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Aliases
Splittings
Subgroups
20 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 2 generators on 830 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);(4,9)(5,8)(6,7)(11,830)(12,829)(13,828)(14,827)(15,826)(16,825)(17,824)(18,823)(19,822)(20,821)(21,820)(22,819)(23,818)(24,817)(25,816)(26,815)(27,814)(28,813)(29,812)(30,811)(31,810)(32,809)(33,808)(34,807)(35,806)(36,805)(37,804)(38,803)(39,802)(40,801)(41,800)(42,799)(43,798)(44,797)(45,796)(46,795)(47,794)(48,793)(49,792)(50,791)(51,790)(52,789)(53,788)(54,787)(55,786)(56,785)(57,784)(58,783)(59,782)(60,781)(61,780)(62,779)(63,778)(64,777)(65,776)(66,775)(67,774)(68,773)(69,772)(70,771)(71,770)(72,769)(73,768)(74,767)(75,766)(76,765)(77,764)(78,763)(79,762)(80,761)(81,760)(82,759)(83,758)(84,757)(85,756)(86,755)(87,754)(88,753)(89,752)(90,751)(91,750)(92,749)(93,748)(94,747)(95,746)(96,745)(97,744)(98,743)(99,742)(100,741)(101,740)(102,739)(103,738)(104,737)(105,736)(106,735)(107,734)(108,733)(109,732)(110,731)(111,730)(112,729)(113,728)(114,727)(115,726)(116,725)(117,724)(118,723)(119,722)(120,721)(121,720)(122,719)(123,718)(124,717)(125,716)(126,715)(127,714)(128,713)(129,712)(130,711)(131,710)(132,709)(133,708)(134,707)(135,706)(136,705)(137,704)(138,703)(139,702)(140,701)(141,700)(142,699)(143,698)(144,697)(145,696)(146,695)(147,694)(148,693)(149,692)(150,691)(151,690)(152,689)(153,688)(154,687)(155,686)(156,685)(157,684)(158,683)(159,682)(160,681)(161,680)(162,679)(163,678)(164,677)(165,676)(166,675)(167,674)(168,673)(169,672)(170,671)(171,670)(172,669)(173,668)(174,667)(175,666)(176,665)(177,664)(178,663)(179,662)(180,661)(181,660)(182,659)(183,658)(184,657)(185,656)(186,655)(187,654)(188,653)(189,652)(190,651)(191,650)(192,649)(193,648)(194,647)(195,646)(196,645)(197,644)(198,643)(199,642)(200,641)(201,640)(202,639)(203,638)(204,637)(205,636)(206,635)(207,634)(208,633)(209,632)(210,631)(211,630)(212,629)(213,628)(214,627)(215,626)(216,625)(217,624)(218,623)(219,622)(220,621)(221,620)(222,619)(223,618)(224,617)(225,616)(226,615)(227,614)(228,613)(229,612)(230,611)(231,610)(232,609)(233,608)(234,607)(235,606)(236,605)(237,604)(238,603)(239,602)(240,601)(241,600)(242,599)(243,598)(244,597)(245,596)(246,595)(247,594)(248,593)(249,592)(250,591)(251,590)(252,589)(253,588)(254,587)(255,586)(256,585)(257,584)(258,583)(259,582)(260,581)(261,580)(262,579)(263,578)(264,577)(265,576)(266,575)(267,574)(268,573)(269,572)(270,571)(271,570)(272,569)(273,568)(274,567)(275,566)(276,565)(277,564)(278,563)(279,562)(280,561)(281,560)(282,559)(283,558)(284,557)(285,556)(286,555)(287,554)(288,553)(289,552)(290,551)(291,550)(292,549)(293,548)(294,547)(295,546)(296,545)(297,544)(298,543)(299,542)(300,541)(301,540)(302,539)(303,538)(304,537)(305,536)(306,535)(307,534)(308,533)(309,532)(310,531)(311,530)(312,529)(313,528)(314,527)(315,526)(316,525)(317,524)(318,523)(319,522)(320,521)(321,520)(322,519)(323,518)(324,517)(325,516)(326,515)(327,514)(328,513)(329,512)(330,511)(331,510)(332,509)(333,508)(334,507)(335,506)(336,505)(337,504)(338,503)(339,502)(340,501)(341,500)(342,499)(343,498)(344,497)(345,496)(346,495)(347,494)(348,493)(349,492)(350,491)(351,490)(352,489)(353,488)(354,487)(355,486)(356,485)(357,484)(358,483)(359,482)(360,481)(361,480)(362,479)(363,478)(364,477)(365,476)(366,475)(367,474)(368,473)(369,472)(370,471)(371,470)(372,469)(373,468)(374,467)(375,466)(376,465)(377,464)(378,463)(379,462)(380,461)(381,460)(382,459)(383,458)(384,457)(385,456)(386,455)(387,454)(388,453)(389,452)(390,451)(391,450)(392,449)(393,448)(394,447)(395,446)(396,445)(397,444)(398,443)(399,442)(400,441)(401,440)(402,439)(403,438)(404,437)(405,436)(406,435)(407,434)(408,433)(409,432)(410,431)(411,430)(412,429)(413,428)(414,427)(415,426)(416,425)(417,424)(418,423)(419,422)(420,421)
Conjugacy classes & character table
5750 conjugacy classes. The character table is too large to display.
Relationships
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22988, 11);
Finite Group Databasebeta