← Prev (#30633631) Next (#30633633) →
Aliases
Splittings
Subgroups
20 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 2 generators on 816 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);(4,7)(5,6)(9,816)(10,815)(11,814)(12,813)(13,812)(14,811)(15,810)(16,809)(17,808)(18,807)(19,806)(20,805)(21,804)(22,803)(23,802)(24,801)(25,800)(26,799)(27,798)(28,797)(29,796)(30,795)(31,794)(32,793)(33,792)(34,791)(35,790)(36,789)(37,788)(38,787)(39,786)(40,785)(41,784)(42,783)(43,782)(44,781)(45,780)(46,779)(47,778)(48,777)(49,776)(50,775)(51,774)(52,773)(53,772)(54,771)(55,770)(56,769)(57,768)(58,767)(59,766)(60,765)(61,764)(62,763)(63,762)(64,761)(65,760)(66,759)(67,758)(68,757)(69,756)(70,755)(71,754)(72,753)(73,752)(74,751)(75,750)(76,749)(77,748)(78,747)(79,746)(80,745)(81,744)(82,743)(83,742)(84,741)(85,740)(86,739)(87,738)(88,737)(89,736)(90,735)(91,734)(92,733)(93,732)(94,731)(95,730)(96,729)(97,728)(98,727)(99,726)(100,725)(101,724)(102,723)(103,722)(104,721)(105,720)(106,719)(107,718)(108,717)(109,716)(110,715)(111,714)(112,713)(113,712)(114,711)(115,710)(116,709)(117,708)(118,707)(119,706)(120,705)(121,704)(122,703)(123,702)(124,701)(125,700)(126,699)(127,698)(128,697)(129,696)(130,695)(131,694)(132,693)(133,692)(134,691)(135,690)(136,689)(137,688)(138,687)(139,686)(140,685)(141,684)(142,683)(143,682)(144,681)(145,680)(146,679)(147,678)(148,677)(149,676)(150,675)(151,674)(152,673)(153,672)(154,671)(155,670)(156,669)(157,668)(158,667)(159,666)(160,665)(161,664)(162,663)(163,662)(164,661)(165,660)(166,659)(167,658)(168,657)(169,656)(170,655)(171,654)(172,653)(173,652)(174,651)(175,650)(176,649)(177,648)(178,647)(179,646)(180,645)(181,644)(182,643)(183,642)(184,641)(185,640)(186,639)(187,638)(188,637)(189,636)(190,635)(191,634)(192,633)(193,632)(194,631)(195,630)(196,629)(197,628)(198,627)(199,626)(200,625)(201,624)(202,623)(203,622)(204,621)(205,620)(206,619)(207,618)(208,617)(209,616)(210,615)(211,614)(212,613)(213,612)(214,611)(215,610)(216,609)(217,608)(218,607)(219,606)(220,605)(221,604)(222,603)(223,602)(224,601)(225,600)(226,599)(227,598)(228,597)(229,596)(230,595)(231,594)(232,593)(233,592)(234,591)(235,590)(236,589)(237,588)(238,587)(239,586)(240,585)(241,584)(242,583)(243,582)(244,581)(245,580)(246,579)(247,578)(248,577)(249,576)(250,575)(251,574)(252,573)(253,572)(254,571)(255,570)(256,569)(257,568)(258,567)(259,566)(260,565)(261,564)(262,563)(263,562)(264,561)(265,560)(266,559)(267,558)(268,557)(269,556)(270,555)(271,554)(272,553)(273,552)(274,551)(275,550)(276,549)(277,548)(278,547)(279,546)(280,545)(281,544)(282,543)(283,542)(284,541)(285,540)(286,539)(287,538)(288,537)(289,536)(290,535)(291,534)(292,533)(293,532)(294,531)(295,530)(296,529)(297,528)(298,527)(299,526)(300,525)(301,524)(302,523)(303,522)(304,521)(305,520)(306,519)(307,518)(308,517)(309,516)(310,515)(311,514)(312,513)(313,512)(314,511)(315,510)(316,509)(317,508)(318,507)(319,506)(320,505)(321,504)(322,503)(323,502)(324,501)(325,500)(326,499)(327,498)(328,497)(329,496)(330,495)(331,494)(332,493)(333,492)(334,491)(335,490)(336,489)(337,488)(338,487)(339,486)(340,485)(341,484)(342,483)(343,482)(344,481)(345,480)(346,479)(347,478)(348,477)(349,476)(350,475)(351,474)(352,473)(353,472)(354,471)(355,470)(356,469)(357,468)(358,467)(359,466)(360,465)(361,464)(362,463)(363,462)(364,461)(365,460)(366,459)(367,458)(368,457)(369,456)(370,455)(371,454)(372,453)(373,452)(374,451)(375,450)(376,449)(377,448)(378,447)(379,446)(380,445)(381,444)(382,443)(383,442)(384,441)(385,440)(386,439)(387,438)(388,437)(389,436)(390,435)(391,434)(392,433)(393,432)(394,431)(395,430)(396,429)(397,428)(398,427)(399,426)(400,425)(401,424)(402,423)(403,422)(404,421)(405,420)(406,419)(407,418)(408,417)(409,416)(410,415)(411,414)(412,413)
Conjugacy classes & character table
4048 conjugacy classes. The character table is too large to display.
Relationships
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16180, 13);
Finite Group Databasebeta