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Aliases
Splittings
Subgroups
30 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 2 generators on 1008 points:
(1,2)(3,4,5,6,7,8,9,10,11)(12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,172,173,174,175,176,177,178,179,180,181,182,183,184,185,186,187,188,189,190,191,192,193,194,195,196,197,198,199,200,201,202,203,204,205,206,207,208,209,210,211,212,213,214,215,216,217,218,219,220,221,222,223,224,225,226,227,228,229,230,231,232,233,234,235,236,237,238,239,240,241,242,243,244,245,246,247,248,249,250,251,252,253,254,255,256,257,258,259,260,261,262,263,264,265,266,267,268,269,270,271,272,273,274,275,276,277,278,279,280,281,282,283,284,285,286,287,288,289,290,291,292,293,294,295,296,297,298,299,300,301,302,303,304,305,306,307,308,309,310,311,312,313,314,315,316,317,318,319,320,321,322,323,324,325,326,327,328,329,330,331,332,333,334,335,336,337,338,339,340,341,342,343,344,345,346,347,348,349,350,351,352,353,354,355,356,357,358,359,360,361,362,363,364,365,366,367,368,369,370,371,372,373,374,375,376,377,378,379,380,381,382,383,384,385,386,387,388,389,390,391,392,393,394,395,396,397,398,399,400,401,402,403,404,405,406,407,408,409,410,411,412,413,414,415,416,417,418,419,420,421,422,423,424,425,426,427,428,429,430,431,432,433,434,435,436,437,438,439,440,441,442,443,444,445,446,447,448,449,450,451,452,453,454,455,456,457,458,459,460,461,462,463,464,465,466,467,468,469,470,471,472,473,474,475,476,477,478,479,480,481,482,483,484,485,486,487,488,489,490,491,492,493,494,495,496,497,498,499,500,501,502,503,504,505,506,507,508,509,510,511,512,513,514,515,516,517,518,519,520,521,522,523,524,525,526,527,528,529,530,531,532,533,534,535,536,537,538,539,540,541,542,543,544,545,546,547,548,549,550,551,552,553,554,555,556,557,558,559,560,561,562,563,564,565,566,567,568,569,570,571,572,573,574,575,576,577,578,579,580,581,582,583,584,585,586,587,588,589,590,591,592,593,594,595,596,597,598,599,600,601,602,603,604,605,606,607,608,609,610,611,612,613,614,615,616,617,618,619,620,621,622,623,624,625,626,627,628,629,630,631,632,633,634,635,636,637,638,639,640,641,642,643,644,645,646,647,648,649,650,651,652,653,654,655,656,657,658,659,660,661,662,663,664,665,666,667,668,669,670,671,672,673,674,675,676,677,678,679,680,681,682,683,684,685,686,687,688,689,690,691,692,693,694,695,696,697,698,699,700,701,702,703,704,705,706,707,708,709,710,711,712,713,714,715,716,717,718,719,720,721,722,723,724,725,726,727,728,729,730,731,732,733,734,735,736,737,738,739,740,741,742,743,744,745,746,747,748,749,750,751,752,753,754,755,756,757,758,759,760,761,762,763,764,765,766,767,768,769,770,771,772,773,774,775,776,777,778,779,780,781,782,783,784,785,786,787,788,789,790,791,792,793,794,795,796,797,798,799,800,801,802,803,804,805,806,807,808,809,810,811,812,813,814,815,816,817,818,819,820,821,822,823,824,825,826,827,828,829,830,831,832,833,834,835,836,837,838,839,840,841,842,843,844,845,846,847,848,849,850,851,852,853,854,855,856,857,858,859,860,861,862,863,864,865,866,867,868,869,870,871,872,873,874,875,876,877,878,879,880,881,882,883,884,885,886,887,888,889,890,891,892,893,894,895,896,897,898,899,900,901,902,903,904,905,906,907,908,909,910,911,912,913,914,915,916,917,918,919,920,921,922,923,924,925,926,927,928,929,930,931,932,933,934,935,936,937,938,939,940,941,942,943,944,945,946,947,948,949,950,951,952,953,954,955,956,957,958,959,960,961,962,963,964,965,966,967,968,969,970,971,972,973,974,975,976,977,978,979,980,981,982,983,984,985,986,987,988,989,990,991,992,993,994,995,996,997,998,999,1000,1001,1002,1003,1004,1005,1006,1007,1008);(4,11)(5,10)(6,9)(7,8)(13,1008)(14,1007)(15,1006)(16,1005)(17,1004)(18,1003)(19,1002)(20,1001)(21,1000)(22,999)(23,998)(24,997)(25,996)(26,995)(27,994)(28,993)(29,992)(30,991)(31,990)(32,989)(33,988)(34,987)(35,986)(36,985)(37,984)(38,983)(39,982)(40,981)(41,980)(42,979)(43,978)(44,977)(45,976)(46,975)(47,974)(48,973)(49,972)(50,971)(51,970)(52,969)(53,968)(54,967)(55,966)(56,965)(57,964)(58,963)(59,962)(60,961)(61,960)(62,959)(63,958)(64,957)(65,956)(66,955)(67,954)(68,953)(69,952)(70,951)(71,950)(72,