Finite Group Databasebeta

?

← Prev (#44569338) Next (#44569340) →

D₁₆₂₀₁ #44569339

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

Aliases

Splittings

Subgroups

8 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 2 generators on 970 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,172,173,174,175,176,177,178,179,180,181,182,183,184,185,186,187,188,189,190,191,192,193,194,195,196,197,198,199,200,201,202,203,204,205,206,207,208,209,210,211,212,213,214,215,216,217,218,219,220,221,222,223,224,225,226,227,228,229,230,231,232,233,234,235,236,237,238,239,240,241,242,243,244,245,246,247,248,249,250,251,252,253,254,255,256,257,258,259,260,261,262,263,264,265,266,267,268,269,270,271,272,273,274,275,276,277,278,279,280,281,282,283,284,285,286,287,288,289,290,291,292,293,294,295,296,297,298,299,300,301,302,303,304,305,306,307,308,309,310,311,312,313,314,315,316,317,318,319,320,321,322,323,324,325,326,327,328,329,330,331,332,333,334,335,336,337,338,339,340,341,342,343,344,345,346,347,348,349,350,351,352,353,354,355,356,357,358,359,360,361,362,363,364,365,366,367,368,369,370,371,372,373,374,375,376,377,378,379,380,381,382,383,384,385,386,387,388,389,390,391,392,393,394,395,396,397,398,399,400,401,402,403,404,405,406,407,408,409,410,411,412,413,414,415,416,417,418,419,420,421,422,423,424,425,426,427,428,429,430,431,432,433,434,435,436,437,438,439,440,441,442,443,444,445,446,447,448,449,450,451,452,453,454,455,456,457,458,459,460,461,462,463,464,465,466,467,468,469,470,471,472,473,474,475,476,477,478,479,480,481,482,483,484,485,486,487,488,489,490,491,492,493,494,495,496,497,498,499,500,501,502,503,504,505,506,507,508,509,510,511,512,513,514,515,516,517,518,519,520,521,522,523,524,525,526,527,528,529,530,531,532,533,534,535,536,537,538,539,540,541,542,543,544,545,546,547,548,549,550,551,552,553,554,555,556,557,558,559,560,561,562,563,564,565,566,567,568,569,570,571,572,573,574,575,576,577,578,579,580,581,582,583,584,585,586,587,588,589,590,591,592,593,594,595,596,597,598,599,600,601,602,603,604,605,606,607,608,609,610,611,612,613,614,615,616,617,618,619,620,621,622,623,624,625,626,627,628,629,630,631,632,633,634,635,636,637,638,639,640,641,642,643,644,645,646,647,648,649,650,651,652,653,654,655,656,657,658,659,660,661,662,663,664,665,666,667,668,669,670,671,672,673,674,675,676,677,678,679,680,681,682,683,684,685,686,687,688,689,690,691,692,693,694,695,696,697,698,699,700,701,702,703,704,705,706,707,708,709,710,711,712,713,714,715,716,717,718,719,720,721,722,723,724,725,726,727,728,729,730,731,732,733,734,735,736,737,738,739,740,741,742,743,744,745,746,747,748,749,750,751,752,753,754,755,756,757,758,759,760,761,762,763,764,765,766,767,768,769,770,771,772,773,774,775,776,777,778,779,780,781,782,783,784,785,786,787,788,789,790,791,792,793,794,795,796,797,798,799,800,801,802,803,804,805,806,807,808,809,810,811,812,813,814,815,816,817,818,819,820,821,822,823,824,825,826,827,828,829,830,831,832,833,834,835,836,837,838,839,840,841,842,843,844,845,846,847,848,849,850,851,852,853,854,855,856,857,858,859,860,861,862,863,864,865,866,867,868,869,870,871,872,873,874,875,876,877,878,879,880,881,882,883,884,885,886,887,888,889,890,891,892,893,894,895,896,897,898,899,900,901,902,903,904,905,906,907,908,909,910,911,912,913,914,915,916,917,918,919,920,921,922,923,924,925,926,927,928,929,930,931,932,933,934,935,936,937,938,939,940,941,942,943,944,945,946,947,948,949,950,951,952,953,954,955,956,957,958,959,960,961,962,963,964,965,966,967,968,969,970);(2,17)(3,16)(4,15)(5,14)(6,13)(7,12)(8,11)(9,10)(19,970)(20,969)(21,968)(22,967)(23,966)(24,965)(25,964)(26,963)(27,962)(28,961)(29,960)(30,959)(31,958)(32,957)(33,956)(34,955)(35,954)(36,953)(37,952)(38,951)(39,950)(40,949)(41,948)(42,947)(43,946)(44,945)(45,944)(46,943)(47,942)(48,941)(49,940)(50,939)(51,938)(52,937)(53,936)(54,935)(55,934)(56,933)(57,932)(58,931)(59,930)(60,929)(61,928)(62,927)(63,926)(64,925)(65,924)(66,923)(67,922)(68,921)(69,920)(70,919)(71,918)(72,917)(73,916