Finite Group Databasebeta

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D₁₃₁₆₈ #39912030

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

Polycyclic presentation:

2^5,823|c^2=de,d^2=e,b^a=bc,c^a=cd,d^a=de,f^a=f^822,c^b=cd,d^b=de,f^b=f^822

Conjugacy classes & character table

6587 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26336, 88);