949)(73,948)(74,947)(75,946)(76,945)(77,944)(78,943)(79,942)(80,941)(81,940)(82,939)(83,938)(84,937)(85,936)(86,935)(87,934)(88,933)(89,932)(90,931)(91,930)(92,929)(93,928)(94,927)(95,926)(96,925)(97,924)(98,923)(99,922)(100,921)(101,920)(102,919)(103,918)(104,917)(105,916)(106,915)(107,914)(108,913)(109,912)(110,911)(111,910)(112,909)(113,908)(114,907)(115,906)(116,905)(117,904)(118,903)(119,902)(120,901)(121,900)(122,899)(123,898)(124,897)(125,896)(126,895)(127,894)(128,893)(129,892)(130,891)(131,890)(132,889)(133,888)(134,887)(135,886)(136,885)(137,884)(138,883)(139,882)(140,881)(141,880)(142,879)(143,878)(144,877)(145,876)(146,875)(147,874)(148,873)(149,872)(150,871)(151,870)(152,869)(153,868)(154,867)(155,866)(156,865)(157,864)(158,863)(159,862)(160,861)(161,860)(162,859)(163,858)(164,857)(165,856)(166,855)(167,854)(168,853)(169,852)(170,851)(171,850)(172,849)(173,848)(174,847)(175,846)(176,845)(177,844)(178,843)(179,842)(180,841)(181,840)(182,839)(183,838)(184,837)(185,836)(186,835)(187,834)(188,833)(189,832)(190,831)(191,830)(192,829)(193,828)(194,827)(195,826)(196,825)(197,824)(198,823)(199,822)(200,821)(201,820)(202,819)(203,818)(204,817)(205,816)(206,815)(207,814)(208,813)(209,812)(210,811)(211,810)(212,809)(213,808)(214,807)(215,806)(216,805)(217,804)(218,803)(219,802)(220,801)(221,800)(222,799)(223,798)(224,797)(225,796)(226,795)(227,794)(228,793)(229,792)(230,791)(231,790)(232,789)(233,788)(234,787)(235,786)(236,785)(237,784)(238,783)(239,782)(240,781)(241,780)(242,779)(243,778)(244,777)(245,776)(246,775)(247,774)(248,773)(249,772)(250,771)(251,770)(252,769)(253,768)(254,767)(255,766)(256,765)(257,764)(258,763)(259,762)(260,761)(261,760)(262,759)(263,758)(264,757)(265,756)(266,755)(267,754)(268,753)(269,752)(270,751)(271,750)(272,749)(273,748)(274,747)(275,746)(276,745)(277,744)(278,743)(279,742)(280,741)(281,740)(282,739)(283,738)(284,737)(285,736)(286,735)(287,734)(288,733)(289,732)(290,731)(291,730)(292,729)(293,728)(294,727)(295,726)(296,725)(297,724)(298,723)(299,722)(300,721)(301,720)(302,719)(303,718)(304,717)(305,716)(306,715)(307,714)(308,713)(309,712)(310,711)(311,710)(312,709)(313,708)(314,707)(315,706)(316,705)(317,704)(318,703)(319,702)(320,701)(321,700)(322,699)(323,698)(324,697)(325,696)(326,695)(327,694)(328,693)(329,692)(330,691)(331,690)(332,689)(333,688)(334,687)(335,686)(336,685)(337,684)(338,683)(339,682)(340,681)(341,680)(342,679)(343,678)(344,677)(345,676)(346,675)(347,674)(348,673)(349,672)(350,671)(351,670)(352,669)(353,668)(354,667)(355,666)(356,665)(357,664)(358,663)(359,662)(360,661)(361,660)(362,659)(363,658)(364,657)(365,656)(366,655)(367,654)(368,653)(369,652)(370,651)(371,650)(372,649)(373,648)(374,647)(375,646)(376,645)(377,644)(378,643)(379,642)(380,641)(381,640)(382,639)(383,638)(384,637)(385,636)(386,635)(387,634)(388,633)(389,632)(390,631)(391,630)(392,629)(393,628)(394,627)(395,626)(396,625)(397,624)(398,623)(399,622)(400,621)(401,620)(402,619)(403,618)(404,617)(405,616)(406,615)(407,614)(408,613)(409,612)(410,611)(411,610)(412,609)(413,608)(414,607)(415,606)(416,605)(417,604)(418,603)(419,602)(420,601)(421,600)(422,599)(423,598)(424,597)(425,596)(426,595)(427,594)(428,593)(429,592)(430,591)(431,590)(432,589)(433,588)(434,587)(435,586)(436,585)(437,584)(438,583)(439,582)(440,581)(441,580)(442,579)(443,578)(444,577)(445,576)(446,575)(447,574)(448,573)(449,572)(450,571)(451,570)(452,569)(453,568)(454,567)(455,566)(456,565)(457,564)(458,563)(459,562)(460,561)(461,560)(462,559)(463,558)(464,557)(465,556)(466,555)(467,554)(468,553)(469,552)(470,551)(471,550)(472,549)(473,548)(474,547)(475,546)(476,545)(477,544)(478,543)(479,542)(480,541)(481,540)(482,539)(483,538)(484,537)(485,536)(486,535)(487,534)(488,533)(489,532)(490,531)(491,530)(492,529)(493,528)(494,527)(495,526)(496,525)(497,524)(498,523)(499,522)(500,521)(501,520)(502,519)(503,518)(504,517)(505,516)(506,515)(507,514)(508,513)(509,512)(510,511)
Conjugacy classes & character table
8976 conjugacy classes. The character table is too large to display.
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(35892, 16);
Finite Group Databasebeta