,202,203,204,205,206,207,208,209,210,211,212,213,214,215,216,217,218,219,220,221,222,223,224,225,226,227,228,229,230,231,232,233,234,235,236,237,238,239,240,241,242,243,244,245,246,247,248,249,250,251,252,253,254,255,256,257,258,259,260,261,262,263,264,265,266,267,268,269,270,271,272,273,274,275,276,277,278,279,280,281,282,283,284,285,286,287,288,289,290,291,292,293,294,295,296,297,298,299,300,301,302,303,304,305,306,307,308,309,310,311,312,313,314,315,316,317,318,319,320,321,322,323,324,325,326,327,328,329,330,331,332,333,334,335,336,337,338,339,340,341,342,343,344,345,346,347,348,349,350,351,352,353,354,355,356,357,358,359,360,361,362,363,364,365,366,367,368,369,370,371,372,373,374,375,376,377,378,379,380,381,382,383,384,385,386,387,388,389,390,391,392,393,394,395,396,397,398,399,400,401,402,403,404,405,406,407,408,409,410,411,412,413,414,415,416,417,418,419,420,421,422,423,424,425,426,427,428,429,430,431,432,433,434,435,436,437,438,439,440,441,442,443,444,445,446,447,448,449,450,451,452,453,454,455,456,457,458,459,460,461,462,463,464,465,466,467,468,469,470,471,472,473,474,475,476,477,478,479,480,481,482,483,484,485,486,487,488,489,490,491,492,493,494,495,496,497,498,499,500,501,502,503,504,505,506,507,508,509,510,511,512,513,514,515,516,517,518,519,520,521,522,523,524,525,526,527,528,529,530,531,532,533,534,535,536,537,538,539,540,541,542,543,544,545,546,547,548,549,550,551,552,553,554,555,556,557,558,559,560,561,562,563,564,565,566,567,568,569,570,571,572,573,574,575,576,577,578,579,580,581,582,583,584,585,586,587,588,589,590,591,592,593,594,595,596,597,598,599,600,601,602,603,604,605,606,607,608,609,610,611,612,613,614,615,616,617,618,619,620,621,622,623,624,625,626,627,628,629,630,631,632,633,634,635,636,637,638,639,640,641,642,643,644,645,646,647,648,649,650,651,652,653,654,655,656,657,658,659,660,661,662,663,664,665,666,667,668,669,670,671,672,673,674,675,676,677,678,679,680,681,682,683,684,685,686,687,688,689,690,691,692,693,694,695,696,697,698,699,700,701,702,703,704,705,706,707,708,709,710,711,712,713,714,715,716,717,718,719,720,721,722,723,724,725,726,727,728,729,730,731,732,733,734,735,736,737,738,739,740,741,742,743,744,745,746,747,748,749,750,751,752,753,754,755,756,757,758,759,760,761,762,763,764,765,766,767,768,769,770,771,772,773,774,775,776,777,778,779,780,781,782,783,784,785,786,787,788,789,790,791,792,793,794,795,796,797,798,799,800,801,802,803,804,805,806,807,808,809,810,811,812,813,814,815,816,817,818,819,820,821,822,823,824,825,826,827,828,829,830,831,832,833,834,835,836,837,838,839,840,841,842,843,844,845,846,847,848,849,850,851,852,853,854,855,856,857,858,859,860,861,862);(1,3,2,4)(6,21)(7,20)(8,19)(9,18)(10,17)(11,16)(12,15)(13,14)(23,862)(24,861)(25,860)(26,859)(27,858)(28,857)(29,856)(30,855)(31,854)(32,853)(33,852)(34,851)(35,850)(36,849)(37,848)(38,847)(39,846)(40,845)(41,844)(42,843)(43,842)(44,841)(45,840)(46,839)(47,838)(48,837)(49,836)(50,835)(51,834)(52,833)(53,832)(54,831)(55,830)(56,829)(57,828)(58,827)(59,826)(60,825)(61,824)(62,823)(63,822)(64,821)(65,820)(66,819)(67,818)(68,817)(69,816)(70,815)(71,814)(72,813)(73,812)(74,811)(75,810)(76,809)(77,808)(78,807)(79,806)(80,805)(81,804)(82,803)(83,802)(84,801)(85,800)(86,799)(87,798)(88,797)(89,796)(90,795)(91,794)(92,793)(93,792)(94,791)(95,790)(96,789)(97,788)(98,787)(99,786)(100,785)(101,784)(102,783)(103,782)(104,781)(105,780)(106,779)(107,778)(108,777)(109,776)(110,775)(111,774