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Aliases
Splittings
Subgroups
20 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 2 generators on 976 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);(4,5)(7,976)(8,975)(9,974)(10,973)(11,972)(12,971)(13,970)(14,969)(15,968)(16,967)(17,966)(18,965)(19,964)(20,963)(21,962)(22,961)(23,960)(24,959)(25,958)(26,957)(27,956)(28,955)(29,954)(30,953)(31,952)(32,951)(33,950)(34,949)(35,948)(36,947)(37,946)(38,945)(39,944)(40,943)(41,942)(42,941)(43,940)(44,939)(45,938)(46,937)(47,936)(48,935)(49,934)(50,933)(51,932)(52,931)(53,930)(54,929)(55,928)(56,927)(57,926)(58,925)(59,924)(60,923)(61,922)(62,921)(63,920)(64,919)(65,918)(66,917)(67,916)(68,915)(69,914)(70,913)(71,912)(72,911)(73,910)(74,909)(75,908)(76,907)(77,906)(78,905)(79,904)(80,903)(81,902)(82,901)(83,900)(84,899)(85,898)(86,897)(87,896)(88,895)(89,894)(90,893)(91,892)(92,891)(93,890)(94,889)(95,888)(96,887)(97,886)(98,885)(99,884)(100,883)(101,882)(102,881)(103,880)(104,879)(105,878)(106,877)(107,876)(108,875)(109,874)(110,873)(111,872)(112,871)(113,870)(114,869)(115,868)(116,867)(117,866)(118,865)(119,864)(120,863)(121,862)(122,861)(123,860)(124,859)(125,858)(126,857)(127,856)(128,855)(129,854)(130,853)(131,852)(132,851)(133,850)(134,849)(135,848)(136,847)(137,846)(138,845)(139,844)(140,843)(141,842)(142,841)(143,840)(144,839)(145,838)(146,837)(147,836)(148,835)(149,834)(150,833)(151,832)(152,831)(153,830)(154,829)(155,828)(156,827)(157,826)(158,825)(159,824)(160,823)(161,822)(162,821)(163,820)(164,819)(165,818)(166,817)(167,816)(168,815)(169,814)(170,813)(171,812)(172,811)(173,810)(174,809)(175,808)(176,807)(177,806)(178,805)(179,804)(180,803)(181,802)(182,801)(183,800)(184,799)(185,798)(186,797)(187,796)(188,795)(189,794)(190,793)(191,792)(192,791)(193,790)(194,789)(195,788)(196,787)(197,786)(198,785)(199,784)(200,783)(201,782)(202,781)(203,780)(204,779)(205,778)(206,777)(207,776)(208,775)(209,774)(210,773)(211,772)(212,771)(213,770)(214,769)(215,768)(216,767)(217,766)(218,765)(219,764)(220,763)(221,762)(222,761)(223,760)(224,759)(225,758)(226,757)(227,756)(228,755)(229,754)(230,753)(231,752)(232,751)(233,750)(234,749)(235,748)(236,747)(237,746)(238,745)(239,744)(240,743)(241,742)(242,741)(243,740)(244,739)(245,738)(246,737)(247,736)(248,735)(249,734)(250,733)(251,732)(252,731)(253,730)(254,729)(255,728)(256,727)(257,726)(258,725)(259,724)(260,723)(261,722)(262,721)(263,720)(264,719)(265,718)(266,717)(267,716)(268,715)(269,714)(270,713)(271,712)(272,711)(273,710)(274,709)(275,708)(276,707)(277,706)(278,705)(279,704)(280,703)(281,702)(282,701)(283,700)(284,699)(285,698)(286,697)(287,696)(288,695)(289,694)(290,693)(291,692)(292,691)(293,690)(294,689)(295,688)(296,687)(297,686)(298,685)(299,684)(300,683)(301,682)(302,681)(303,680)(304,679)(305,678)(306,677)(307,676)(308,675)(309,674)(310,673)(311,672)(312,671)(313,670)(314,669)(315,668)(316,667)(317,666)(318,665)(319,664)(320,663)(321,662)(322,661)(323,660)(324,659)(325,658)(326,657)(327,656)(328,655)(329,654)(330,653)(331,652)(332,651)(333,650)(334,649)(335,648)(336,647)(337,646)(338,645)(339,644)(340,643)(341,642)(342,641)(343,640)(344,639)(345,638)(346,637)(347,636)(348,635)(349,634)(350,633)(351,632)(352,631)(353,630)(354,629)(355,628)(356,627)(357,626)(358,625)(359,624)(360,623)(361,622)(362,621)(363,620)(364,619)(365,618)(366,617)(367,616)(368,615)(369,614)(370,613)(371,612)(372,611)(373,610)(374,609)(375,608)(376,607)(377,606)(378,605)(379,604)(380,603)(381,602)(382,601)(383,600)(384,599)(385,598)(386,597)(387,596)(388,595)(389,594)(390,593)(391,592)(392,591)(393,590)(394,589)(395,588)(396,587)(397,586)(398,585)(399,584)(400,583)(401,582)(402,581)(403,580)(404,579)(405,578)(406,577)(407,576)(408,575)(409,574)(410,573)(411,572)(412,571)(413,570)(414,569)(415,568)(416,567)(417,566)(418,565)(419,564)(420,563)(421,562)(422,561)(423,560)(424,559)(425,558)(426,557)(427,556)(428,555)(429,554)(430,553)(431,552)(432,551)(433,550)(434,549)(435,548)(436,547)(437,546)(438,545)(439,544)(440,543)(441,542)(442,541)(443,540)(444,539)(445,538)(446,537)(447,536)(448,535)(449,534)(450,533)(451,532)(452,531)(453,530)(454,529)(455,528)(456,527)(457,526)(458,525)(459,524)(460,523)(461,522)(462,521)(463,520)(464,519)(465,518)(466,517)(467,516)(468,515)(469,514)(470,513)(471,512)(472,511)(473,510)(474,509)(475,508)(476,507)(477,506)(478,505)(479,504)(480,503)(481,502)(482,501)(483,500)(484,499)(485,498)(486,497)(487,496)(488,495)(489,494)(490,493)(491,492)
Conjugacy classes & character table
2916 conjugacy classes. The character table is too large to display.
Relationships
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11652, 8);
Finite Group Databasebeta