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Dic4885 #34086338
Aliases
Splittings
Subgroups
12 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 2 generators on 986 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);(1,3,2,4)(6,9)(7,8)(11,986)(12,985)(13,984)(14,983)(15,982)(16,981)(17,980)(18,979)(19,978)(20,977)(21,976)(22,975)(23,974)(24,973)(25,972)(26,971)(27,970)(28,969)(29,968)(30,967)(31,966)(32,965)(33,964)(34,963)(35,962)(36,961)(37,960)(38,959)(39,958)(40,957)(41,956)(42,955)(43,954)(44,953)(45,952)(46,951)(47,950)(48,949)(49,948)(50,947)(51,946)(52,945)(53,944)(54,943)(55,942)(56,941)(57,940)(58,939)(59,938)(60,937)(61,936)(62,935)(63,934)(64,933)(65,932)(66,931)(67,930)(68,929)(69,928)(70,927)(71,926)(72,925)(73,924)(74,923)(75,922)(76,921)(77,920)(78,919)(79,918)(80,917)(81,916)(82,915)(83,914)(84,913)(85,912)(86,911)(87,910)(88,909)(89,908)(90,907)(91,906)(92,905)(93,904)(94,903)(95,902)(96,901)(97,900)(98,899)(99,898)(100,897)(101,896)(102,895)(103,894)(104,893)(105,892)(106,891)(107,890)(108,889)(109,888)(110,887)(111,886)(112,885)(113,884)(114,883)(115,882)(116,881)(117,880)(118,879)(119,878)(120,877)(121,876)(122,875)(123,874)(124,873)(125,872)(126,871)(127,870)(128,869)(129,868)(130,867)(131,866)(132,865)(133,864)(134,863)(135,862)(136,861)(137,860)(138,859)(139,858)(140,857)(141,856)(142,855)(143,854)(144,853)(145,852)(146,851)(147,850)(148,849)(149,848)(150,847)(151,846)(152,845)(153,844)(154,843)(155,842)(156,841)(157,840)(158,839)(159,838)(160,837)(161,836)(162,835)(163,834)(164,833)(165,832)(166,831)(167,830)(168,829)(169,828)(170,827)(171,826)(172,825)(173,824)(174,823)(175,822)(176,821)(177,820)(178,819)(179,818)(180,817)(181,816)(182,815)(183,814)(184,813)(185,812)(186,811)(187,810)(188,809)(189,808)(190,807)(191,806)(192,805)(193,804)(194,803)(195,802)(196,801)(197,800)(198,799)(199,798)(200,797)(201,796)(202,795)(203,794)(204,793)(205,792)(206,791)(207,790)(208,789)(209,788)(210,787)(211,786)(212,785)(213,784)(214,783)(215,782)(216,781)(217,780)(218,779)(219,778)(220,777)(221,776)(222,775)(223,774)(224,773)(225,772)(226,771)(227,770)(228,769)(229,768)(230,767)(231,766)(232,765)(233,764)(234,763)(235,762)(236,761)(237,760)(238,759)(239,758)(240,757)(241,756)(242,755)(243,754)(244,753)(245,752)(246,751)(247,750)(248,749)(249,748)(250,747)(251,746)(252,745)(253,744)(254,743)(255,742)(256,741)(257,740)(258,739)(259,738)(260,737)(261,736)(262,735)(263,734)(264,733)(265,732)(266,731)(267,730)(268,729)(269,728)(270,727)(271,726)(272,725)(273,724)(274,723)(275,722)(276,721)(277,720)(278,719)(279,718)(280,717)(281,716)(282,715)(283,714)(284,713)(285,712)(286,711)(287,710)(288,709)(289,708)(290,707)(291,706)(292,705)(293,704)(294,703)(295,702)(296,701)(297,700)(298,699)(299,698)(300,697)(301,696)(302,695)(303,694)(304,693)(305,692)(306,691)(307,690)(308,689)(309,688)(310,687)(311,686)(312,685)(313,684)(314,683)(315,682)(316,681)(317,680)(318,679)(319,678)(320,677)(321,676)(322,675)(323,674)(324,673)(325,672)(326,671)(327,670)(328,669)(329,668)(330,667)(331,666)(332,665)(333,664)(334,663)(335,662)(336,661)(337,660)(338,659)(339,658)(340,657)(341,656)(342,655)(343,654)(344,653)(345,652)(346,651)(347,650)(348,649)(349,648)(350,647)(351,646)(352,645)(353,644)(354,643)(355,642)(356,641)(357,640)(358,639)(359,638)(360,637)(361,636)(362,635)(363,634)(364,633)(365,632)(366,631)(367,630)(368,629)(369,628)(370,627)(371,626)(372,625)(373,624)(374,623)(375,622)(376,621)(377,620)(378,619)(379,618)(380,617)(381,616)(382,615)(383,614)(384,613)(385,612)(386,611)(387,610)(388,609)(389,608)(390,607)(391,606)(392,605)(393,604)(394,603)(395,602)(396,601)(397,600)(398,599)(399,598)(400,597)(401,596)(402,595)(403,594)(404,593)(405,592)(406,591)(407,590)(408,589)(409,588)(410,587)(411,586)(412,585)(413,584)(414,583)(415,582)(416,581)(417,580)(418,579)(419,578)(420,577)(421,576)(422,575)(423,574)(424,573)(425,572)(426,571)(427,570)(428,569)(429,568)(430,567)(431,566)(432,565)(433,564)(434,563)(435,562)(436,561)(437,560)(438,559)(439,558)(440,557)(441,556)(442,555)(443,554)(444,553)(445,552)(446,551)(447,550)(448,549)(449,548)(450,547)(451,546)(452,545)(453,544)(454,543)(455,542)(456,541)(457,540)(458,539)(459,538)(460,537)(461,536)(462,535)(463,534)(464,533)(465,532)(466,531)(467,530)(468,529)(469,528)(470,527)(471,526)(472,525)(473,524)(474,523)(475,522)(476,521)(477,520)(478,519)(479,518)(480,517)(481,516)(482,515)(483,514)(484,513)(485,512)(486,511)(487,510)(488,509)(489,508)(490,507)(491,506)(492,505)(493,504)(494,503)(495,502)(496,501)(497,500)(498,499)
Polycyclic presentation:
2,5,977,2|a^2=d,b^a=b^4,c^a=c^976
Conjugacy classes & character table
4888 conjugacy classes. The character table is too large to display.
Relationships
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19540, 4);
Finite Group Databasebeta