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D809 #13108092
Aliases
Splittings
Subgroups
4 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 2 generators on 809 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);(2,809)(3,808)(4,807)(5,806)(6,805)(7,804)(8,803)(9,802)(10,801)(11,800)(12,799)(13,798)(14,797)(15,796)(16,795)(17,794)(18,793)(19,792)(20,791)(21,790)(22,789)(23,788)(24,787)(25,786)(26,785)(27,784)(28,783)(29,782)(30,781)(31,780)(32,779)(33,778)(34,777)(35,776)(36,775)(37,774)(38,773)(39,772)(40,771)(41,770)(42,769)(43,768)(44,767)(45,766)(46,765)(47,764)(48,763)(49,762)(50,761)(51,760)(52,759)(53,758)(54,757)(55,756)(56,755)(57,754)(58,753)(59,752)(60,751)(61,750)(62,749)(63,748)(64,747)(65,746)(66,745)(67,744)(68,743)(69,742)(70,741)(71,740)(72,739)(73,738)(74,737)(75,736)(76,735)(77,734)(78,733)(79,732)(80,731)(81,730)(82,729)(83,728)(84,727)(85,726)(86,725)(87,724)(88,723)(89,722)(90,721)(91,720)(92,719)(93,718)(94,717)(95,716)(96,715)(97,714)(98,713)(99,712)(100,711)(101,710)(102,709)(103,708)(104,707)(105,706)(106,705)(107,704)(108,703)(109,702)(110,701)(111,700)(112,699)(113,698)(114,697)(115,696)(116,695)(117,694)(118,693)(119,692)(120,691)(121,690)(122,689)(123,688)(124,687)(125,686)(126,685)(127,684)(128,683)(129,682)(130,681)(131,680)(132,679)(133,678)(134,677)(135,676)(136,675)(137,674)(138,673)(139,672)(140,671)(141,670)(142,669)(143,668)(144,667)(145,666)(146,665)(147,664)(148,663)(149,662)(150,661)(151,660)(152,659)(153,658)(154,657)(155,656)(156,655)(157,654)(158,653)(159,652)(160,651)(161,650)(162,649)(163,648)(164,647)(165,646)(166,645)(167,644)(168,643)(169,642)(170,641)(171,640)(172,639)(173,638)(174,637)(175,636)(176,635)(177,634)(178,633)(179,632)(180,631)(181,630)(182,629)(183,628)(184,627)(185,626)(186,625)(187,624)(188,623)(189,622)(190,621)(191,620)(192,619)(193,618)(194,617)(195,616)(196,615)(197,614)(198,613)(199,612)(200,611)(201,610)(202,609)(203,608)(204,607)(205,606)(206,605)(207,604)(208,603)(209,602)(210,601)(211,600)(212,599)(213,598)(214,597)(215,596)(216,595)(217,594)(218,593)(219,592)(220,591)(221,590)(222,589)(223,588)(224,587)(225,586)(226,585)(227,584)(228,583)(229,582)(230,581)(231,580)(232,579)(233,578)(234,577)(235,576)(236,575)(237,574)(238,573)(239,572)(240,571)(241,570)(242,569)(243,568)(244,567)(245,566)(246,565)(247,564)(248,563)(249,562)(250,561)(251,560)(252,559)(253,558)(254,557)(255,556)(256,555)(257,554)(258,553)(259,552)(260,551)(261,550)(262,549)(263,548)(264,547)(265,546)(266,545)(267,544)(268,543)(269,542)(270,541)(271,540)(272,539)(273,538)(274,537)(275,536)(276,535)(277,534)(278,533)(279,532)(280,531)(281,530)(282,529)(283,528)(284,527)(285,526)(286,525)(287,524)(288,523)(289,522)(290,521)(291,520)(292,519)(293,518)(294,517)(295,516)(296,515)(297,514)(298,513)(299,512)(300,511)(301,510)(302,509)(303,508)(304,507)(305,506)(306,505)(307,504)(308,503)(309,502)(310,501)(311,500)(312,499)(313,498)(314,497)(315,496)(316,495)(317,494)(318,493)(319,492)(320,491)(321,490)(322,489)(323,488)(324,487)(325,486)(326,485)(327,484)(328,483)(329,482)(330,481)(331,480)(332,479)(333,478)(334,477)(335,476)(336,475)(337,474)(338,473)(339,472)(340,471)(341,470)(342,469)(343,468)(344,467)(345,466)(346,465)(347,464)(348,463)(349,462)(350,461)(351,460)(352,459)(353,458)(354,457)(355,456)(356,455)(357,454)(358,453)(359,452)(360,451)(361,450)(362,449)(363,448)(364,447)(365,446)(366,445)(367,444)(368,443)(369,442)(370,441)(371,440)(372,439)(373,438)(374,437)(375,436)(376,435)(377,434)(378,433)(379,432)(380,431)(381,430)(382,429)(383,428)(384,427)(385,426)(386,425)(387,424)(388,423)(389,422)(390,421)(391,420)(392,419)(393,418)(394,417)(395,416)(396,415)(397,414)(398,413)(399,412)(400,411)(401,410)(402,409)(403,408)(404,407)(405,406)
Polycyclic presentation:
2,809|b^a=b^808
Conjugacy classes & character table
406 conjugacy classes — view the full character table.
Relationships
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1618, 1);
Finite Group Databasebeta