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D13379 #40999353
Aliases
Splittings
Subgroups
8 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 2 generators on 804 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);(2,17)(3,16)(4,15)(5,14)(6,13)(7,12)(8,11)(9,10)(19,804)(20,803)(21,802)(22,801)(23,800)(24,799)(25,798)(26,797)(27,796)(28,795)(29,794)(30,793)(31,792)(32,791)(33,790)(34,789)(35,788)(36,787)(37,786)(38,785)(39,784)(40,783)(41,782)(42,781)(43,780)(44,779)(45,778)(46,777)(47,776)(48,775)(49,774)(50,773)(51,772)(52,771)(53,770)(54,769)(55,768)(56,767)(57,766)(58,765)(59,764)(60,763)(61,762)(62,761)(63,760)(64,759)(65,758)(66,757)(67,756)(68,755)(69,754)(70,753)(71,752)(72,751)(73,750)(74,749)(75,748)(76,747)(77,746)(78,745)(79,744)(80,743)(81,742)(82,741)(83,740)(84,739)(85,738)(86,737)(87,736)(88,735)(89,734)(90,733)(91,732)(92,731)(93,730)(94,729)(95,728)(96,727)(97,726)(98,725)(99,724)(100,723)(101,722)(102,721)(103,720)(104,719)(105,718)(106,717)(107,716)(108,715)(109,714)(110,713)(111,712)(112,711)(113,710)(114,709)(115,708)(116,707)(117,706)(118,705)(119,704)(120,703)(121,702)(122,701)(123,700)(124,699)(125,698)(126,697)(127,696)(128,695)(129,694)(130,693)(131,692)(132,691)(133,690)(134,689)(135,688)(136,687)(137,686)(138,685)(139,684)(140,683)(141,682)(142,681)(143,680)(144,679)(145,678)(146,677)(147,676)(148,675)(149,674)(150,673)(151,672)(152,671)(153,670)(154,669)(155,668)(156,667)(157,666)(158,665)(159,664)(160,663)(161,662)(162,661)(163,660)(164,659)(165,658)(166,657)(167,656)(168,655)(169,654)(170,653)(171,652)(172,651)(173,650)(174,649)(175,648)(176,647)(177,646)(178,645)(179,644)(180,643)(181,642)(182,641)(183,640)(184,639)(185,638)(186,637)(187,636)(188,635)(189,634)(190,633)(191,632)(192,631)(193,630)(194,629)(195,628)(196,627)(197,626)(198,625)(199,624)(200,623)(201,622)(202,621)(203,620)(204,619)(205,618)(206,617)(207,616)(208,615)(209,614)(210,613)(211,612)(212,611)(213,610)(214,609)(215,608)(216,607)(217,606)(218,605)(219,604)(220,603)(221,602)(222,601)(223,600)(224,599)(225,598)(226,597)(227,596)(228,595)(229,594)(230,593)(231,592)(232,591)(233,590)(234,589)(235,588)(236,587)(237,586)(238,585)(239,584)(240,583)(241,582)(242,581)(243,580)(244,579)(245,578)(246,577)(247,576)(248,575)(249,574)(250,573)(251,572)(252,571)(253,570)(254,569)(255,568)(256,567)(257,566)(258,565)(259,564)(260,563)(261,562)(262,561)(263,560)(264,559)(265,558)(266,557)(267,556)(268,555)(269,554)(270,553)(271,552)(272,551)(273,550)(274,549)(275,548)(276,547)(277,546)(278,545)(279,544)(280,543)(281,542)(282,541)(283,540)(284,539)(285,538)(286,537)(287,536)(288,535)(289,534)(290,533)(291,532)(292,531)(293,530)(294,529)(295,528)(296,527)(297,526)(298,525)(299,524)(300,523)(301,522)(302,521)(303,520)(304,519)(305,518)(306,517)(307,516)(308,515)(309,514)(310,513)(311,512)(312,511)(313,510)(314,509)(315,508)(316,507)(317,506)(318,505)(319,504)(320,503)(321,502)(322,501)(323,500)(324,499)(325,498)(326,497)(327,496)(328,495)(329,494)(330,493)(331,492)(332,491)(333,490)(334,489)(335,488)(336,487)(337,486)(338,485)(339,484)(340,483)(341,482)(342,481)(343,480)(344,479)(345,478)(346,477)(347,476)(348,475)(349,474)(350,473)(351,472)(352,471)(353,470)(354,469)(355,468)(356,467)(357,466)(358,465)(359,464)(360,463)(361,462)(362,461)(363,460)(364,459)(365,458)(366,457)(367,456)(368,455)(369,454)(370,453)(371,452)(372,451)(373,450)(374,449)(375,448)(376,447)(377,446)(378,445)(379,444)(380,443)(381,442)(382,441)(383,440)(384,439)(385,438)(386,437)(387,436)(388,435)(389,434)(390,433)(391,432)(392,431)(393,430)(394,429)(395,428)(396,427)(397,426)(398,425)(399,424)(400,423)(401,422)(402,421)(403,420)(404,419)(405,418)(406,417)(407,416)(408,415)(409,414)(410,413)(411,412)
Polycyclic presentation:
2,17,787|b^a=b^16,c^a=c^786
Conjugacy classes & character table
6691 conjugacy classes. The character table is too large to display.
Relationships
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(26758, 3);
Finite Group Databasebeta