← Prev (#16860934) Next (#16860936) →
Dic1009 #16860935
Aliases
Splittings
Subgroups
6 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 2 generators on 1013 points:
(1,2)(3,4)(5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,172,173,174,175,176,177,178,179,180,181,182,183,184,185,186,187,188,189,190,191,192,193,194,195,196,197,198,199,200,201,202,203,204,205,206,207,208,209,210,211,212,213,214,215,216,217,218,219,220,221,222,223,224,225,226,227,228,229,230,231,232,233,234,235,236,237,238,239,240,241,242,243,244,245,246,247,248,249,250,251,252,253,254,255,256,257,258,259,260,261,262,263,264,265,266,267,268,269,270,271,272,273,274,275,276,277,278,279,280,281,282,283,284,285,286,287,288,289,290,291,292,293,294,295,296,297,298,299,300,301,302,303,304,305,306,307,308,309,310,311,312,313,314,315,316,317,318,319,320,321,322,323,324,325,326,327,328,329,330,331,332,333,334,335,336,337,338,339,340,341,342,343,344,345,346,347,348,349,350,351,352,353,354,355,356,357,358,359,360,361,362,363,364,365,366,367,368,369,370,371,372,373,374,375,376,377,378,379,380,381,382,383,384,385,386,387,388,389,390,391,392,393,394,395,396,397,398,399,400,401,402,403,404,405,406,407,408,409,410,411,412,413,414,415,416,417,418,419,420,421,422,423,424,425,426,427,428,429,430,431,432,433,434,435,436,437,438,439,440,441,442,443,444,445,446,447,448,449,450,451,452,453,454,455,456,457,458,459,460,461,462,463,464,465,466,467,468,469,470,471,472,473,474,475,476,477,478,479,480,481,482,483,484,485,486,487,488,489,490,491,492,493,494,495,496,497,498,499,500,501,502,503,504,505,506,507,508,509,510,511,512,513,514,515,516,517,518,519,520,521,522,523,524,525,526,527,528,529,530,531,532,533,534,535,536,537,538,539,540,541,542,543,544,545,546,547,548,549,550,551,552,553,554,555,556,557,558,559,560,561,562,563,564,565,566,567,568,569,570,571,572,573,574,575,576,577,578,579,580,581,582,583,584,585,586,587,588,589,590,591,592,593,594,595,596,597,598,599,600,601,602,603,604,605,606,607,608,609,610,611,612,613,614,615,616,617,618,619,620,621,622,623,624,625,626,627,628,629,630,631,632,633,634,635,636,637,638,639,640,641,642,643,644,645,646,647,648,649,650,651,652,653,654,655,656,657,658,659,660,661,662,663,664,665,666,667,668,669,670,671,672,673,674,675,676,677,678,679,680,681,682,683,684,685,686,687,688,689,690,691,692,693,694,695,696,697,698,699,700,701,702,703,704,705,706,707,708,709,710,711,712,713,714,715,716,717,718,719,720,721,722,723,724,725,726,727,728,729,730,731,732,733,734,735,736,737,738,739,740,741,742,743,744,745,746,747,748,749,750,751,752,753,754,755,756,757,758,759,760,761,762,763,764,765,766,767,768,769,770,771,772,773,774,775,776,777,778,779,780,781,782,783,784,785,786,787,788,789,790,791,792,793,794,795,796,797,798,799,800,801,802,803,804,805,806,807,808,809,810,811,812,813,814,815,816,817,818,819,820,821,822,823,824,825,826,827,828,829,830,831,832,833,834,835,836,837,838,839,840,841,842,843,844,845,846,847,848,849,850,851,852,853,854,855,856,857,858,859,860,861,862,863,864,865,866,867,868,869,870,871,872,873,874,875,876,877,878,879,880,881,882,883,884,885,886,887,888,889,890,891,892,893,894,895,896,897,898,899,900,901,902,903,904,905,906,907,908,909,910,911,912,913,914,915,916,917,918,919,920,921,922,923,924,925,926,927,928,929,930,931,932,933,934,935,936,937,938,939,940,941,942,943,944,945,946,947,948,949,950,951,952,953,954,955,956,957,958,959,960,961,962,963,964,965,966,967,968,969,970,971,972,973,974,975,976,977,978,979,980,981,982,983,984,985,986,987,988,989,990,991,992,993,994,995,996,997,998,999,1000,1001,1002,1003,1004,1005,1006,1007,1008,1009,1010,1011,1012,1013);(1,3,2,4)(6,1013)(7,1012)(8,1011)(9,1010)(10,1009)(11,1008)(12,1007)(13,1006)(14,1005)(15,1004)(16,1003)(17,1002)(18,1001)(19,1000)(20,999)(21,998)(22,997)(23,996)(24,995)(25,994)(26,993)(27,992)(28,991)(29,990)(30,989)(31,988)(32,987)(33,986)(34,985)(35,984)(36,983)(37,982)(38,981)(39,980)(40,979)(41,978)(42,977)(43,976)(44,975)(45,974)(46,973)(47,972)(48,971)(49,970)(50,969)(51,968)(52,967)(53,966)(54,965)(55,964)(56,963)(57,962)(58,961)(59,960)(60,959)(61,958)(62,957)(63,956)(64,955)(65,954)(66,953)(67,952)(68,951)(69,950)(70,949)(71,948