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Dic961 #16838644
Aliases
Splittings
Subgroups
9 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 2 generators on 965 points:
(1,2)(3,4)(5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,172,173,174,175,176,177,178,179,180,181,182,183,184,185,186,187,188,189,190,191,192,193,194,195,196,197,198,199,200,201,202,203,204,205,206,207,208,209,210,211,212,213,214,215,216,217,218,219,220,221,222,223,224,225,226,227,228,229,230,231,232,233,234,235,236,237,238,239,240,241,242,243,244,245,246,247,248,249,250,251,252,253,254,255,256,257,258,259,260,261,262,263,264,265,266,267,268,269,270,271,272,273,274,275,276,277,278,279,280,281,282,283,284,285,286,287,288,289,290,291,292,293,294,295,296,297,298,299,300,301,302,303,304,305,306,307,308,309,310,311,312,313,314,315,316,317,318,319,320,321,322,323,324,325,326,327,328,329,330,331,332,333,334,335,336,337,338,339,340,341,342,343,344,345,346,347,348,349,350,351,352,353,354,355,356,357,358,359,360,361,362,363,364,365,366,367,368,369,370,371,372,373,374,375,376,377,378,379,380,381,382,383,384,385,386,387,388,389,390,391,392,393,394,395,396,397,398,399,400,401,402,403,404,405,406,407,408,409,410,411,412,413,414,415,416,417,418,419,420,421,422,423,424,425,426,427,428,429,430,431,432,433,434,435,436,437,438,439,440,441,442,443,444,445,446,447,448,449,450,451,452,453,454,455,456,457,458,459,460,461,462,463,464,465,466,467,468,469,470,471,472,473,474,475,476,477,478,479,480,481,482,483,484,485,486,487,488,489,490,491,492,493,494,495,496,497,498,499,500,501,502,503,504,505,506,507,508,509,510,511,512,513,514,515,516,517,518,519,520,521,522,523,524,525,526,527,528,529,530,531,532,533,534,535,536,537,538,539,540,541,542,543,544,545,546,547,548,549,550,551,552,553,554,555,556,557,558,559,560,561,562,563,564,565,566,567,568,569,570,571,572,573,574,575,576,577,578,579,580,581,582,583,584,585,586,587,588,589,590,591,592,593,594,595,596,597,598,599,600,601,602,603,604,605,606,607,608,609,610,611,612,613,614,615,616,617,618,619,620,621,622,623,624,625,626,627,628,629,630,631,632,633,634,635,636,637,638,639,640,641,642,643,644,645,646,647,648,649,650,651,652,653,654,655,656,657,658,659,660,661,662,663,664,665,666,667,668,669,670,671,672,673,674,675,676,677,678,679,680,681,682,683,684,685,686,687,688,689,690,691,692,693,694,695,696,697,698,699,700,701,702,703,704,705,706,707,708,709,710,711,712,713,714,715,716,717,718,719,720,721,722,723,724,725,726,727,728,729,730,731,732,733,734,735,736,737,738,739,740,741,742,743,744,745,746,747,748,749,750,751,752,753,754,755,756,757,758,759,760,761,762,763,764,765,766,767,768,769,770,771,772,773,774,775,776,777,778,779,780,781,782,783,784,785,786,787,788,789,790,791,792,793,794,795,796,797,798,799,800,801,802,803,804,805,806,807,808,809,810,811,812,813,814,815,816,817,818,819,820,821,822,823,824,825,826,827,828,829,830,831,832,833,834,835,836,837,838,839,840,841,842,843,844,845,846,847,848,849,850,851,852,853,854,855,856,857,858,859,860,861,862,863,864,865,866,867,868,869,870,871,872,873,874,875,876,877,878,879,880,881,882,883,884,885,886,887,888,889,890,891,892,893,894,895,896,897,898,899,900,901,902,903,904,905,906,907,908,909,910,911,912,913,914,915,916,917,918,919,920,921,922,923,924,925,926,927,928,929,930,931,932,933,934,935,936,937,938,939,940,941,942,943,944,945,946,947,948,949,950,951,952,953,954,955,956,957,958,959,960,961,962,963,964,965);(1,3,2,4)(6,965)(7,964)(8,963)(9,962)(10,961)(11,960)(12,959)(13,958)(14,957)(15,956)(16,955)(17,954)(18,953)(19,952)(20,951)(21,950)(22,949)(23,948)(24,947)(25,946)(26,945)(27,944)(28,943)(29,942)(30,941)(31,940)(32,939)(33,938)(34,937)(35,936)(36,935)(37,934)(38,933)(39,932)(40,931)(41,930)(42,929)(43,928)(44,927)(45,926)(46,925)(47,924)(48,923)(49,922)(50,921)(51,920)(52,919)(53,918)(54,917)(55,916)(56,915)(57,914)(58,913)(59,912)(60,911)(61,910)(62,909)(63,908)(64,907)(65,906)(66,905)(67,904)(68,903)(69,902)(70,901)(71,900)(