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Dic7929 #44540514
Aliases
Splittings
Subgroups
18 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 2 generators on 894 points:
(1,2)(3,4)(5,6,7,8,9,10,11,12,13)(14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,172,173,174,175,176,177,178,179,180,181,182,183,184,185,186,187,188,189,190,191,192,193,194,195,196,197,198,199,200,201,202,203,204,205,206,207,208,209,210,211,212,213,214,215,216,217,218,219,220,221,222,223,224,225,226,227,228,229,230,231,232,233,234,235,236,237,238,239,240,241,242,243,244,245,246,247,248,249,250,251,252,253,254,255,256,257,258,259,260,261,262,263,264,265,266,267,268,269,270,271,272,273,274,275,276,277,278,279,280,281,282,283,284,285,286,287,288,289,290,291,292,293,294,295,296,297,298,299,300,301,302,303,304,305,306,307,308,309,310,311,312,313,314,315,316,317,318,319,320,321,322,323,324,325,326,327,328,329,330,331,332,333,334,335,336,337,338,339,340,341,342,343,344,345,346,347,348,349,350,351,352,353,354,355,356,357,358,359,360,361,362,363,364,365,366,367,368,369,370,371,372,373,374,375,376,377,378,379,380,381,382,383,384,385,386,387,388,389,390,391,392,393,394,395,396,397,398,399,400,401,402,403,404,405,406,407,408,409,410,411,412,413,414,415,416,417,418,419,420,421,422,423,424,425,426,427,428,429,430,431,432,433,434,435,436,437,438,439,440,441,442,443,444,445,446,447,448,449,450,451,452,453,454,455,456,457,458,459,460,461,462,463,464,465,466,467,468,469,470,471,472,473,474,475,476,477,478,479,480,481,482,483,484,485,486,487,488,489,490,491,492,493,494,495,496,497,498,499,500,501,502,503,504,505,506,507,508,509,510,511,512,513,514,515,516,517,518,519,520,521,522,523,524,525,526,527,528,529,530,531,532,533,534,535,536,537,538,539,540,541,542,543,544,545,546,547,548,549,550,551,552,553,554,555,556,557,558,559,560,561,562,563,564,565,566,567,568,569,570,571,572,573,574,575,576,577,578,579,580,581,582,583,584,585,586,587,588,589,590,591,592,593,594,595,596,597,598,599,600,601,602,603,604,605,606,607,608,609,610,611,612,613,614,615,616,617,618,619,620,621,622,623,624,625,626,627,628,629,630,631,632,633,634,635,636,637,638,639,640,641,642,643,644,645,646,647,648,649,650,651,652,653,654,655,656,657,658,659,660,661,662,663,664,665,666,667,668,669,670,671,672,673,674,675,676,677,678,679,680,681,682,683,684,685,686,687,688,689,690,691,692,693,694,695,696,697,698,699,700,701,702,703,704,705,706,707,708,709,710,711,712,713,714,715,716,717,718,719,720,721,722,723,724,725,726,727,728,729,730,731,732,733,734,735,736,737,738,739,740,741,742,743,744,745,746,747,748,749,750,751,752,753,754,755,756,757,758,759,760,761,762,763,764,765,766,767,768,769,770,771,772,773,774,775,776,777,778,779,780,781,782,783,784,785,786,787,788,789,790,791,792,793,794,795,796,797,798,799,800,801,802,803,804,805,806,807,808,809,810,811,812,813,814,815,816,817,818,819,820,821,822,823,824,825,826,827,828,829,830,831,832,833,834,835,836,837,838,839,840,841,842,843,844,845,846,847,848,849,850,851,852,853,854,855,856,857,858,859,860,861,862,863,864,865,866,867,868,869,870,871,872,873,874,875,876,877,878,879,880,881,882,883,884,885,886,887,888,889,890,891,892,893,894);(1,3,2,4)(6,13)(7,12)(8,11)(9,10)(15,894)(16,893)(17,892)(18,891)(19,890)(20,889)(21,888)(22,887)(23,886)(24,885)(25,884)(26,883)(27,882)(28,881)(29,880)(30,879)(31,878)(32,877)(33,876)(34,875)(35,874)(36,873)(37,872)(38,871)(39,870)(40,869)(41,868)(42,867)(43,866)(44,865)(45,864)(46,863)(47,862)(48,861)(49,860)(50,859)(51,858)(52,857)(53,856)(54,855)(55,854)(56,853)(57,852)(58,851)(59,850)(60,849)(61,848)(62,847)(63,846)(64,845)(65,844)(66,843)(67,842)(68,841)(69,840)(70,839)(71,838)(72,837)(73,836)(74,835)(