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D8739 #31775698
Aliases
Splittings
Subgroups
12 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 2 generators on 980 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);(2,9)(3,8)(4,7)(5,6)(11,980)(12,979)(13,978)(14,977)(15,976)(16,975)(17,974)(18,973)(19,972)(20,971)(21,970)(22,969)(23,968)(24,967)(25,966)(26,965)(27,964)(28,963)(29,962)(30,961)(31,960)(32,959)(33,958)(34,957)(35,956)(36,955)(37,954)(38,953)(39,952)(40,951)(41,950)(42,949)(43,948)(44,947)(45,946)(46,945)(47,944)(48,943)(49,942)(50,941)(51,940)(52,939)(53,938)(54,937)(55,936)(56,935)(57,934)(58,933)(59,932)(60,931)(61,930)(62,929)(63,928)(64,927)(65,926)(66,925)(67,924)(68,923)(69,922)(70,921)(71,920)(72,919)(73,918)(74,917)(75,916)(76,915)(77,914)(78,913)(79,912)(80,911)(81,910)(82,909)(83,908)(84,907)(85,906)(86,905)(87,904)(88,903)(89,902)(90,901)(91,900)(92,899)(93,898)(94,897)(95,896)(96,895)(97,894)(98,893)(99,892)(100,891)(101,890)(102,889)(103,888)(104,887)(105,886)(106,885)(107,884)(108,883)(109,882)(110,881)(111,880)(112,879)(113,878)(114,877)(115,876)(116,875)(117,874)(118,873)(119,872)(120,871)(121,870)(122,869)(123,868)(124,867)(125,866)(126,865)(127,864)(128,863)(129,862)(130,861)(131,860)(132,859)(133,858)(134,857)(135,856)(136,855)(137,854)(138,853)(139,852)(140,851)(141,850)(142,849)(143,848)(144,847)(145,846)(146,845)(147,844)(148,843)(149,842)(150,841)(151,840)(152,839)(153,838)(154,837)(155,836)(156,835)(157,834)(158,833)(159,832)(160,831)(161,830)(162,829)(163,828)(164,827)(165,826)(166,825)(167,824)(168,823)(169,822)(170,821)(171,820)(172,819)(173,818)(174,817)(175,816)(176,815)(177,814)(178,813)(179,812)(180,811)(181,810)(182,809)(183,808)(184,807)(185,806)(186,805)(187,804)(188,803)(189,802)(190,801)(191,800)(192,799)(193,798)(194,797)(195,796)(196,795)(197,794)(198,793)(199,792)(200,791)(201,790)(202,789)(203,788)(204,787)(205,786)(206,785)(207,784)(208,783)(209,782)(210,781)(211,780)(212,779)(213,778)(214,777)(215,776)(216,775)(217,774)(218,773)(219,772)(220,771)(221,770)(222,769)(223,768)(224,767)(225,766)(226,765)(227,764)(228,763)(229,762)(230,761)(231,760)(232,759)(233,758)(234,757)(235,756)(236,755)(237,754)(238,753)(239,752)(240,751)(241,750)(242,749)(243,748)(244,747)(245,746)(246,745)(247,744)(248,743)(249,742)(250,741)(251,740)(252,739)(253,738)(254,737)(255,736)(256,735)(257,734)(258,733)(259,732)(260,731)(261,730)(262,729)(263,728)(264,727)(265,726)(266,725)(267,724)(268,723)(269,722)(270,721)(271,720)(272,719)(273,718)(274,717)(275,716)(276,715)(277,714)(278,713)(279,712)(280,711)(281,710)(282,709)(283,708)(284,707)(285,706)(286,705)(287,704)(288,703)(289,702)(290,701)(291,700)(292,699)(293,698)(294,697)(295,696)(296,695)(297,694)(298,693)(299,692)(300,691)(301,690)(302,689)(303,688)(304,687)(305,686)(306,685)(307,684)(308,683)(309,682)(310,681)(311,680)(312,679)(313,678)(314,677)(315,676)(316,675)(317,674)(318,673)(319,672)(320,671)(321,670)(322,669)(323,668)(324,667)(325,666)(326,665)(327,664)(328,663)(329,662)(330,661)(331,660)(332,659)(333,658)(334,657)(335,656)(336,655)(337,654)(338,653)(339,652)(340,651)(341,650)(342,649)(343,648)(344,647)(345,646)(346,645)(347,644)(348,643)(349,642)(350,641)(351,640)(352,639)(353,638)(354,637)(355,636)(356,635)(357,634)(358,633)(359,632)(360,631)(361,630)(362,629)(363,628)(364,627)(365,626)(366,625)(367,624)(368,623)(369,622)(370,621)(371,620)(372,619)(373,618)(374,617)(375,616)(376,615)(377,614)(378,613)(379,612)(380,611)(381,610)(382,609)(383,608)(384,607)(385,606)(386,605)(387,604)(388,603)(389,602)(390,601)(391,600)(392,599)(393,598)(394,597)(395,596)(396,595)(397,594)(398,593)(399,592)(400,591)(401,590)(402,589)(403,588)(404,587)(405,586)(406,585)(407,584)(408,583)(409,582)(410,581)(411,580)(412,579)(413,578)(414,577)(415,576)(416,575)(417,574)(418,573)(419,572)(420,571)(421,570)(422,569)(423,568)(424,567)(425,566)(426,565)(427,564)(428,563)(429,562)(430,561)(431,560)(432,559)(433,558)(434,557)(435,556)(436,555)(437,554)(438,553)(439,552)(440,551)(441,550)(442,549)(443,548)(444,547)(445,546)(446,545)(447,544)(448,543)(449,542)(450,541)(451,540)(452,539)(453,538)(454,537)(455,536)(456,535)(457,534)(458,533)(459,532)(460,531)(461,530)(462,529)(463,528)(464,527)(465,526)(466,525)(467,524)(468,523)(469,522)(470,521)(471,520)(472,519)(473,518)(474,517)(475,516)(476,515)(477,514)(478,513)(479,512)(480,511)(481,510)(482,509)(483,508)(484,507)(485,506)(486,505)(487,504)(488,503)(489,502)(490,501)(491,500)(492,499)(493,498)(494,497)(495,496)
Polycyclic presentation:
2,3,971,3|b^3=d^2,b^a=b^2d,c^a=c^970,d^a=d^2
Conjugacy classes & character table
4371 conjugacy classes. The character table is too large to display.
Relationships
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17478, 4);
Finite Group Databasebeta