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D967 #14515401
Aliases
Splittings
Subgroups
4 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 2 generators on 967 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,172,173,174,175,176,177,178,179,180,181,182,183,184,185,186,187,188,189,190,191,192,193,194,195,196,197,198,199,200,201,202,203,204,205,206,207,208,209,210,211,212,213,214,215,216,217,218,219,220,221,222,223,224,225,226,227,228,229,230,231,232,233,234,235,236,237,238,239,240,241,242,243,244,245,246,247,248,249,250,251,252,253,254,255,256,257,258,259,260,261,262,263,264,265,266,267,268,269,270,271,272,273,274,275,276,277,278,279,280,281,282,283,284,285,286,287,288,289,290,291,292,293,294,295,296,297,298,299,300,301,302,303,304,305,306,307,308,309,310,311,312,313,314,315,316,317,318,319,320,321,322,323,324,325,326,327,328,329,330,331,332,333,334,335,336,337,338,339,340,341,342,343,344,345,346,347,348,349,350,351,352,353,354,355,356,357,358,359,360,361,362,363,364,365,366,367,368,369,370,371,372,373,374,375,376,377,378,379,380,381,382,383,384,385,386,387,388,389,390,391,392,393,394,395,396,397,398,399,400,401,402,403,404,405,406,407,408,409,410,411,412,413,414,415,416,417,418,419,420,421,422,423,424,425,426,427,428,429,430,431,432,433,434,435,436,437,438,439,440,441,442,443,444,445,446,447,448,449,450,451,452,453,454,455,456,457,458,459,460,461,462,463,464,465,466,467,468,469,470,471,472,473,474,475,476,477,478,479,480,481,482,483,484,485,486,487,488,489,490,491,492,493,494,495,496,497,498,499,500,501,502,503,504,505,506,507,508,509,510,511,512,513,514,515,516,517,518,519,520,521,522,523,524,525,526,527,528,529,530,531,532,533,534,535,536,537,538,539,540,541,542,543,544,545,546,547,548,549,550,551,552,553,554,555,556,557,558,559,560,561,562,563,564,565,566,567,568,569,570,571,572,573,574,575,576,577,578,579,580,581,582,583,584,585,586,587,588,589,590,591,592,593,594,595,596,597,598,599,600,601,602,603,604,605,606,607,608,609,610,611,612,613,614,615,616,617,618,619,620,621,622,623,624,625,626,627,628,629,630,631,632,633,634,635,636,637,638,639,640,641,642,643,644,645,646,647,648,649,650,651,652,653,654,655,656,657,658,659,660,661,662,663,664,665,666,667,668,669,670,671,672,673,674,675,676,677,678,679,680,681,682,683,684,685,686,687,688,689,690,691,692,693,694,695,696,697,698,699,700,701,702,703,704,705,706,707,708,709,710,711,712,713,714,715,716,717,718,719,720,721,722,723,724,725,726,727,728,729,730,731,732,733,734,735,736,737,738,739,740,741,742,743,744,745,746,747,748,749,750,751,752,753,754,755,756,757,758,759,760,761,762,763,764,765,766,767,768,769,770,771,772,773,774,775,776,777,778,779,780,781,782,783,784,785,786,787,788,789,790,791,792,793,794,795,796,797,798,799,800,801,802,803,804,805,806,807,808,809,810,811,812,813,814,815,816,817,818,819,820,821,822,823,824,825,826,827,828,829,830,831,832,833,834,835,836,837,838,839,840,841,842,843,844,845,846,847,848,849,850,851,852,853,854,855,856,857,858,859,860,861,862,863,864,865,866,867,868,869,870,871,872,873,874,875,876,877,878,879,880,881,882,883,884,885,886,887,888,889,890,891,892,893,894,895,896,897,898,899,900,901,902,903,904,905,906,907,908,909,910,911,912,913,914,915,916,917,918,919,920,921,922,923,924,925,926,927,928,929,930,931,932,933,934,935,936,937,938,939,940,941,942,943,944,945,946,947,948,949,950,951,952,953,954,955,956,957,958,959,960,961,962,963,964,965,966,967);(2,967)(3,966)(4,965)(5,964)(6,963)(7,962)(8,961)(9,960)(10,959)(11,958)(12,957)(13,956)(14,955)(15,954)(16,953)(17,952)(18,951)(19,950)(20,949)(21,948)(22,947)(23,946)(24,945)(25,944)(26,943)(27,942)(28,941)(29,940)(30,939)(31,938)(32,937)(33,936)(34,935)(35,934)(36,933)(37,932)(38,931)(39,930)(40,929)(41,928)(42,927)(43,926)(44,925)(45,924)(46,923)(47,922)(48,921)(49,920)(50,919)(51,918)(52,917)(53,916)(54,915)(55