← Prev (#26014540) Next (#26014542) →
Aliases
Splittings
Subgroups
20 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 2 generators on 942 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);(4,5)(7,942)(8,941)(9,940)(10,939)(11,938)(12,937)(13,936)(14,935)(15,934)(16,933)(17,932)(18,931)(19,930)(20,929)(21,928)(22,927)(23,926)(24,925)(25,924)(26,923)(27,922)(28,921)(29,920)(30,919)(31,918)(32,917)(33,916)(34,915)(35,914)(36,913)(37,912)(38,911)(39,910)(40,909)(41,908)(42,907)(43,906)(44,905)(45,904)(46,903)(47,902)(48,901)(49,900)(50,899)(51,898)(52,897)(53,896)(54,895)(55,894)(56,893)(57,892)(58,891)(59,890)(60,889)(61,888)(62,887)(63,886)(64,885)(65,884)(66,883)(67,882)(68,881)(69,880)(70,879)(71,878)(72,877)(73,876)(74,875)(75,874)(76,873)(77,872)(78,871)(79,870)(80,869)(81,868)(82,867)(83,866)(84,865)(85,864)(86,863)(87,862)(88,861)(89,860)(90,859)(91,858)(92,857)(93,856)(94,855)(95,854)(96,853)(97,852)(98,851)(99,850)(100,849)(101,848)(102,847)(103,846)(104,845)(105,844)(106,843)(107,842)(108,841)(109,840)(110,839)(111,838)(112,837)(113,836)(114,835)(115,834)(116,833)(117,832)(118,831)(119,830)(120,829)(121,828)(122,827)(123,826)(124,825)(125,824)(126,823)(127,822)(128,821)(129,820)(130,819)(131,818)(132,817)(133,816)(134,815)(135,814)(136,813)(137,812)(138,811)(139,810)(140,809)(141,808)(142,807)(143,806)(144,805)(145,804)(146,803)(147,802)(148,801)(149,800)(150,799)(151,798)(152,797)(153,796)(154,795)(155,794)(156,793)(157,792)(158,791)(159,790)(160,789)(161,788)(162,787)(163,786)(164,785)(165,784)(166,783)(167,782)(168,781)(169,780)(170,779)(171,778)(172,777)(173,776)(174,775)(175,774)(176,773)(177,772)(178,771)(179,770)(180,769)(181,768)(182,767)(183,766)(184,765)(185,764)(186,763)(187,762)(188,761)(189,760)(190,759)(191,758)(192,757)(193,756)(194,755)(195,754)(196,753)(197,752)(198,751)(199,750)(200,749)(201,748)(202,747)(203,746)(204,745)(205,744)(206,743)(207,742)(208,741)(209,740)(210,739)(211,738)(212,737)(213,736)(214,735)(215,734)(216,733)(217,732)(218,731)(219,730)(220,729)(221,728)(222,727)(223,726)(224,725)(225,724)(226,723)(227,722)(228,721)(229,720)(230,719)(231,718)(232,717)(233,716)(234,715)(235,714)(236,713)(237,712)(238,711)(239,710)(240,709)(241,708)(242,707)(243,706)(244,705)(245,704)(246,703)(247,702)(248,701)(249,700)(250,699)(251,698)(252,697)(253,696)(254,695)(255,694)(256,693)(257,692)(258,691)(259,690)(260,689)(261,688)(262,687)(263,686)(264,685)(265,684)(266,683)(267,682)(268,681)(269,680)(270,679)(271,678)(272,677)(273,676)(274,675)(275,674)(276,673)(277,672)(278,671)(279,670)(280,669)(281,668)(282,667)(283,666)(284,665)(285,664)(286,663)(287,662)(288,661)(289,660)(290,659)(291,658)(292,657)(293,656)(294,655)(295,654)(296,653)(297,652)(298,651)(299,650)(300,649)(301,648)(302,647)(303,646)(304,645)(305,644)(306,643)(307,642)(308,641)(309,640)(310,639)(311,638)(312,637)(313,636)(314,635)(315,634)(316,633)(317,632)(318,631)(319,630)(320,629)(321,628)(322,627)(323,626)(324,625)(325,624)(326,623)(327,622)(328,621)(329,620)(330,619)(331,618)(332,617)(333,616)(334,615)(335,614)(336,613)(337,612)(338,611)(339,610)(340,609)(341,608)(342,607)(343,606)(344,605)(345,604)(346,603)(347,602)(348,601)(349,600)(350,599)(351,598)(352,597)(353,596)(354,595)(355,594)(356,593)(357,592)(358,591)(359,590)(360,589)(361,588)(362,587)(363,586)(364,585)(365,584)(366,583)(367,582)(368,581)(369,580)(370,579)(371,578)(372,577)(373,576)(374,575)(375,574)(376,573)(377,572)(378,571)(379,570)(380,569)(381,568)(382,567)(383,566)(384,565)(385,564)(386,563)(387,562)(388,561)(389,560)(390,559)(391,558)(392,557)(393,556)(394,555)(395,554)(396,553)(397,552)(398,551)(399,550)(400,549)(401,548)(402,547)(403,546)(404,545)(405,544)(406,543)(407,542)(408,541)(409,540)(410,539)(411,538)(412,537)(413,536)(414,535)(415,534)(416,533)(417,532)(418,531)(419,530)(420,529)(421,528)(422,527)(423,526)(424,525)(425,524)(426,523)(427,522)(428,521)(429,520)(430,519)(431,518)(432,517)(433,516)(434,515)(435,514)(436,513)(437,512)(438,511)(439,510)(440,509)(441,508)(442,507)(443,506)(444,505)(445,504)(446,503)(447,502)(448,501)(449,500)(450,499)(451,498)(452,497)(453,496)(454,495)(455,494)(456,493)(457,492)(458,491)(459,490)(460,489)(461,488)(462,487)(463,486)(464,485)(465,484)(466,483)(467,482)(468,481)(469,480)(470,479)(471,478)(472,477)(473,476)(474,475)
Conjugacy classes & character table
2814 conjugacy classes. The character table is too large to display.
Relationships
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11244, 16);
Finite Group Databasebeta