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Aliases
Splittings
Subgroups
20 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 2 generators on 818 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);(4,7)(5,6)(9,818)(10,817)(11,816)(12,815)(13,814)(14,813)(15,812)(16,811)(17,810)(18,809)(19,808)(20,807)(21,806)(22,805)(23,804)(24,803)(25,802)(26,801)(27,800)(28,799)(29,798)(30,797)(31,796)(32,795)(33,794)(34,793)(35,792)(36,791)(37,790)(38,789)(39,788)(40,787)(41,786)(42,785)(43,784)(44,783)(45,782)(46,781)(47,780)(48,779)(49,778)(50,777)(51,776)(52,775)(53,774)(54,773)(55,772)(56,771)(57,770)(58,769)(59,768)(60,767)(61,766)(62,765)(63,764)(64,763)(65,762)(66,761)(67,760)(68,759)(69,758)(70,757)(71,756)(72,755)(73,754)(74,753)(75,752)(76,751)(77,750)(78,749)(79,748)(80,747)(81,746)(82,745)(83,744)(84,743)(85,742)(86,741)(87,740)(88,739)(89,738)(90,737)(91,736)(92,735)(93,734)(94,733)(95,732)(96,731)(97,730)(98,729)(99,728)(100,727)(101,726)(102,725)(103,724)(104,723)(105,722)(106,721)(107,720)(108,719)(109,718)(110,717)(111,716)(112,715)(113,714)(114,713)(115,712)(116,711)(117,710)(118,709)(119,708)(120,707)(121,706)(122,705)(123,704)(124,703)(125,702)(126,701)(127,700)(128,699)(129,698)(130,697)(131,696)(132,695)(133,694)(134,693)(135,692)(136,691)(137,690)(138,689)(139,688)(140,687)(141,686)(142,685)(143,684)(144,683)(145,682)(146,681)(147,680)(148,679)(149,678)(150,677)(151,676)(152,675)(153,674)(154,673)(155,672)(156,671)(157,670)(158,669)(159,668)(160,667)(161,666)(162,665)(163,664)(164,663)(165,662)(166,661)(167,660)(168,659)(169,658)(170,657)(171,656)(172,655)(173,654)(174,653)(175,652)(176,651)(177,650)(178,649)(179,648)(180,647)(181,646)(182,645)(183,644)(184,643)(185,642)(186,641)(187,640)(188,639)(189,638)(190,637)(191,636)(192,635)(193,634)(194,633)(195,632)(196,631)(197,630)(198,629)(199,628)(200,627)(201,626)(202,625)(203,624)(204,623)(205,622)(206,621)(207,620)(208,619)(209,618)(210,617)(211,616)(212,615)(213,614)(214,613)(215,612)(216,611)(217,610)(218,609)(219,608)(220,607)(221,606)(222,605)(223,604)(224,603)(225,602)(226,601)(227,600)(228,599)(229,598)(230,597)(231,596)(232,595)(233,594)(234,593)(235,592)(236,591)(237,590)(238,589)(239,588)(240,587)(241,586)(242,585)(243,584)(244,583)(245,582)(246,581)(247,580)(248,579)(249,578)(250,577)(251,576)(252,575)(253,574)(254,573)(255,572)(256,571)(257,570)(258,569)(259,568)(260,567)(261,566)(262,565)(263,564)(264,563)(265,562)(266,561)(267,560)(268,559)(269,558)(270,557)(271,556)(272,555)(273,554)(274,553)(275,552)(276,551)(277,550)(278,549)(279,548)(280,547)(281,546)(282,545)(283,544)(284,543)(285,542)(286,541)(287,540)(288,539)(289,538)(290,537)(291,536)(292,535)(293,534)(294,533)(295,532)(296,531)(297,530)(298,529)(299,528)(300,527)(301,526)(302,525)(303,524)(304,523)(305,522)(306,521)(307,520)(308,519)(309,518)(310,517)(311,516)(312,515)(313,514)(314,513)(315,512)(316,511)(317,510)(318,509)(319,508)(320,507)(321,506)(322,505)(323,504)(324,503)(325,502)(326,501)(327,500)(328,499)(329,498)(330,497)(331,496)(332,495)(333,494)(334,493)(335,492)(336,491)(337,490)(338,489)(339,488)(340,487)(341,486)(342,485)(343,484)(344,483)(345,482)(346,481)(347,480)(348,479)(349,478)(350,477)(351,476)(352,475)(353,474)(354,473)(355,472)(356,471)(357,470)(358,469)(359,468)(360,467)(361,466)(362,465)(363,464)(364,463)(365,462)(366,461)(367,460)(368,459)(369,458)(370,457)(371,456)(372,455)(373,454)(374,453)(375,452)(376,451)(377,450)(378,449)(379,448)(380,447)(381,446)(382,445)(383,444)(384,443)(385,442)(386,441)(387,440)(388,439)(389,438)(390,437)(391,436)(392,435)(393,434)(394,433)(395,432)(396,431)(397,430)(398,429)(399,428)(400,427)(401,426)(402,425)(403,424)(404,423)(405,422)(406,421)(407,420)(408,419)(409,418)(410,417)(411,416)(412,415)(413,414)
Conjugacy classes & character table
4058 conjugacy classes. The character table is too large to display.
Relationships
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16220, 13);
Finite Group Databasebeta