Finite Group Databasebeta

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D₁₄₀₉₆ #43245447

• 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 897 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16)(17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,172,173,174,175,176,177,178,179,180,181,182,183,184,185,186,187,188,189,190,191,192,193,194,195,196,197,198,199,200,201,202,203,204,205,206,207,208,209,210,211,212,213,214,215,216,217,218,219,220,221,222,223,224,225,226,227,228,229,230,231,232,233,234,235,236,237,238,239,240,241,242,243,244,245,246,247,248,249,250,251,252,253,254,255,256,257,258,259,260,261,262,263,264,265,266,267,268,269,270,271,272,273,274,275,276,277,278,279,280,281,282,283,284,285,286,287,288,289,290,291,292,293,294,295,296,297,298,299,300,301,302,303,304,305,306,307,308,309,310,311,312,313,314,315,316,317,318,319,320,321,322,323,324,325,326,327,328,329,330,331,332,333,334,335,336,337,338,339,340,341,342,343,344,345,346,347,348,349,350,351,352,353,354,355,356,357,358,359,360,361,362,363,364,365,366,367,368,369,370,371,372,373,374,375,376,377,378,379,380,381,382,383,384,385,386,387,388,389,390,391,392,393,394,395,396,397,398,399,400,401,402,403,404,405,406,407,408,409,410,411,412,413,414,415,416,417,418,419,420,421,422,423,424,425,426,427,428,429,430,431,432,433,434,435,436,437,438,439,440,441,442,443,444,445,446,447,448,449,450,451,452,453,454,455,456,457,458,459,460,461,462,463,464,465,466,467,468,469,470,471,472,473,474,475,476,477,478,479,480,481,482,483,484,485,486,487,488,489,490,491,492,493,494,495,496,497,498,499,500,501,502,503,504,505,506,507,508,509,510,511,512,513,514,515,516,517,518,519,520,521,522,523,524,525,526,527,528,529,530,531,532,533,534,535,536,537,538,539,540,541,542,543,544,545,546,547,548,549,550,551,552,553,554,555,556,557,558,559,560,561,562,563,564,565,566,567,568,569,570,571,572,573,574,575,576,577,578,579,580,581,582,583,584,585,586,587,588,589,590,591,592,593,594,595,596,597,598,599,600,601,602,603,604,605,606,607,608,609,610,611,612,613,614,615,616,617,618,619,620,621,622,623,624,625,626,627,628,629,630,631,632,633,634,635,636,637,638,639,640,641,642,643,644,645,646,647,648,649,650,651,652,653,654,655,656,657,658,659,660,661,662,663,664,665,666,667,668,669,670,671,672,673,674,675,676,677,678,679,680,681,682,683,684,685,686,687,688,689,690,691,692,693,694,695,696,697,698,699,700,701,702,703,704,705,706,707,708,709,710,711,712,713,714,715,716,717,718,719,720,721,722,723,724,725,726,727,728,729,730,731,732,733,734,735,736,737,738,739,740,741,742,743,744,745,746,747,748,749,750,751,752,753,754,755,756,757,758,759,760,761,762,763,764,765,766,767,768,769,770,771,772,773,774,775,776,777,778,779,780,781,782,783,784,785,786,787,788,789,790,791,792,793,794,795,796,797,798,799,800,801,802,803,804,805,806,807,808,809,810,811,812,813,814,815,816,817,818,819,820,821,822,823,824,825,826,827,828,829,830,831,832,833,834,835,836,837,838,839,840,841,842,843,844,845,846,847,848,849,850,851,852,853,854,855,856,857,858,859,860,861,862,863,864,865,866,867,868,869,870,871,872,873,874,875,876,877,878,879,880,881,882,883,884,885,886,887,888,889,890,891,892,893,894,895,896,897);(2,16)(3,15)(4,14)(5,13)(6,12)(7,11)(8,10)(18,897)(19,896)(20,895)(21,894)(22,893)(23,892)(24,891)(25,890)(26,889)(27,888)(28,887)(29,886)(30,885)(31,884)(32,883)(33,882)(34,881)(35,880)(36,879)(37,878)(38,877)(39,876)(40,875)(41,874)(42,873)(43,872)(44,871)(45,870)(46,869)(47,868)(48,867)(49,866)(50,865)(51,864)(52,863)(53,862)(54,861)(55,860)(56,859)(57,858)(58,857)(59,856)(60,855)(61,854)(62,853)(63,852)(64,851)(65,850)(66,849)(67,848)(68,847)(69,846)(70,845)(71,844)(72,