Finite Group Databasebeta

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D₁₃₄₂₄ #41001499

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

Aliases

Splittings

Subgroups

28 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

Polycyclic presentation:

2^5,839|c^2=de,d^2=e,b^a=bc,c^a=cd,d^a=de,f^a=f^838,c^b=cd,d^b=de,f^b=f^838

Conjugacy classes & character table

6715 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26848, 88);