)(72,947)(73,946)(74,945)(75,944)(76,943)(77,942)(78,941)(79,940)(80,939)(81,938)(82,937)(83,936)(84,935)(85,934)(86,933)(87,932)(88,931)(89,930)(90,929)(91,928)(92,927)(93,926)(94,925)(95,924)(96,923)(97,922)(98,921)(99,920)(100,919)(101,918)(102,917)(103,916)(104,915)(105,914)(106,913)(107,912)(108,911)(109,910)(110,909)(111,908)(112,907)(113,906)(114,905)(115,904)(116,903)(117,902)(118,901)(119,900)(120,899)(121,898)(122,897)(123,896)(124,895)(125,894)(126,893)(127,892)(128,891)(129,890)(130,889)(131,888)(132,887)(133,886)(134,885)(135,884)(136,883)(137,882)(138,881)(139,880)(140,879)(141,878)(142,877)(143,876)(144,875)(145,874)(146,873)(147,872)(148,871)(149,870)(150,869)(151,868)(152,867)(153,866)(154,865)(155,864)(156,863)(157,862)(158,861)(159,860)(160,859)(161,858)(162,857)(163,856)(164,855)(165,854)(166,853)(167,852)(168,851)(169,850)(170,849)(171,848)(172,847)(173,846)(174,845)(175,844)(176,843)(177,842)(178,841)(179,840)(180,839)(181,838)(182,837)(183,836)(184,835)(185,834)(186,833)(187,832)(188,831)(189,830)(190,829)(191,828)(192,827)(193,826)(194,825)(195,824)(196,823)(197,822)(198,821)(199,820)(200,819)(201,818)(202,817)(203,816)(204,815)(205,814)(206,813)(207,812)(208,811)(209,810)(210,809)(211,808)(212,807)(213,806)(214,805)(215,804)(216,803)(217,802)(218,801)(219,800)(220,799)(221,798)(222,797)(223,796)(224,795)(225,794)(226,793)(227,792)(228,791)(229,790)(230,789)(231,788)(232,787)(233,786)(234,785)(235,784)(236,783)(237,782)(238,781)(239,780)(240,779)(241,778)(242,777)(243,776)(244,775)(245,774)(246,773)(247,772)(248,771)(249,770)(250,769)(251,768)(252,767)(253,766)(254,765)(255,764)(256,763)(257,762)(258,761)(259,760)(260,759)(261,758)(262,757)(263,756)(264,755)(265,754)(266,753)(267,752)(268,751)(269,750)(270,749)(271,748)(272,747)(273,746)(274,745)(275,744)(276,743)(277,742)(278,741)(279,740)(280,739)(281,738)(282,737)(283,736)(284,735)(285,734)(286,733)(287,732)(288,731)(289,730)(290,729)(291,728)(292,727)(293,726)(294,725)(295,724)(296,723)(297,722)(298,721)(299,720)(300,719)(301,718)(302,717)(303,716)(304,715)(305,714)(306,713)(307,712)(308,711)(309,710)(310,709)(311,708)(312,707)(313,706)(314,705)(315,704)(316,703)(317,702)(318,701)(319,700)(320,699)(321,698)(322,697)(323,696)(324,695)(325,694)(326,693)(327,692)(328,691)(329,690)(330,689)(331,688)(332,687)(333,686)(334,685)(335,684)(336,683)(337,682)(338,681)(339,680)(340,679)(341,678)(342,677)(343,676)(344,675)(345,674)(346,673)(347,672)(348,671)(349,670)(350,669)(351,668)(352,667)(353,666)(354,665)(355,664)(356,663)(357,662)(358,661)(359,660)(360,659)(361,658)(362,657)(363,656)(364,655)(365,654)(366,653)(367,652)(368,651)(369,650)(370,649)(371,648)(372,647)(373,646)(374,645)(375,644)(376,643)(377,642)(378,641)(379,640)(380,639)(381,638)(382,637)(383,636)(384,635)(385,634)(386,633)(387,632)(388,631)(389,630)(390,629)(391,628)(392,627)(393,626)(394,625)(395,624)(396,623)(397,622)(398,621)(399,620)(400,619)(401,618)(402,617)(403,616)(404,615)(405,614)(406,613)(407,612)(408,611)(409,610)(410,609)(411,608)(412,607)(413,606)(414,605)(415,604)(416,603)(417,602)(418,601)(419,600)(420,599)(421,598)(422,597)(423,596)(424,595)(425,594)(426,593)(427,592)(428,591)(429,590)(430,589)(431,588)(432,587)(433,586)(434,585)(435,584)(436,583)(437,582)(438,581)(439,580)(440,579)(441,578)(442,577)(443,576)(444,575)(445,574)(446,573)(447,572)(448,571)(449,570)(450,569)(451,568)(452,567)(453,566)(454,565)(455,564)(456,563)(457,562)(458,561)(459,560)(460,559)(461,558)(462,557)(463,556)(464,555)(465,554)(466,553)(467,552)(468,551)(469,550)(470,549)(471,548)(472,547)(473,546)(474,545)(475,544)(476,543)(477,542)(478,541)(479,540)(480,539)(481,538)(482,537)(483,536)(484,535)(485,534)(486,533)(487,532)(488,531)(489,530)(490,529)(491,528)(492,527)(493,526)(494,525)(495,524)(496,523)(497,522)(498,521)(499,520)(500,519)(501,518)(502,517)(503,516)(504,515)(505,514)(506,513)(507,512)(508,511)(509,510)
Polycyclic presentation:
2^2,1009|a^2=b,c^a=c^1008
Conjugacy classes & character table
1012 conjugacy classes — view the full character table.
Relationships
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4036, 1);
Finite Group Databasebeta