72,899)(73,898)(74,897)(75,896)(76,895)(77,894)(78,893)(79,892)(80,891)(81,890)(82,889)(83,888)(84,887)(85,886)(86,885)(87,884)(88,883)(89,882)(90,881)(91,880)(92,879)(93,878)(94,877)(95,876)(96,875)(97,874)(98,873)(99,872)(100,871)(101,870)(102,869)(103,868)(104,867)(105,866)(106,865)(107,864)(108,863)(109,862)(110,861)(111,860)(112,859)(113,858)(114,857)(115,856)(116,855)(117,854)(118,853)(119,852)(120,851)(121,850)(122,849)(123,848)(124,847)(125,846)(126,845)(127,844)(128,843)(129,842)(130,841)(131,840)(132,839)(133,838)(134,837)(135,836)(136,835)(137,834)(138,833)(139,832)(140,831)(141,830)(142,829)(143,828)(144,827)(145,826)(146,825)(147,824)(148,823)(149,822)(150,821)(151,820)(152,819)(153,818)(154,817)(155,816)(156,815)(157,814)(158,813)(159,812)(160,811)(161,810)(162,809)(163,808)(164,807)(165,806)(166,805)(167,804)(168,803)(169,802)(170,801)(171,800)(172,799)(173,798)(174,797)(175,796)(176,795)(177,794)(178,793)(179,792)(180,791)(181,790)(182,789)(183,788)(184,787)(185,786)(186,785)(187,784)(188,783)(189,782)(190,781)(191,780)(192,779)(193,778)(194,777)(195,776)(196,775)(197,774)(198,773)(199,772)(200,771)(201,770)(202,769)(203,768)(204,767)(205,766)(206,765)(207,764)(208,763)(209,762)(210,761)(211,760)(212,759)(213,758)(214,757)(215,756)(216,755)(217,754)(218,753)(219,752)(220,751)(221,750)(222,749)(223,748)(224,747)(225,746)(226,745)(227,744)(228,743)(229,742)(230,741)(231,740)(232,739)(233,738)(234,737)(235,736)(236,735)(237,734)(238,733)(239,732)(240,731)(241,730)(242,729)(243,728)(244,727)(245,726)(246,725)(247,724)(248,723)(249,722)(250,721)(251,720)(252,719)(253,718)(254,717)(255,716)(256,715)(257,714)(258,713)(259,712)(260,711)(261,710)(262,709)(263,708)(264,707)(265,706)(266,705)(267,704)(268,703)(269,702)(270,701)(271,700)(272,699)(273,698)(274,697)(275,696)(276,695)(277,694)(278,693)(279,692)(280,691)(281,690)(282,689)(283,688)(284,687)(285,686)(286,685)(287,684)(288,683)(289,682)(290,681)(291,680)(292,679)(293,678)(294,677)(295,676)(296,675)(297,674)(298,673)(299,672)(300,671)(301,670)(302,669)(303,668)(304,667)(305,666)(306,665)(307,664)(308,663)(309,662)(310,661)(311,660)(312,659)(313,658)(314,657)(315,656)(316,655)(317,654)(318,653)(319,652)(320,651)(321,650)(322,649)(323,648)(324,647)(325,646)(326,645)(327,644)(328,643)(329,642)(330,641)(331,640)(332,639)(333,638)(334,637)(335,636)(336,635)(337,634)(338,633)(339,632)(340,631)(341,630)(342,629)(343,628)(344,627)(345,626)(346,625)(347,624)(348,623)(349,622)(350,621)(351,620)(352,619)(353,618)(354,617)(355,616)(356,615)(357,614)(358,613)(359,612)(360,611)(361,610)(362,609)(363,608)(364,607)(365,606)(366,605)(367,604)(368,603)(369,602)(370,601)(371,600)(372,599)(373,598)(374,597)(375,596)(376,595)(377,594)(378,593)(379,592)(380,591)(381,590)(382,589)(383,588)(384,587)(385,586)(386,585)(387,584)(388,583)(389,582)(390,581)(391,580)(392,579)(393,578)(394,577)(395,576)(396,575)(397,574)(398,573)(399,572)(400,571)(401,570)(402,569)(403,568)(404,567)(405,566)(406,565)(407,564)(408,563)(409,562)(410,561)(411,560)(412,559)(413,558)(414,557)(415,556)(416,555)(417,554)(418,553)(419,552)(420,551)(421,550)(422,549)(423,548)(424,547)(425,546)(426,545)(427,544)(428,543)(429,542)(430,541)(431,540)(432,539)(433,538)(434,537)(435,536)(436,535)(437,534)(438,533)(439,532)(440,531)(441,530)(442,529)(443,528)(444,527)(445,526)(446,525)(447,524)(448,523)(449,522)(450,521)(451,520)(452,519)(453,518)(454,517)(455,516)(456,515)(457,514)(458,513)(459,512)(460,511)(461,510)(462,509)(463,508)(464,507)(465,506)(466,505)(467,504)(468,503)(469,502)(470,501)(471,500)(472,499)(473,498)(474,497)(475,496)(476,495)(477,494)(478,493)(479,492)(480,491)(481,490)(482,489)(483,488)(484,487)(485,486)
Polycyclic presentation:
2,31,2,31|a^2=c,b^31=d^30,b^a=b^30d,d^a=d^30
Conjugacy classes & character table
964 conjugacy classes — view the full character table.
Relationships
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3844, 2);
Finite Group Databasebeta