)(74,915)(75,914)(76,913)(77,912)(78,911)(79,910)(80,909)(81,908)(82,907)(83,906)(84,905)(85,904)(86,903)(87,902)(88,901)(89,900)(90,899)(91,898)(92,897)(93,896)(94,895)(95,894)(96,893)(97,892)(98,891)(99,890)(100,889)(101,888)(102,887)(103,886)(104,885)(105,884)(106,883)(107,882)(108,881)(109,880)(110,879)(111,878)(112,877)(113,876)(114,875)(115,874)(116,873)(117,872)(118,871)(119,870)(120,869)(121,868)(122,867)(123,866)(124,865)(125,864)(126,863)(127,862)(128,861)(129,860)(130,859)(131,858)(132,857)(133,856)(134,855)(135,854)(136,853)(137,852)(138,851)(139,850)(140,849)(141,848)(142,847)(143,846)(144,845)(145,844)(146,843)(147,842)(148,841)(149,840)(150,839)(151,838)(152,837)(153,836)(154,835)(155,834)(156,833)(157,832)(158,831)(159,830)(160,829)(161,828)(162,827)(163,826)(164,825)(165,824)(166,823)(167,822)(168,821)(169,820)(170,819)(171,818)(172,817)(173,816)(174,815)(175,814)(176,813)(177,812)(178,811)(179,810)(180,809)(181,808)(182,807)(183,806)(184,805)(185,804)(186,803)(187,802)(188,801)(189,800)(190,799)(191,798)(192,797)(193,796)(194,795)(195,794)(196,793)(197,792)(198,791)(199,790)(200,789)(201,788)(202,787)(203,786)(204,785)(205,784)(206,783)(207,782)(208,781)(209,780)(210,779)(211,778)(212,777)(213,776)(214,775)(215,774)(216,773)(217,772)(218,771)(219,770)(220,769)(221,768)(222,767)(223,766)(224,765)(225,764)(226,763)(227,762)(228,761)(229,760)(230,759)(231,758)(232,757)(233,756)(234,755)(235,754)(236,753)(237,752)(238,751)(239,750)(240,749)(241,748)(242,747)(243,746)(244,745)(245,744)(246,743)(247,742)(248,741)(249,740)(250,739)(251,738)(252,737)(253,736)(254,735)(255,734)(256,733)(257,732)(258,731)(259,730)(260,729)(261,728)(262,727)(263,726)(264,725)(265,724)(266,723)(267,722)(268,721)(269,720)(270,719)(271,718)(272,717)(273,716)(274,715)(275,714)(276,713)(277,712)(278,711)(279,710)(280,709)(281,708)(282,707)(283,706)(284,705)(285,704)(286,703)(287,702)(288,701)(289,700)(290,699)(291,698)(292,697)(293,696)(294,695)(295,694)(296,693)(297,692)(298,691)(299,690)(300,689)(301,688)(302,687)(303,686)(304,685)(305,684)(306,683)(307,682)(308,681)(309,680)(310,679)(311,678)(312,677)(313,676)(314,675)(315,674)(316,673)(317,672)(318,671)(319,670)(320,669)(321,668)(322,667)(323,666)(324,665)(325,664)(326,663)(327,662)(328,661)(329,660)(330,659)(331,658)(332,657)(333,656)(334,655)(335,654)(336,653)(337,652)(338,651)(339,650)(340,649)(341,648)(342,647)(343,646)(344,645)(345,644)(346,643)(347,642)(348,641)(349,640)(350,639)(351,638)(352,637)(353,636)(354,635)(355,634)(356,633)(357,632)(358,631)(359,630)(360,629)(361,628)(362,627)(363,626)(364,625)(365,624)(366,623)(367,622)(368,621)(369,620)(370,619)(371,618)(372,617)(373,616)(374,615)(375,614)(376,613)(377,612)(378,611)(379,610)(380,609)(381,608)(382,607)(383,606)(384,605)(385,604)(386,603)(387,602)(388,601)(389,600)(390,599)(391,598)(392,597)(393,596)(394,595)(395,594)(396,593)(397,592)(398,591)(399,590)(400,589)(401,588)(402,587)(403,586)(404,585)(405,584)(406,583)(407,582)(408,581)(409,580)(410,579)(411,578)(412,577)(413,576)(414,575)(415,574)(416,573)(417,572)(418,571)(419,570)(420,569)(421,568)(422,567)(423,566)(424,565)(425,564)(426,563)(427,562)(428,561)(429,560)(430,559)(431,558)(432,557)(433,556)(434,555)(435,554)(436,553)(437,552)(438,551)(439,550)(440,549)(441,548)(442,547)(443,546)(444,545)(445,544)(446,543)(447,542)(448,541)(449,540)(450,539)(451,538)(452,537)(453,536)(454,535)(455,534)(456,533)(457,532)(458,531)(459,530)(460,529)(461,528)(462,527)(463,526)(464,525)(465,524)(466,523)(467,522)(468,521)(469,520)(470,519)(471,518)(472,517)(473,516)(474,515)(475,514)(476,513)(477,512)(478,511)(479,510)(480,509)(481,508)(482,507)(483,506)(484,505)(485,504)(486,503)(487,502)(488,501)(489,500)(490,499)(491,498)(492,497)(493,496)(494,495)

Polycyclic presentation:

2,17,953|b^a=b^16,c^a=c^952

Conjugacy classes & character table

8102 conjugacy classes. The character table is too large to display.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32402, 5);