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D9427 #34038151
Aliases
Splittings
Subgroups
8 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 2 generators on 868 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,172,173,174,175,176,177,178,179,180,181,182,183,184,185,186,187,188,189,190,191,192,193,194,195,196,197,198,199,200,201,202,203,204,205,206,207,208,209,210,211,212,213,214,215,216,217,218,219,220,221,222,223,224,225,226,227,228,229,230,231,232,233,234,235,236,237,238,239,240,241,242,243,244,245,246,247,248,249,250,251,252,253,254,255,256,257,258,259,260,261,262,263,264,265,266,267,268,269,270,271,272,273,274,275,276,277,278,279,280,281,282,283,284,285,286,287,288,289,290,291,292,293,294,295,296,297,298,299,300,301,302,303,304,305,306,307,308,309,310,311,312,313,314,315,316,317,318,319,320,321,322,323,324,325,326,327,328,329,330,331,332,333,334,335,336,337,338,339,340,341,342,343,344,345,346,347,348,349,350,351,352,353,354,355,356,357,358,359,360,361,362,363,364,365,366,367,368,369,370,371,372,373,374,375,376,377,378,379,380,381,382,383,384,385,386,387,388,389,390,391,392,393,394,395,396,397,398,399,400,401,402,403,404,405,406,407,408,409,410,411,412,413,414,415,416,417,418,419,420,421,422,423,424,425,426,427,428,429,430,431,432,433,434,435,436,437,438,439,440,441,442,443,444,445,446,447,448,449,450,451,452,453,454,455,456,457,458,459,460,461,462,463,464,465,466,467,468,469,470,471,472,473,474,475,476,477,478,479,480,481,482,483,484,485,486,487,488,489,490,491,492,493,494,495,496,497,498,499,500,501,502,503,504,505,506,507,508,509,510,511,512,513,514,515,516,517,518,519,520,521,522,523,524,525,526,527,528,529,530,531,532,533,534,535,536,537,538,539,540,541,542,543,544,545,546,547,548,549,550,551,552,553,554,555,556,557,558,559,560,561,562,563,564,565,566,567,568,569,570,571,572,573,574,575,576,577,578,579,580,581,582,583,584,585,586,587,588,589,590,591,592,593,594,595,596,597,598,599,600,601,602,603,604,605,606,607,608,609,610,611,612,613,614,615,616,617,618,619,620,621,622,623,624,625,626,627,628,629,630,631,632,633,634,635,636,637,638,639,640,641,642,643,644,645,646,647,648,649,650,651,652,653,654,655,656,657,658,659,660,661,662,663,664,665,666,667,668,669,670,671,672,673,674,675,676,677,678,679,680,681,682,683,684,685,686,687,688,689,690,691,692,693,694,695,696,697,698,699,700,701,702,703,704,705,706,707,708,709,710,711,712,713,714,715,716,717,718,719,720,721,722,723,724,725,726,727,728,729,730,731,732,733,734,735,736,737,738,739,740,741,742,743,744,745,746,747,748,749,750,751,752,753,754,755,756,757,758,759,760,761,762,763,764,765,766,767,768,769,770,771,772,773,774,775,776,777,778,779,780,781,782,783,784,785,786,787,788,789,790,791,792,793,794,795,796,797,798,799,800,801,802,803,804,805,806,807,808,809,810,811,812,813,814,815,816,817,818,819,820,821,822,823,824,825,826,827,828,829,830,831,832,833,834,835,836,837,838,839,840,841,842,843,844,845,846,847,848,849,850,851,852,853,854,855,856,857,858,859,860,861,862,863,864,865,866,867,868);(2,11)(3,10)(4,9)(5,8)(6,7)(13,868)(14,867)(15,866)(16,865)(17,864)(18,863)(19,862)(20,861)(21,860)(22,859)(23,858)(24,857)(25,856)(26,855)(27,854)(28,853)(29,852)(30,851)(31,850)(32,849)(33,848)(34,847)(35,846)(36,845)(37,844)(38,843)(39,842)(40,841)(41,840)(42,839)(43,838)(44,837)(45,836)(46,835)(47,834)(48,833)(49,832)(50,831)(51,830)(52,829)(53,828)(54,827)(55,826)(56,825)(57,824)(58,823)(59,822)(60,821)(61,820)(62,819)(63,818)(64,817)(65,816)(66,815)(67,814)(68,813)(69,812)(70,811)(71,810)(72,809)(73,808)(74,