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D14655 #44418328
Aliases
Splittings
Subgroups
16 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 2 generators on 985 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);(2,3)(5,8)(6,7)(10,985)(11,984)(12,983)(13,982)(14,981)(15,980)(16,979)(17,978)(18,977)(19,976)(20,975)(21,974)(22,973)(23,972)(24,971)(25,970)(26,969)(27,968)(28,967)(29,966)(30,965)(31,964)(32,963)(33,962)(34,961)(35,960)(36,959)(37,958)(38,957)(39,956)(40,955)(41,954)(42,953)(43,952)(44,951)(45,950)(46,949)(47,948)(48,947)(49,946)(50,945)(51,944)(52,943)(53,942)(54,941)(55,940)(56,939)(57,938)(58,937)(59,936)(60,935)(61,934)(62,933)(63,932)(64,931)(65,930)(66,929)(67,928)(68,927)(69,926)(70,925)(71,924)(72,923)(73,922)(74,921)(75,920)(76,919)(77,918)(78,917)(79,916)(80,915)(81,914)(82,913)(83,912)(84,911)(85,910)(86,909)(87,908)(88,907)(89,906)(90,905)(91,904)(92,903)(93,902)(94,901)(95,900)(96,899)(97,898)(98,897)(99,896)(100,895)(101,894)(102,893)(103,892)(104,891)(105,890)(106,889)(107,888)(108,887)(109,886)(110,885)(111,884)(112,883)(113,882)(114,881)(115,880)(116,879)(117,878)(118,877)(119,876)(120,875)(121,874)(122,873)(123,872)(124,871)(125,870)(126,869)(127,868)(128,867)(129,866)(130,865)(131,864)(132,863)(133,862)(134,861)(135,860)(136,859)(137,858)(138,857)(139,856)(140,855)(141,854)(142,853)(143,852)(144,851)(145,850)(146,849)(147,848)(148,847)(149,846)(150,845)(151,844)(152,843)(153,842)(154,841)(155,840)(156,839)(157,838)(158,837)(159,836)(160,835)(161,834)(162,833)(163,832)(164,831)(165,830)(166,829)(167,828)(168,827)(169,826)(170,825)(171,824)(172,823)(173,822)(174,821)(175,820)(176,819)(177,818)(178,817)(179,816)(180,815)(181,814)(182,813)(183,812)(184,811)(185,810)(186,809)(187,808)(188,807)(189,806)(190,805)(191,804)(192,803)(193,802)(194,801)(195,800)(196,799)(197,798)(198,797)(199,796)(200,795)(201,794)(202,793)(203,792)(204,791)(205,790)(206,789)(207,788)(208,787)(209,786)(210,785)(211,784)(212,783)(213,782)(214,781)(215,780)(216,779)(217,778)(218,777)(219,776)(220,775)(221,774)(222,773)(223,772)(224,771)(225,770)(226,769)(227,768)(228,767)(229,766)(230,765)(231,764)(232,763)(233,762)(234,761)(235,760)(236,759)(237,758)(238,757)(239,756)(240,755)(241,754)(242,753)(243,752)(244,751)(245,750)(246,749)(247,748)(248,747)(249,746)(250,745)(251,744)(252,743)(253,742)(254,741)(255,740)(256,739)(257,738)(258,737)(259,736)(260,735)(261,734)(262,733)(263,732)(264,731)(265,730)(266,729)(267,728)(268,727)(269,726)(270,725)(271,724)(272,723)(273,722)(274,721)(275,720)(276,719)(277,718)(278,717)(279,716)(280,715)(281,714)(282,713)(283,712)(284,711)(285,710)(286,709)(287,708)(288,707)(289,706)(290,705)(291,704)(292,703)(293,702)(294,701)(295,700)(296,699)(297,698)(298,697)(299,696)(300,695)(301,694)(302,693)(303,692)(304,691)(305,690)(306,689)(307,688)(308,687)(309,686)(310,685)(311,684)(312,683)(313,682)(314,681)(315,680)(316,679)(317,678)(318,677)(319,676)(320,675)(321,674)(322,673)(323,672)(324,671)(325,670)(326,669)(327,668)(328,667)(329,666)(330,665)(331,664)(332,663)(333,662)(334,661)(335,660)(336,659)(337,658)(338,657)(339,656)(340,655)(341,654)(342,653)(343,652)(344,651)(345,650)(346,649)(347,648)(348,647)(349,646)(350,645)(351,644)(352,643)(353,642)(354,641)(355,640)(356,639)(357,638)(358,637)(359,636)(360,635)(361,634)(362,633)(363,632)(364,631)(365,630)(366,629)(367,628)(368,627)(369,626)(370,625)(371,624)(372,623)(373,622)(374,621)(375,620)(376,619)(377,618)(378,617)(379,616)(380,615)(381,614)(382,613)(383,612)(384,611)(385,610)(386,609)(387,608)(388,607)(389,606)(390,605)(391,604)(392,603)(393,602)(394,601)(395,600)(396,599)(397,598)(398,597)(399,596)(400,595)(401,594)(402,593)(403,592)(404,591)(405,590)(406,589)(407,588)(408,587)(409,586)(410,585)(411,584)(412,583)(413,582)(414,581)(415,580)(416,579)(417,578)(418,577)(419,576)(420,575)(421,574)(422,573)(423,572)(424,571)(425,570)(426,569)(427,568)(428,567)(429,566)(430,565)(431,564)(432,563)(433,562)(434,561)(435,560)(436,559)(437,558)(438,557)(439,556)(440,555)(441,554)(442,553)(443,552)(444,551)(445,550)(446,549)(447,548)(448,547)(449,546)(450,545)(451,544)(452,543)(453,542)(454,541)(455,540)(456,539)(457,538)(458,537)(459,536)(460,535)(461,534)(462,533)(463,532)(464,531)(465,530)(466,529)(467,528)(468,527)(469,526)(470,525)(471,524)(472,523)(473,522)(474,521)(475,520)(476,519)(477,518)(478,517)(479,516)(480,515)(481,514)(482,513)(483,512)(484,511)(485,510)(486,509)(487,508)(488,507)(489,506)(490,505)(491,504)(492,503)(493,502)(494,501)(495,500)(496,499)(497,498)
Polycyclic presentation:
2,3,5,977|b^a=b^2,c^a=c^4,d^a=d^976
Conjugacy classes & character table
7329 conjugacy classes. The character table is too large to display.
Relationships
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(29310, 8);
Finite Group Databasebeta