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Aliases
Splittings
Subgroups
20 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 2 generators on 828 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);(4,7)(5,6)(9,828)(10,827)(11,826)(12,825)(13,824)(14,823)(15,822)(16,821)(17,820)(18,819)(19,818)(20,817)(21,816)(22,815)(23,814)(24,813)(25,812)(26,811)(27,810)(28,809)(29,808)(30,807)(31,806)(32,805)(33,804)(34,803)(35,802)(36,801)(37,800)(38,799)(39,798)(40,797)(41,796)(42,795)(43,794)(44,793)(45,792)(46,791)(47,790)(48,789)(49,788)(50,787)(51,786)(52,785)(53,784)(54,783)(55,782)(56,781)(57,780)(58,779)(59,778)(60,777)(61,776)(62,775)(63,774)(64,773)(65,772)(66,771)(67,770)(68,769)(69,768)(70,767)(71,766)(72,765)(73,764)(74,763)(75,762)(76,761)(77,760)(78,759)(79,758)(80,757)(81,756)(82,755)(83,754)(84,753)(85,752)(86,751)(87,750)(88,749)(89,748)(90,747)(91,746)(92,745)(93,744)(94,743)(95,742)(96,741)(97,740)(98,739)(99,738)(100,737)(101,736)(102,735)(103,734)(104,733)(105,732)(106,731)(107,730)(108,729)(109,728)(110,727)(111,726)(112,725)(113,724)(114,723)(115,722)(116,721)(117,720)(118,719)(119,718)(120,717)(121,716)(122,715)(123,714)(124,713)(125,712)(126,711)(127,710)(128,709)(129,708)(130,707)(131,706)(132,705)(133,704)(134,703)(135,702)(136,701)(137,700)(138,699)(139,698)(140,697)(141,696)(142,695)(143,694)(144,693)(145,692)(146,691)(147,690)(148,689)(149,688)(150,687)(151,686)(152,685)(153,684)(154,683)(155,682)(156,681)(157,680)(158,679)(159,678)(160,677)(161,676)(162,675)(163,674)(164,673)(165,672)(166,671)(167,670)(168,669)(169,668)(170,667)(171,666)(172,665)(173,664)(174,663)(175,662)(176,661)(177,660)(178,659)(179,658)(180,657)(181,656)(182,655)(183,654)(184,653)(185,652)(186,651)(187,650)(188,649)(189,648)(190,647)(191,646)(192,645)(193,644)(194,643)(195,642)(196,641)(197,640)(198,639)(199,638)(200,637)(201,636)(202,635)(203,634)(204,633)(205,632)(206,631)(207,630)(208,629)(209,628)(210,627)(211,626)(212,625)(213,624)(214,623)(215,622)(216,621)(217,620)(218,619)(219,618)(220,617)(221,616)(222,615)(223,614)(224,613)(225,612)(226,611)(227,610)(228,609)(229,608)(230,607)(231,606)(232,605)(233,604)(234,603)(235,602)(236,601)(237,600)(238,599)(239,598)(240,597)(241,596)(242,595)(243,594)(244,593)(245,592)(246,591)(247,590)(248,589)(249,588)(250,587)(251,586)(252,585)(253,584)(254,583)(255,582)(256,581)(257,580)(258,579)(259,578)(260,577)(261,576)(262,575)(263,574)(264,573)(265,572)(266,571)(267,570)(268,569)(269,568)(270,567)(271,566)(272,565)(273,564)(274,563)(275,562)(276,561)(277,560)(278,559)(279,558)(280,557)(281,556)(282,555)(283,554)(284,553)(285,552)(286,551)(287,550)(288,549)(289,548)(290,547)(291,546)(292,545)(293,544)(294,543)(295,542)(296,541)(297,540)(298,539)(299,538)(300,537)(301,536)(302,535)(303,534)(304,533)(305,532)(306,531)(307,530)(308,529)(309,528)(310,527)(311,526)(312,525)(313,524)(314,523)(315,522)(316,521)(317,520)(318,519)(319,518)(320,517)(321,516)(322,515)(323,514)(324,513)(325,512)(326,511)(327,510)(328,509)(329,508)(330,507)(331,506)(332,505)(333,504)(334,503)(335,502)(336,501)(337,500)(338,499)(339,498)(340,497)(341,496)(342,495)(343,494)(344,493)(345,492)(346,491)(347,490)(348,489)(349,488)(350,487)(351,486)(352,485)(353,484)(354,483)(355,482)(356,481)(357,480)(358,479)(359,478)(360,477)(361,476)(362,475)(363,474)(364,473)(365,472)(366,471)(367,470)(368,469)(369,468)(370,467)(371,466)(372,465)(373,464)(374,463)(375,462)(376,461)(377,460)(378,459)(379,458)(380,457)(381,456)(382,455)(383,454)(384,453)(385,452)(386,451)(387,450)(388,449)(389,448)(390,447)(391,446)(392,445)(393,444)(394,443)(395,442)(396,441)(397,440)(398,439)(399,438)(400,437)(401,436)(402,435)(403,434)(404,433)(405,432)(406,431)(407,430)(408,429)(409,428)(410,427)(411,426)(412,425)(413,424)(414,423)(415,422)(416,421)(417,420)(418,419)
Conjugacy classes & character table
4108 conjugacy classes. The character table is too large to display.
Relationships
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16420, 18);
Finite Group Databasebeta