← Prev (#27210658) Next (#27210660) →
D6632 #27210659
Aliases
Splittings
Subgroups
22 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 2 generators on 837 points:
(1,2,3,4,5,6,7,8)(9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,172,173,174,175,176,177,178,179,180,181,182,183,184,185,186,187,188,189,190,191,192,193,194,195,196,197,198,199,200,201,202,203,204,205,206,207,208,209,210,211,212,213,214,215,216,217,218,219,220,221,222,223,224,225,226,227,228,229,230,231,232,233,234,235,236,237,238,239,240,241,242,243,244,245,246,247,248,249,250,251,252,253,254,255,256,257,258,259,260,261,262,263,264,265,266,267,268,269,270,271,272,273,274,275,276,277,278,279,280,281,282,283,284,285,286,287,288,289,290,291,292,293,294,295,296,297,298,299,300,301,302,303,304,305,306,307,308,309,310,311,312,313,314,315,316,317,318,319,320,321,322,323,324,325,326,327,328,329,330,331,332,333,334,335,336,337,338,339,340,341,342,343,344,345,346,347,348,349,350,351,352,353,354,355,356,357,358,359,360,361,362,363,364,365,366,367,368,369,370,371,372,373,374,375,376,377,378,379,380,381,382,383,384,385,386,387,388,389,390,391,392,393,394,395,396,397,398,399,400,401,402,403,404,405,406,407,408,409,410,411,412,413,414,415,416,417,418,419,420,421,422,423,424,425,426,427,428,429,430,431,432,433,434,435,436,437,438,439,440,441,442,443,444,445,446,447,448,449,450,451,452,453,454,455,456,457,458,459,460,461,462,463,464,465,466,467,468,469,470,471,472,473,474,475,476,477,478,479,480,481,482,483,484,485,486,487,488,489,490,491,492,493,494,495,496,497,498,499,500,501,502,503,504,505,506,507,508,509,510,511,512,513,514,515,516,517,518,519,520,521,522,523,524,525,526,527,528,529,530,531,532,533,534,535,536,537,538,539,540,541,542,543,544,545,546,547,548,549,550,551,552,553,554,555,556,557,558,559,560,561,562,563,564,565,566,567,568,569,570,571,572,573,574,575,576,577,578,579,580,581,582,583,584,585,586,587,588,589,590,591,592,593,594,595,596,597,598,599,600,601,602,603,604,605,606,607,608,609,610,611,612,613,614,615,616,617,618,619,620,621,622,623,624,625,626,627,628,629,630,631,632,633,634,635,636,637,638,639,640,641,642,643,644,645,646,647,648,649,650,651,652,653,654,655,656,657,658,659,660,661,662,663,664,665,666,667,668,669,670,671,672,673,674,675,676,677,678,679,680,681,682,683,684,685,686,687,688,689,690,691,692,693,694,695,696,697,698,699,700,701,702,703,704,705,706,707,708,709,710,711,712,713,714,715,716,717,718,719,720,721,722,723,724,725,726,727,728,729,730,731,732,733,734,735,736,737,738,739,740,741,742,743,744,745,746,747,748,749,750,751,752,753,754,755,756,757,758,759,760,761,762,763,764,765,766,767,768,769,770,771,772,773,774,775,776,777,778,779,780,781,782,783,784,785,786,787,788,789,790,791,792,793,794,795,796,797,798,799,800,801,802,803,804,805,806,807,808,809,810,811,812,813,814,815,816,817,818,819,820,821,822,823,824,825,826,827,828,829,830,831,832,833,834,835,836,837);(2,8)(3,7)(4,6)(10,837)(11,836)(12,835)(13,834)(14,833)(15,832)(16,831)(17,830)(18,829)(19,828)(20,827)(21,826)(22,825)(23,824)(24,823)(25,822)(26,821)(27,820)(28,819)(29,818)(30,817)(31,816)(32,815)(33,814)(34,813)(35,812)(36,811)(37,810)(38,809)(39,808)(40,807)(41,806)(42,805)(43,804)(44,803)(45,802)(46,801)(47,800)(48,799)(49,798)(50,797)(51,796)(52,795)(53,794)(54,793)(55,792)(56,791)(57,790)(58,789)(59,788)(60,787)(61,786)(62,785)(63,784)(64,783)(65,782)(66,781)(67,780)(68,779)(69,778)(70,777)(71,776)(72,775