)(112,773)(113,772)(114,771)(115,770)(116,769)(117,768)(118,767)(119,766)(120,765)(121,764)(122,763)(123,762)(124,761)(125,760)(126,759)(127,758)(128,757)(129,756)(130,755)(131,754)(132,753)(133,752)(134,751)(135,750)(136,749)(137,748)(138,747)(139,746)(140,745)(141,744)(142,743)(143,742)(144,741)(145,740)(146,739)(147,738)(148,737)(149,736)(150,735)(151,734)(152,733)(153,732)(154,731)(155,730)(156,729)(157,728)(158,727)(159,726)(160,725)(161,724)(162,723)(163,722)(164,721)(165,720)(166,719)(167,718)(168,717)(169,716)(170,715)(171,714)(172,713)(173,712)(174,711)(175,710)(176,709)(177,708)(178,707)(179,706)(180,705)(181,704)(182,703)(183,702)(184,701)(185,700)(186,699)(187,698)(188,697)(189,696)(190,695)(191,694)(192,693)(193,692)(194,691)(195,690)(196,689)(197,688)(198,687)(199,686)(200,685)(201,684)(202,683)(203,682)(204,681)(205,680)(206,679)(207,678)(208,677)(209,676)(210,675)(211,674)(212,673)(213,672)(214,671)(215,670)(216,669)(217,668)(218,667)(219,666)(220,665)(221,664)(222,663)(223,662)(224,661)(225,660)(226,659)(227,658)(228,657)(229,656)(230,655)(231,654)(232,653)(233,652)(234,651)(235,650)(236,649)(237,648)(238,647)(239,646)(240,645)(241,644)(242,643)(243,642)(244,641)(245,640)(246,639)(247,638)(248,637)(249,636)(250,635)(251,634)(252,633)(253,632)(254,631)(255,630)(256,629)(257,628)(258,627)(259,626)(260,625)(261,624)(262,623)(263,622)(264,621)(265,620)(266,619)(267,618)(268,617)(269,616)(270,615)(271,614)(272,613)(273,612)(274,611)(275,610)(276,609)(277,608)(278,607)(279,606)(280,605)(281,604)(282,603)(283,602)(284,601)(285,600)(286,599)(287,598)(288,597)(289,596)(290,595)(291,594)(292,593)(293,592)(294,591)(295,590)(296,589)(297,588)(298,587)(299,586)(300,585)(301,584)(302,583)(303,582)(304,581)(305,580)(306,579)(307,578)(308,577)(309,576)(310,575)(311,574)(312,573)(313,572)(314,571)(315,570)(316,569)(317,568)(318,567)(319,566)(320,565)(321,564)(322,563)(323,562)(324,561)(325,560)(326,559)(327,558)(328,557)(329,556)(330,555)(331,554)(332,553)(333,552)(334,551)(335,550)(336,549)(337,548)(338,547)(339,546)(340,545)(341,544)(342,543)(343,542)(344,541)(345,540)(346,539)(347,538)(348,537)(349,536)(350,535)(351,534)(352,533)(353,532)(354,531)(355,530)(356,529)(357,528)(358,527)(359,526)(360,525)(361,524)(362,523)(363,522)(364,521)(365,520)(366,519)(367,518)(368,517)(369,516)(370,515)(371,514)(372,513)(373,512)(374,511)(375,510)(376,509)(377,508)(378,507)(379,506)(380,505)(381,504)(382,503)(383,502)(384,501)(385,500)(386,499)(387,498)(388,497)(389,496)(390,495)(391,494)(392,493)(393,492)(394,491)(395,490)(396,489)(397,488)(398,487)(399,486)(400,485)(401,484)(402,483)(403,482)(404,481)(405,480)(406,479)(407,478)(408,477)(409,476)(410,475)(411,474)(412,473)(413,472)(414,471)(415,470)(416,469)(417,468)(418,467)(419,466)(420,465)(421,464)(422,463)(423,462)(424,461)(425,460)(426,459)(427,458)(428,457)(429,456)(430,455)(431,454)(432,453)(433,452)(434,451)(435,450)(436,449)(437,448)(438,447)(439,446)(440,445)(441,444)(442,443)

Polycyclic presentation:

2^2,17,29^2|a^2=b,d^29=e,c^a=c^16,d^a=d^28e^28,e^a=e^28

Conjugacy classes & character table

14300 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, 17, 29, 29]);;
gap> SetPower(coll, 1, F.2);;
gap> SetPower(coll, 4, F.5);;
gap> SetConjugate(coll, 3, 1, F.3^16);;
gap> SetConjugate(coll, 4, 1, F.4^28*F.5^28);;
gap> SetConjugate(coll, 5, 1, F.5^28);;
gap> UpdatePolycyclicCollector(coll);;
gap> G := GroupByRws(coll);