75,834)(76,833)(77,832)(78,831)(79,830)(80,829)(81,828)(82,827)(83,826)(84,825)(85,824)(86,823)(87,822)(88,821)(89,820)(90,819)(91,818)(92,817)(93,816)(94,815)(95,814)(96,813)(97,812)(98,811)(99,810)(100,809)(101,808)(102,807)(103,806)(104,805)(105,804)(106,803)(107,802)(108,801)(109,800)(110,799)(111,798)(112,797)(113,796)(114,795)(115,794)(116,793)(117,792)(118,791)(119,790)(120,789)(121,788)(122,787)(123,786)(124,785)(125,784)(126,783)(127,782)(128,781)(129,780)(130,779)(131,778)(132,777)(133,776)(134,775)(135,774)(136,773)(137,772)(138,771)(139,770)(140,769)(141,768)(142,767)(143,766)(144,765)(145,764)(146,763)(147,762)(148,761)(149,760)(150,759)(151,758)(152,757)(153,756)(154,755)(155,754)(156,753)(157,752)(158,751)(159,750)(160,749)(161,748)(162,747)(163,746)(164,745)(165,744)(166,743)(167,742)(168,741)(169,740)(170,739)(171,738)(172,737)(173,736)(174,735)(175,734)(176,733)(177,732)(178,731)(179,730)(180,729)(181,728)(182,727)(183,726)(184,725)(185,724)(186,723)(187,722)(188,721)(189,720)(190,719)(191,718)(192,717)(193,716)(194,715)(195,714)(196,713)(197,712)(198,711)(199,710)(200,709)(201,708)(202,707)(203,706)(204,705)(205,704)(206,703)(207,702)(208,701)(209,700)(210,699)(211,698)(212,697)(213,696)(214,695)(215,694)(216,693)(217,692)(218,691)(219,690)(220,689)(221,688)(222,687)(223,686)(224,685)(225,684)(226,683)(227,682)(228,681)(229,680)(230,679)(231,678)(232,677)(233,676)(234,675)(235,674)(236,673)(237,672)(238,671)(239,670)(240,669)(241,668)(242,667)(243,666)(244,665)(245,664)(246,663)(247,662)(248,661)(249,660)(250,659)(251,658)(252,657)(253,656)(254,655)(255,654)(256,653)(257,652)(258,651)(259,650)(260,649)(261,648)(262,647)(263,646)(264,645)(265,644)(266,643)(267,642)(268,641)(269,640)(270,639)(271,638)(272,637)(273,636)(274,635)(275,634)(276,633)(277,632)(278,631)(279,630)(280,629)(281,628)(282,627)(283,626)(284,625)(285,624)(286,623)(287,622)(288,621)(289,620)(290,619)(291,618)(292,617)(293,616)(294,615)(295,614)(296,613)(297,612)(298,611)(299,610)(300,609)(301,608)(302,607)(303,606)(304,605)(305,604)(306,603)(307,602)(308,601)(309,600)(310,599)(311,598)(312,597)(313,596)(314,595)(315,594)(316,593)(317,592)(318,591)(319,590)(320,589)(321,588)(322,587)(323,586)(324,585)(325,584)(326,583)(327,582)(328,581)(329,580)(330,579)(331,578)(332,577)(333,576)(334,575)(335,574)(336,573)(337,572)(338,571)(339,570)(340,569)(341,568)(342,567)(343,566)(344,565)(345,564)(346,563)(347,562)(348,561)(349,560)(350,559)(351,558)(352,557)(353,556)(354,555)(355,554)(356,553)(357,552)(358,551)(359,550)(360,549)(361,548)(362,547)(363,546)(364,545)(365,544)(366,543)(367,542)(368,541)(369,540)(370,539)(371,538)(372,537)(373,536)(374,535)(375,534)(376,533)(377,532)(378,531)(379,530)(380,529)(381,528)(382,527)(383,526)(384,525)(385,524)(386,523)(387,522)(388,521)(389,520)(390,519)(391,518)(392,517)(393,516)(394,515)(395,514)(396,513)(397,512)(398,511)(399,510)(400,509)(401,508)(402,507)(403,506)(404,505)(405,504)(406,503)(407,502)(408,501)(409,500)(410,499)(411,498)(412,497)(413,496)(414,495)(415,494)(416,493)(417,492)(418,491)(419,490)(420,489)(421,488)(422,487)(423,486)(424,485)(425,484)(426,483)(427,482)(428,481)(429,480)(430,479)(431,478)(432,477)(433,476)(434,475)(435,474)(436,473)(437,472)(438,471)(439,470)(440,469)(441,468)(442,467)(443,466)(444,465)(445,464)(446,463)(447,462)(448,461)(449,460)(450,459)(451,458)(452,457)(453,456)(454,455)
Polycyclic presentation:
2,3,881,2,3|a^2=d,b^3=e^2,b^a=b^2e,c^a=c^880,e^a=e^2
Conjugacy classes & character table
7932 conjugacy classes. The character table is too large to display.
Relationships
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31716, 4);
Finite Group Databasebeta