)(73,774)(74,773)(75,772)(76,771)(77,770)(78,769)(79,768)(80,767)(81,766)(82,765)(83,764)(84,763)(85,762)(86,761)(87,760)(88,759)(89,758)(90,757)(91,756)(92,755)(93,754)(94,753)(95,752)(96,751)(97,750)(98,749)(99,748)(100,747)(101,746)(102,745)(103,744)(104,743)(105,742)(106,741)(107,740)(108,739)(109,738)(110,737)(111,736)(112,735)(113,734)(114,733)(115,732)(116,731)(117,730)(118,729)(119,728)(120,727)(121,726)(122,725)(123,724)(124,723)(125,722)(126,721)(127,720)(128,719)(129,718)(130,717)(131,716)(132,715)(133,714)(134,713)(135,712)(136,711)(137,710)(138,709)(139,708)(140,707)(141,706)(142,705)(143,704)(144,703)(145,702)(146,701)(147,700)(148,699)(149,698)(150,697)(151,696)(152,695)(153,694)(154,693)(155,692)(156,691)(157,690)(158,689)(159,688)(160,687)(161,686)(162,685)(163,684)(164,683)(165,682)(166,681)(167,680)(168,679)(169,678)(170,677)(171,676)(172,675)(173,674)(174,673)(175,672)(176,671)(177,670)(178,669)(179,668)(180,667)(181,666)(182,665)(183,664)(184,663)(185,662)(186,661)(187,660)(188,659)(189,658)(190,657)(191,656)(192,655)(193,654)(194,653)(195,652)(196,651)(197,650)(198,649)(199,648)(200,647)(201,646)(202,645)(203,644)(204,643)(205,642)(206,641)(207,640)(208,639)(209,638)(210,637)(211,636)(212,635)(213,634)(214,633)(215,632)(216,631)(217,630)(218,629)(219,628)(220,627)(221,626)(222,625)(223,624)(224,623)(225,622)(226,621)(227,620)(228,619)(229,618)(230,617)(231,616)(232,615)(233,614)(234,613)(235,612)(236,611)(237,610)(238,609)(239,608)(240,607)(241,606)(242,605)(243,604)(244,603)(245,602)(246,601)(247,600)(248,599)(249,598)(250,597)(251,596)(252,595)(253,594)(254,593)(255,592)(256,591)(257,590)(258,589)(259,588)(260,587)(261,586)(262,585)(263,584)(264,583)(265,582)(266,581)(267,580)(268,579)(269,578)(270,577)(271,576)(272,575)(273,574)(274,573)(275,572)(276,571)(277,570)(278,569)(279,568)(280,567)(281,566)(282,565)(283,564)(284,563)(285,562)(286,561)(287,560)(288,559)(289,558)(290,557)(291,556)(292,555)(293,554)(294,553)(295,552)(296,551)(297,550)(298,549)(299,548)(300,547)(301,546)(302,545)(303,544)(304,543)(305,542)(306,541)(307,540)(308,539)(309,538)(310,537)(311,536)(312,535)(313,534)(314,533)(315,532)(316,531)(317,530)(318,529)(319,528)(320,527)(321,526)(322,525)(323,524)(324,523)(325,522)(326,521)(327,520)(328,519)(329,518)(330,517)(331,516)(332,515)(333,514)(334,513)(335,512)(336,511)(337,510)(338,509)(339,508)(340,507)(341,506)(342,505)(343,504)(344,503)(345,502)(346,501)(347,500)(348,499)(349,498)(350,497)(351,496)(352,495)(353,494)(354,493)(355,492)(356,491)(357,490)(358,489)(359,488)(360,487)(361,486)(362,485)(363,484)(364,483)(365,482)(366,481)(367,480)(368,479)(369,478)(370,477)(371,476)(372,475)(373,474)(374,473)(375,472)(376,471)(377,470)(378,469)(379,468)(380,467)(381,466)(382,465)(383,464)(384,463)(385,462)(386,461)(387,460)(388,459)(389,458)(390,457)(391,456)(392,455)(393,454)(394,453)(395,452)(396,451)(397,450)(398,449)(399,448)(400,447)(401,446)(402,445)(403,444)(404,443)(405,442)(406,441)(407,440)(408,439)(409,438)(410,437)(411,436)(412,435)(413,434)(414,433)(415,432)(416,431)(417,430)(418,429)(419,428)(420,427)(421,426)(422,425)(423,424)
Polycyclic presentation:
2^4,829|c^2=d,b^a=bc,c^a=cd,e^a=e^828,c^b=cd,e^b=e^828
Conjugacy classes & character table
3319 conjugacy classes. The character table is too large to display.
Relationships
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13264, 26);
Finite Group Databasebeta