807)(75,806)(76,805)(77,804)(78,803)(79,802)(80,801)(81,800)(82,799)(83,798)(84,797)(85,796)(86,795)(87,794)(88,793)(89,792)(90,791)(91,790)(92,789)(93,788)(94,787)(95,786)(96,785)(97,784)(98,783)(99,782)(100,781)(101,780)(102,779)(103,778)(104,777)(105,776)(106,775)(107,774)(108,773)(109,772)(110,771)(111,770)(112,769)(113,768)(114,767)(115,766)(116,765)(117,764)(118,763)(119,762)(120,761)(121,760)(122,759)(123,758)(124,757)(125,756)(126,755)(127,754)(128,753)(129,752)(130,751)(131,750)(132,749)(133,748)(134,747)(135,746)(136,745)(137,744)(138,743)(139,742)(140,741)(141,740)(142,739)(143,738)(144,737)(145,736)(146,735)(147,734)(148,733)(149,732)(150,731)(151,730)(152,729)(153,728)(154,727)(155,726)(156,725)(157,724)(158,723)(159,722)(160,721)(161,720)(162,719)(163,718)(164,717)(165,716)(166,715)(167,714)(168,713)(169,712)(170,711)(171,710)(172,709)(173,708)(174,707)(175,706)(176,705)(177,704)(178,703)(179,702)(180,701)(181,700)(182,699)(183,698)(184,697)(185,696)(186,695)(187,694)(188,693)(189,692)(190,691)(191,690)(192,689)(193,688)(194,687)(195,686)(196,685)(197,684)(198,683)(199,682)(200,681)(201,680)(202,679)(203,678)(204,677)(205,676)(206,675)(207,674)(208,673)(209,672)(210,671)(211,670)(212,669)(213,668)(214,667)(215,666)(216,665)(217,664)(218,663)(219,662)(220,661)(221,660)(222,659)(223,658)(224,657)(225,656)(226,655)(227,654)(228,653)(229,652)(230,651)(231,650)(232,649)(233,648)(234,647)(235,646)(236,645)(237,644)(238,643)(239,642)(240,641)(241,640)(242,639)(243,638)(244,637)(245,636)(246,635)(247,634)(248,633)(249,632)(250,631)(251,630)(252,629)(253,628)(254,627)(255,626)(256,625)(257,624)(258,623)(259,622)(260,621)(261,620)(262,619)(263,618)(264,617)(265,616)(266,615)(267,614)(268,613)(269,612)(270,611)(271,610)(272,609)(273,608)(274,607)(275,606)(276,605)(277,604)(278,603)(279,602)(280,601)(281,600)(282,599)(283,598)(284,597)(285,596)(286,595)(287,594)(288,593)(289,592)(290,591)(291,590)(292,589)(293,588)(294,587)(295,586)(296,585)(297,584)(298,583)(299,582)(300,581)(301,580)(302,579)(303,578)(304,577)(305,576)(306,575)(307,574)(308,573)(309,572)(310,571)(311,570)(312,569)(313,568)(314,567)(315,566)(316,565)(317,564)(318,563)(319,562)(320,561)(321,560)(322,559)(323,558)(324,557)(325,556)(326,555)(327,554)(328,553)(329,552)(330,551)(331,550)(332,549)(333,548)(334,547)(335,546)(336,545)(337,544)(338,543)(339,542)(340,541)(341,540)(342,539)(343,538)(344,537)(345,536)(346,535)(347,534)(348,533)(349,532)(350,531)(351,530)(352,529)(353,528)(354,527)(355,526)(356,525)(357,524)(358,523)(359,522)(360,521)(361,520)(362,519)(363,518)(364,517)(365,516)(366,515)(367,514)(368,513)(369,512)(370,511)(371,510)(372,509)(373,508)(374,507)(375,506)(376,505)(377,504)(378,503)(379,502)(380,501)(381,500)(382,499)(383,498)(384,497)(385,496)(386,495)(387,494)(388,493)(389,492)(390,491)(391,490)(392,489)(393,488)(394,487)(395,486)(396,485)(397,484)(398,483)(399,482)(400,481)(401,480)(402,479)(403,478)(404,477)(405,476)(406,475)(407,474)(408,473)(409,472)(410,471)(411,470)(412,469)(413,468)(414,467)(415,466)(416,465)(417,464)(418,463)(419,462)(420,461)(421,460)(422,459)(423,458)(424,457)(425,456)(426,455)(427,454)(428,453)(429,452)(430,451)(431,450)(432,449)(433,448)(434,447)(435,446)(436,445)(437,444)(438,443)(439,442)(440,441)
Polycyclic presentation:
2,11,857|b^a=b^10,c^a=c^856
Conjugacy classes & character table
4715 conjugacy classes. The character table is too large to display.
Relationships
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18854, 3);
Finite Group Databasebeta