Finite Group Databasebeta

?

← Prev (#14520496) Next (#14520498) →

D₉₉₁ #14520497

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

Aliases

Splittings

Subgroups

4 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 2 generators on 991 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,172,173,174,175,176,177,178,179,180,181,182,183,184,185,186,187,188,189,190,191,192,193,194,195,196,197,198,199,200,201,202,203,204,205,206,207,208,209,210,211,212,213,214,215,216,217,218,219,220,221,222,223,224,225,226,227,228,229,230,231,232,233,234,235,236,237,238,239,240,241,242,243,244,245,246,247,248,249,250,251,252,253,254,255,256,257,258,259,260,261,262,263,264,265,266,267,268,269,270,271,272,273,274,275,276,277,278,279,280,281,282,283,284,285,286,287,288,289,290,291,292,293,294,295,296,297,298,299,300,301,302,303,304,305,306,307,308,309,310,311,312,313,314,315,316,317,318,319,320,321,322,323,324,325,326,327,328,329,330,331,332,333,334,335,336,337,338,339,340,341,342,343,344,345,346,347,348,349,350,351,352,353,354,355,356,357,358,359,360,361,362,363,364,365,366,367,368,369,370,371,372,373,374,375,376,377,378,379,380,381,382,383,384,385,386,387,388,389,390,391,392,393,394,395,396,397,398,399,400,401,402,403,404,405,406,407,408,409,410,411,412,413,414,415,416,417,418,419,420,421,422,423,424,425,426,427,428,429,430,431,432,433,434,435,436,437,438,439,440,441,442,443,444,445,446,447,448,449,450,451,452,453,454,455,456,457,458,459,460,461,462,463,464,465,466,467,468,469,470,471,472,473,474,475,476,477,478,479,480,481,482,483,484,485,486,487,488,489,490,491,492,493,494,495,496,497,498,499,500,501,502,503,504,505,506,507,508,509,510,511,512,513,514,515,516,517,518,519,520,521,522,523,524,525,526,527,528,529,530,531,532,533,534,535,536,537,538,539,540,541,542,543,544,545,546,547,548,549,550,551,552,553,554,555,556,557,558,559,560,561,562,563,564,565,566,567,568,569,570,571,572,573,574,575,576,577,578,579,580,581,582,583,584,585,586,587,588,589,590,591,592,593,594,595,596,597,598,599,600,601,602,603,604,605,606,607,608,609,610,611,612,613,614,615,616,617,618,619,620,621,622,623,624,625,626,627,628,629,630,631,632,633,634,635,636,637,638,639,640,641,642,643,644,645,646,647,648,649,650,651,652,653,654,655,656,657,658,659,660,661,662,663,664,665,666,667,668,669,670,671,672,673,674,675,676,677,678,679,680,681,682,683,684,685,686,687,688,689,690,691,692,693,694,695,696,697,698,699,700,701,702,703,704,705,706,707,708,709,710,711,712,713,714,715,716,717,718,719,720,721,722,723,724,725,726,727,728,729,730,731,732,733,734,735,736,737,738,739,740,741,742,743,744,745,746,747,748,749,750,751,752,753,754,755,756,757,758,759,760,761,762,763,764,765,766,767,768,769,770,771,772,773,774,775,776,777,778,779,780,781,782,783,784,785,786,787,788,789,790,791,792,793,794,795,796,797,798,799,800,801,802,803,804,805,806,807,808,809,810,811,812,813,814,815,816,817,818,819,820,821,822,823,824,825,826,827,828,829,830,831,832,833,834,835,836,837,838,839,840,841,842,843,844,845,846,847,848,849,850,851,852,853,854,855,856,857,858,859,860,861,862,863,864,865,866,867,868,869,870,871,872,873,874,875,876,877,878,879,880,881,882,883,884,885,886,887,888,889,890,891,892,893,894,895,896,897,898,899,900,901,902,903,904,905,906,907,908,909,910,911,912,913,914,915,916,917,918,919,920,921,922,923,924,925,926,927,928,929,930,931,932,933,934,935,936,937,938,939,940,941,942,943,944,945,946,947,948,949,950,951,952,953,954,955,956,957,958,959,960,961,962,963,964,965,966,967,968,969,970,971,972,973,974,975,976,977,978,979,980,981,982,983,984,985,986,987,988,989,990,991);(2,991)(3,990)(4,989)(5,988)(6,987)(7,986)(8,985)(9,984)(10,983)(11,982)(12,981)(13,980)(14,979)(15,978)(16,977)(17,976)(18,975)(19,974)(20,973)(21,972)(22,971)(23,970)(24,969)(25,968)(26,967)(27,966)(28,965)(29,964)(30,963)(31,962)(32,961)(33,960)(34,959)(35,958)(36,957)(37,956)(38,955)(39,954)(40,953)(41,952)(42,951)(43,950)(44,949)(45,948)(46,947)(47,946)(48,945)(49,944)(50,943)(51,942)(52,941)(53,940)(54,939)(55,938)(56,937)(57,936)(58,935)(59,934)(