843)(73,842)(74,841)(75,840)(76,839)(77,838)(78,837)(79,836)(80,835)(81,834)(82,833)(83,832)(84,831)(85,830)(86,829)(87,828)(88,827)(89,826)(90,825)(91,824)(92,823)(93,822)(94,821)(95,820)(96,819)(97,818)(98,817)(99,816)(100,815)(101,814)(102,813)(103,812)(104,811)(105,810)(106,809)(107,808)(108,807)(109,806)(110,805)(111,804)(112,803)(113,802)(114,801)(115,800)(116,799)(117,798)(118,797)(119,796)(120,795)(121,794)(122,793)(123,792)(124,791)(125,790)(126,789)(127,788)(128,787)(129,786)(130,785)(131,784)(132,783)(133,782)(134,781)(135,780)(136,779)(137,778)(138,777)(139,776)(140,775)(141,774)(142,773)(143,772)(144,771)(145,770)(146,769)(147,768)(148,767)(149,766)(150,765)(151,764)(152,763)(153,762)(154,761)(155,760)(156,759)(157,758)(158,757)(159,756)(160,755)(161,754)(162,753)(163,752)(164,751)(165,750)(166,749)(167,748)(168,747)(169,746)(170,745)(171,744)(172,743)(173,742)(174,741)(175,740)(176,739)(177,738)(178,737)(179,736)(180,735)(181,734)(182,733)(183,732)(184,731)(185,730)(186,729)(187,728)(188,727)(189,726)(190,725)(191,724)(192,723)(193,722)(194,721)(195,720)(196,719)(197,718)(198,717)(199,716)(200,715)(201,714)(202,713)(203,712)(204,711)(205,710)(206,709)(207,708)(208,707)(209,706)(210,705)(211,704)(212,703)(213,702)(214,701)(215,700)(216,699)(217,698)(218,697)(219,696)(220,695)(221,694)(222,693)(223,692)(224,691)(225,690)(226,689)(227,688)(228,687)(229,686)(230,685)(231,684)(232,683)(233,682)(234,681)(235,680)(236,679)(237,678)(238,677)(239,676)(240,675)(241,674)(242,673)(243,672)(244,671)(245,670)(246,669)(247,668)(248,667)(249,666)(250,665)(251,664)(252,663)(253,662)(254,661)(255,660)(256,659)(257,658)(258,657)(259,656)(260,655)(261,654)(262,653)(263,652)(264,651)(265,650)(266,649)(267,648)(268,647)(269,646)(270,645)(271,644)(272,643)(273,642)(274,641)(275,640)(276,639)(277,638)(278,637)(279,636)(280,635)(281,634)(282,633)(283,632)(284,631)(285,630)(286,629)(287,628)(288,627)(289,626)(290,625)(291,624)(292,623)(293,622)(294,621)(295,620)(296,619)(297,618)(298,617)(299,616)(300,615)(301,614)(302,613)(303,612)(304,611)(305,610)(306,609)(307,608)(308,607)(309,606)(310,605)(311,604)(312,603)(313,602)(314,601)(315,600)(316,599)(317,598)(318,597)(319,596)(320,595)(321,594)(322,593)(323,592)(324,591)(325,590)(326,589)(327,588)(328,587)(329,586)(330,585)(331,584)(332,583)(333,582)(334,581)(335,580)(336,579)(337,578)(338,577)(339,576)(340,575)(341,574)(342,573)(343,572)(344,571)(345,570)(346,569)(347,568)(348,567)(349,566)(350,565)(351,564)(352,563)(353,562)(354,561)(355,560)(356,559)(357,558)(358,557)(359,556)(360,555)(361,554)(362,553)(363,552)(364,551)(365,550)(366,549)(367,548)(368,547)(369,546)(370,545)(371,544)(372,543)(373,542)(374,541)(375,540)(376,539)(377,538)(378,537)(379,536)(380,535)(381,534)(382,533)(383,532)(384,531)(385,530)(386,529)(387,528)(388,527)(389,526)(390,525)(391,524)(392,523)(393,522)(394,521)(395,520)(396,519)(397,518)(398,517)(399,516)(400,515)(401,514)(402,513)(403,512)(404,511)(405,510)(406,509)(407,508)(408,507)(409,506)(410,505)(411,504)(412,503)(413,502)(414,501)(415,500)(416,499)(417,498)(418,497)(419,496)(420,495)(421,494)(422,493)(423,492)(424,491)(425,490)(426,489)(427,488)(428,487)(429,486)(430,485)(431,484)(432,483)(433,482)(434,481)(435,480)(436,479)(437,478)(438,477)(439,476)(440,475)(441,474)(442,473)(443,472)(444,471)(445,470)(446,469)(447,468)(448,467)(449,466)(450,465)(451,464)(452,463)(453,462)(454,461)(455,460)(456,459)(457,458)

Polycyclic presentation:

2^5,881|c^2=de,d^2=e,b^a=bc,c^a=cd,d^a=de,f^a=f^880,c^b=cd,d^b=de,f^b=f^880

Conjugacy classes & character table

7051 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(28192, 88);