← Prev (#38761908) Next (#38761910) →
D12701 #38761909
Aliases
Splittings
Subgroups
8 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 2 generators on 990 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);(2,13)(3,12)(4,11)(5,10)(6,9)(7,8)(15,990)(16,989)(17,988)(18,987)(19,986)(20,985)(21,984)(22,983)(23,982)(24,981)(25,980)(26,979)(27,978)(28,977)(29,976)(30,975)(31,974)(32,973)(33,972)(34,971)(35,970)(36,969)(37,968)(38,967)(39,966)(40,965)(41,964)(42,963)(43,962)(44,961)(45,960)(46,959)(47,958)(48,957)(49,956)(50,955)(51,954)(52,953)(53,952)(54,951)(55,950)(56,949)(57,948)(58,947)(59,946)(60,945)(61,944)(62,943)(63,942)(64,941)(65,940)(66,939)(67,938)(68,937)(69,936)(70,935)(71,934)(72,933)(73,932)(74,931)(75,930)(76,929)(77,928)(78,927)(79,926)(80,925)(81,924)(82,923)(83,922)(84,921)(85,920)(86,919)(87,918)(88,917)(89,916)(90,915)(91,914)(92,913)(93,912)(94,911)(95,910)(96,909)(97,908)(98,907)(99,906)(100,905)(101,904)(102,903)(103,902)(104,901)(105,900)(106,899)(107,898)(108,897)(109,896)(110,895)(111,894)(112,893)(113,892)(114,891)(115,890)(116,889)(117,888)(118,887)(119,886)(120,885)(121,884)(122,883)(123,882)(124,881)(125,880)(126,879)(127,878)(128,877)(129,876)(130,875)(131,874)(132,873)(133,872)(134,871)(135,870)(136,869)(137,868)(138,867)(139,866)(140,865)(141,864)(142,863)(143,862)(144,861)(145,860)(146,859)(147,858)(148,857)(149,856)(150,855)(151,854)(152,853)(153,852)(154,851)(155,850)(156,849)(157,848)(158,847)(159,846)(160,845)(161,844)(162,843)(163,842)(164,841)(165,840)(166,839)(167,838)(168,837)(169,836)(170,835)(171,834)(172,833)(173,832)(174,831)(175,830)(176,829)(177,828)(178,827)(179,826)(180,825)(181,824)(182,823)(183,822)(184,821)(185,820)(186,819)(187,818)(188,817)(189,816)(190,815)(191,814)(192,813)(193,812)(194,811)(195,810)(196,809)(197,808)(198,807)(199,806)(200,805)(201,804)(202,803)(203,802)(204,801)(205,800)(206,799)(207,798)(208,797)(209,796)(210,795)(211,794)(212,793)(213,792)(214,791)(215,790)(216,789)(217,788)(218,787)(219,786)(220,785)(221,784)(222,783)(223,782)(224,781)(225,780)(226,779)(227,778)(228,777)(229,776)(230,775)(231,774)(232,773)(233,772)(234,771)(235,770)(236,769)(237,768)(238,767)(239,766)(240,765)(241,764)(242,763)(243,762)(244,761)(245,760)(246,759)(247,758)(248,757)(249,756)(250,755)(251,754)(252,753)(253,752)(254,751)(255,750)(256,749)(257,748)(258,747)(259,746)(260,745)(261,744)(262,743)(263,742)(264,741)(265,740)(266,739)(267,738)(268,737)(269,736)(270,735)(271,734)(272,733)(273,732)(274,731)(275,730)(276,729)(277,728)(278,727)(279,726)(280,725)(281,724)(282,723)(283,722)(284,721)(285,720)(286,719)(287,718)(288,717)(289,716)(290,715)(291,714)(292,713)(293,712)(294,711)(295,710)(296,709)(297,708)(298,707)(299,706)(300,705)(301,704)(302,703)(303,702)(304,701)(305,700)(306,699)(307,698)(308,697)(309,696)(310,695)(311,694)(312,693)(313,692)(314,691)(315,690)(316,689)(317,688)(318,687)(319,686)(320,685)(321,684)(322,683)(323,682)(324,681)(325,680)(326,679)(327,678)(328,677)(329,676)(330,675)(331,674)(332,673)(333,672)(334,671)(335,670)(336,669)(337,668)(338,667)(339,666)(340,665)(341,664)(342,663)(343,662)(344,661)(345,660)(346,659)(347,658)(348,657)(349,656)(350,655)(351,654)(352,653)(353,652)(354,651)(355,650)(356,649)(357,648)(358,647)(359,646)(360,645)(361,644)(362,643)(363,642)(364,641)(365,640)(366,639)(367,638)(368,637)(369,636)(370,635)(371,634)(372,633)(373,632)(374,631)(375,630)(376,629)(377,628)(378,627)(379,626)(380,625)(381,624)(382,623)(383,622)(384,621)(385,620)(386,619)(387,618)(388,617)(389,616)(390,615)(391,614)(392,613)(393,612)(394,611)(395,610)(396,609)(397,608)(398,607)(399,606)(400,605)(401,604)(402,603)(403,602)(404,601)(405,600)(406,599)(407,598)(408,597)(409,596)(410,595)(411,594)(412,593)(413,592)(414,591)(415,590)(416,589)(417,588)(418,587)(419,586)(420,585)(421,584)(422,583)(423,582)(424,581)(425,580)(426,579)(427,578)(428,577)(429,576)(430,575)(431,574)(432,573)(433,572)(434,571)(435,570)(436,569)(437,568)(438,567)(439,566)(440,565)(441,564)(442,563)(443,562)(444,561)(445,560)(446,559)(447,558)(448,557)(449,556)(450,555)(451,554)(452,553)(453,552)(454,551)(455,550)(456,549)(457,548)(458,547)(459,546)(460,545)(461,544)(462,543)(463,542)(464,541)(465,540)(466,539)(467,538)(468,537)(469,536)(470,535)(471,534)(472,533)(473,532)(474,531)(475,530)(476,529)(477,528)(478,527)(479,526)(480,525)(481,524)(482,523)(483,522)(484,521)(485,520)(486,519)(487,518)(488,517)(489,516)(490,515)(491,514)(492,513)(493,512)(494,511)(495,510)(496,509)(497,508)(498,507)(499,506)(500,505)(501,504)(502,503)
Polycyclic presentation:
2,13,977|b^a=b^12,c^a=c^976
Conjugacy classes & character table
6352 conjugacy classes. The character table is too large to display.
Relationships
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(25402, 3);
Finite Group Databasebeta