60,933)(61,932)(62,931)(63,930)(64,929)(65,928)(66,927)(67,926)(68,925)(69,924)(70,923)(71,922)(72,921)(73,920)(74,919)(75,918)(76,917)(77,916)(78,915)(79,914)(80,913)(81,912)(82,911)(83,910)(84,909)(85,908)(86,907)(87,906)(88,905)(89,904)(90,903)(91,902)(92,901)(93,900)(94,899)(95,898)(96,897)(97,896)(98,895)(99,894)(100,893)(101,892)(102,891)(103,890)(104,889)(105,888)(106,887)(107,886)(108,885)(109,884)(110,883)(111,882)(112,881)(113,880)(114,879)(115,878)(116,877)(117,876)(118,875)(119,874)(120,873)(121,872)(122,871)(123,870)(124,869)(125,868)(126,867)(127,866)(128,865)(129,864)(130,863)(131,862)(132,861)(133,860)(134,859)(135,858)(136,857)(137,856)(138,855)(139,854)(140,853)(141,852)(142,851)(143,850)(144,849)(145,848)(146,847)(147,846)(148,845)(149,844)(150,843)(151,842)(152,841)(153,840)(154,839)(155,838)(156,837)(157,836)(158,835)(159,834)(160,833)(161,832)(162,831)(163,830)(164,829)(165,828)(166,827)(167,826)(168,825)(169,824)(170,823)(171,822)(172,821)(173,820)(174,819)(175,818)(176,817)(177,816)(178,815)(179,814)(180,813)(181,812)(182,811)(183,810)(184,809)(185,808)(186,807)(187,806)(188,805)(189,804)(190,803)(191,802)(192,801)(193,800)(194,799)(195,798)(196,797)(197,796)(198,795)(199,794)(200,793)(201,792)(202,791)(203,790)(204,789)(205,788)(206,787)(207,786)(208,785)(209,784)(210,783)(211,782)(212,781)(213,780)(214,779)(215,778)(216,777)(217,776)(218,775)(219,774)(220,773)(221,772)(222,771)(223,770)(224,769)(225,768)(226,767)(227,766)(228,765)(229,764)(230,763)(231,762)(232,761)(233,760)(234,759)(235,758)(236,757)(237,756)(238,755)(239,754)(240,753)(241,752)(242,751)(243,750)(244,749)(245,748)(246,747)(247,746)(248,745)(249,744)(250,743)(251,742)(252,741)(253,740)(254,739)(255,738)(256,737)(257,736)(258,735)(259,734)(260,733)(261,732)(262,731)(263,730)(264,729)(265,728)(266,727)(267,726)(268,725)(269,724)(270,723)(271,722)(272,721)(273,720)(274,719)(275,718)(276,717)(277,716)(278,715)(279,714)(280,713)(281,712)(282,711)(283,710)(284,709)(285,708)(286,707)(287,706)(288,705)(289,704)(290,703)(291,702)(292,701)(293,700)(294,699)(295,698)(296,697)(297,696)(298,695)(299,694)(300,693)(301,692)(302,691)(303,690)(304,689)(305,688)(306,687)(307,686)(308,685)(309,684)(310,683)(311,682)(312,681)(313,680)(314,679)(315,678)(316,677)(317,676)(318,675)(319,674)(320,673)(321,672)(322,671)(323,670)(324,669)(325,668)(326,667)(327,666)(328,665)(329,664)(330,663)(331,662)(332,661)(333,660)(334,659)(335,658)(336,657)(337,656)(338,655)(339,654)(340,653)(341,652)(342,651)(343,650)(344,649)(345,648)(346,647)(347,646)(348,645)(349,644)(350,643)(351,642)(352,641)(353,640)(354,639)(355,638)(356,637)(357,636)(358,635)(359,634)(360,633)(361,632)(362,631)(363,630)(364,629)(365,628)(366,627)(367,626)(368,625)(369,624)(370,623)(371,622)(372,621)(373,620)(374,619)(375,618)(376,617)(377,616)(378,615)(379,614)(380,613)(381,612)(382,611)(383,610)(384,609)(385,608)(386,607)(387,606)(388,605)(389,604)(390,603)(391,602)(392,601)(393,600)(394,599)(395,598)(396,597)(397,596)(398,595)(399,594)(400,593)(401,592)(402,591)(403,590)(404,589)(405,588)(406,587)(407,586)(408,585)(409,584)(410,583)(411,582)(412,581)(413,580)(414,579)(415,578)(416,577)(417,576)(418,575)(419,574)(420,573)(421,572)(422,571)(423,570)(424,569)(425,568)(426,567)(427,566)(428,565)(429,564)(430,563)(431,562)(432,561)(433,560)(434,559)(435,558)(436,557)(437,556)(438,555)(439,554)(440,553)(441,552)(442,551)(443,550)(444,549)(445,548)(446,547)(447,546)(448,545)(449,544)(450,543)(451,542)(452,541)(453,540)(454,539)(455,538)(456,537)(457,536)(458,535)(459,534)(460,533)(461,532)(462,531)(463,530)(464,529)(465,528)(466,527)(467,526)(468,525)(469,524)(470,523)(471,522)(472,521)(473,520)(474,519)(475,518)(476,517)(477,516)(478,515)(479,514)(480,513)(481,512)(482,511)(483,510)(484,509)(485,508)(486,507)(487,506)(488,505)(489,504)(490,503)(491,502)(492,501)(493,500)(494,499)(495,498)(496,497)

Polycyclic presentation:

2,991|b^a=b^990

Conjugacy classes & character table

497 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1982, 1);