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Dic4285 #30686209
Aliases
Splittings
Subgroups
12 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 2 generators on 866 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);(1,3,2,4)(6,9)(7,8)(11,866)(12,865)(13,864)(14,863)(15,862)(16,861)(17,860)(18,859)(19,858)(20,857)(21,856)(22,855)(23,854)(24,853)(25,852)(26,851)(27,850)(28,849)(29,848)(30,847)(31,846)(32,845)(33,844)(34,843)(35,842)(36,841)(37,840)(38,839)(39,838)(40,837)(41,836)(42,835)(43,834)(44,833)(45,832)(46,831)(47,830)(48,829)(49,828)(50,827)(51,826)(52,825)(53,824)(54,823)(55,822)(56,821)(57,820)(58,819)(59,818)(60,817)(61,816)(62,815)(63,814)(64,813)(65,812)(66,811)(67,810)(68,809)(69,808)(70,807)(71,806)(72,805)(73,804)(74,803)(75,802)(76,801)(77,800)(78,799)(79,798)(80,797)(81,796)(82,795)(83,794)(84,793)(85,792)(86,791)(87,790)(88,789)(89,788)(90,787)(91,786)(92,785)(93,784)(94,783)(95,782)(96,781)(97,780)(98,779)(99,778)(100,777)(101,776)(102,775)(103,774)(104,773)(105,772)(106,771)(107,770)(108,769)(109,768)(110,767)(111,766)(112,765)(113,764)(114,763)(115,762)(116,761)(117,760)(118,759)(119,758)(120,757)(121,756)(122,755)(123,754)(124,753)(125,752)(126,751)(127,750)(128,749)(129,748)(130,747)(131,746)(132,745)(133,744)(134,743)(135,742)(136,741)(137,740)(138,739)(139,738)(140,737)(141,736)(142,735)(143,734)(144,733)(145,732)(146,731)(147,730)(148,729)(149,728)(150,727)(151,726)(152,725)(153,724)(154,723)(155,722)(156,721)(157,720)(158,719)(159,718)(160,717)(161,716)(162,715)(163,714)(164,713)(165,712)(166,711)(167,710)(168,709)(169,708)(170,707)(171,706)(172,705)(173,704)(174,703)(175,702)(176,701)(177,700)(178,699)(179,698)(180,697)(181,696)(182,695)(183,694)(184,693)(185,692)(186,691)(187,690)(188,689)(189,688)(190,687)(191,686)(192,685)(193,684)(194,683)(195,682)(196,681)(197,680)(198,679)(199,678)(200,677)(201,676)(202,675)(203,674)(204,673)(205,672)(206,671)(207,670)(208,669)(209,668)(210,667)(211,666)(212,665)(213,664)(214,663)(215,662)(216,661)(217,660)(218,659)(219,658)(220,657)(221,656)(222,655)(223,654)(224,653)(225,652)(226,651)(227,650)(228,649)(229,648)(230,647)(231,646)(232,645)(233,644)(234,643)(235,642)(236,641)(237,640)(238,639)(239,638)(240,637)(241,636)(242,635)(243,634)(244,633)(245,632)(246,631)(247,630)(248,629)(249,628)(250,627)(251,626)(252,625)(253,624)(254,623)(255,622)(256,621)(257,620)(258,619)(259,618)(260,617)(261,616)(262,615)(263,614)(264,613)(265,612)(266,611)(267,610)(268,609)(269,608)(270,607)(271,606)(272,605)(273,604)(274,603)(275,602)(276,601)(277,600)(278,599)(279,598)(280,597)(281,596)(282,595)(283,594)(284,593)(285,592)(286,591)(287,590)(288,589)(289,588)(290,587)(291,586)(292,585)(293,584)(294,583)(295,582)(296,581)(297,580)(298,579)(299,578)(300,577)(301,576)(302,575)(303,574)(304,573)(305,572)(306,571)(307,570)(308,569)(309,568)(310,567)(311,566)(312,565)(313,564)(314,563)(315,562)(316,561)(317,560)(318,559)(319,558)(320,557)(321,556)(322,555)(323,554)(324,553)(325,552)(326,551)(327,550)(328,549)(329,548)(330,547)(331,546)(332,545)(333,544)(334,543)(335,542)(336,541)(337,540)(338,539)(339,538)(340,537)(341,536)(342,535)(343,534)(344,533)(345,532)(346,531)(347,530)(348,529)(349,528)(350,527)(351,526)(352,525)(353,524)(354,523)(355,522)(356,521)(357,520)(358,519)(359,518)(360,517)(361,516)(362,515)(363,514)(364,513)(365,512)(366,511)(367,510)(368,509)(369,508)(370,507)(371,506)(372,505)(373,504)(374,503)(375,502)(376,501)(377,500)(378,499)(379,498)(380,497)(381,496)(382,495)(383,494)(384,493)(385,492)(386,491)(387,490)(388,489)(389,488)(390,487)(391,486)(392,485)(393,484)(394,483)(395,482)(396,481)(397,480)(398,479)(399,478)(400,477)(401,476)(402,475)(403,474)(404,473)(405,472)(406,471)(407,470)(408,469)(409,468)(410,467)(411,466)(412,465)(413,464)(414,463)(415,462)(416,461)(417,460)(418,459)(419,458)(420,457)(421,456)(422,455)(423,454)(424,453)(425,452)(426,451)(427,450)(428,449)(429,448)(430,447)(431,446)(432,445)(433,444)(434,443)(435,442)(436,441)(437,440)(438,439)
Polycyclic presentation:
2,5,857,2|a^2=d,b^a=b^4,c^a=c^856
Conjugacy classes & character table
4288 conjugacy classes. The character table is too large to display.
Relationships
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17140, 4);
Finite Group Databasebeta