,914)(56,913)(57,912)(58,911)(59,910)(60,909)(61,908)(62,907)(63,906)(64,905)(65,904)(66,903)(67,902)(68,901)(69,900)(70,899)(71,898)(72,897)(73,896)(74,895)(75,894)(76,893)(77,892)(78,891)(79,890)(80,889)(81,888)(82,887)(83,886)(84,885)(85,884)(86,883)(87,882)(88,881)(89,880)(90,879)(91,878)(92,877)(93,876)(94,875)(95,874)(96,873)(97,872)(98,871)(99,870)(100,869)(101,868)(102,867)(103,866)(104,865)(105,864)(106,863)(107,862)(108,861)(109,860)(110,859)(111,858)(112,857)(113,856)(114,855)(115,854)(116,853)(117,852)(118,851)(119,850)(120,849)(121,848)(122,847)(123,846)(124,845)(125,844)(126,843)(127,842)(128,841)(129,840)(130,839)(131,838)(132,837)(133,836)(134,835)(135,834)(136,833)(137,832)(138,831)(139,830)(140,829)(141,828)(142,827)(143,826)(144,825)(145,824)(146,823)(147,822)(148,821)(149,820)(150,819)(151,818)(152,817)(153,816)(154,815)(155,814)(156,813)(157,812)(158,811)(159,810)(160,809)(161,808)(162,807)(163,806)(164,805)(165,804)(166,803)(167,802)(168,801)(169,800)(170,799)(171,798)(172,797)(173,796)(174,795)(175,794)(176,793)(177,792)(178,791)(179,790)(180,789)(181,788)(182,787)(183,786)(184,785)(185,784)(186,783)(187,782)(188,781)(189,780)(190,779)(191,778)(192,777)(193,776)(194,775)(195,774)(196,773)(197,772)(198,771)(199,770)(200,769)(201,768)(202,767)(203,766)(204,765)(205,764)(206,763)(207,762)(208,761)(209,760)(210,759)(211,758)(212,757)(213,756)(214,755)(215,754)(216,753)(217,752)(218,751)(219,750)(220,749)(221,748)(222,747)(223,746)(224,745)(225,744)(226,743)(227,742)(228,741)(229,740)(230,739)(231,738)(232,737)(233,736)(234,735)(235,734)(236,733)(237,732)(238,731)(239,730)(240,729)(241,728)(242,727)(243,726)(244,725)(245,724)(246,723)(247,722)(248,721)(249,720)(250,719)(251,718)(252,717)(253,716)(254,715)(255,714)(256,713)(257,712)(258,711)(259,710)(260,709)(261,708)(262,707)(263,706)(264,705)(265,704)(266,703)(267,702)(268,701)(269,700)(270,699)(271,698)(272,697)(273,696)(274,695)(275,694)(276,693)(277,692)(278,691)(279,690)(280,689)(281,688)(282,687)(283,686)(284,685)(285,684)(286,683)(287,682)(288,681)(289,680)(290,679)(291,678)(292,677)(293,676)(294,675)(295,674)(296,673)(297,672)(298,671)(299,670)(300,669)(301,668)(302,667)(303,666)(304,665)(305,664)(306,663)(307,662)(308,661)(309,660)(310,659)(311,658)(312,657)(313,656)(314,655)(315,654)(316,653)(317,652)(318,651)(319,650)(320,649)(321,648)(322,647)(323,646)(324,645)(325,644)(326,643)(327,642)(328,641)(329,640)(330,639)(331,638)(332,637)(333,636)(334,635)(335,634)(336,633)(337,632)(338,631)(339,630)(340,629)(341,628)(342,627)(343,626)(344,625)(345,624)(346,623)(347,622)(348,621)(349,620)(350,619)(351,618)(352,617)(353,616)(354,615)(355,614)(356,613)(357,612)(358,611)(359,610)(360,609)(361,608)(362,607)(363,606)(364,605)(365,604)(366,603)(367,602)(368,601)(369,600)(370,599)(371,598)(372,597)(373,596)(374,595)(375,594)(376,593)(377,592)(378,591)(379,590)(380,589)(381,588)(382,587)(383,586)(384,585)(385,584)(386,583)(387,582)(388,581)(389,580)(390,579)(391,578)(392,577)(393,576)(394,575)(395,574)(396,573)(397,572)(398,571)(399,570)(400,569)(401,568)(402,567)(403,566)(404,565)(405,564)(406,563)(407,562)(408,561)(409,560)(410,559)(411,558)(412,557)(413,556)(414,555)(415,554)(416,553)(417,552)(418,551)(419,550)(420,549)(421,548)(422,547)(423,546)(424,545)(425,544)(426,543)(427,542)(428,541)(429,540)(430,539)(431,538)(432,537)(433,536)(434,535)(435,534)(436,533)(437,532)(438,531)(439,530)(440,529)(441,528)(442,527)(443,526)(444,525)(445,524)(446,523)(447,522)(448,521)(449,520)(450,519)(451,518)(452,517)(453,516)(454,515)(455,514)(456,513)(457,512)(458,511)(459,510)(460,509)(461,508)(462,507)(463,506)(464,505)(465,504)(466,503)(467,502)(468,501)(469,500)(470,499)(471,498)(472,497)(473,496)(474,495)(475,494)(476,493)(477,492)(478,491)(479,490)(480,489)(481,488)(482,487)(483,486)(484,485)
Polycyclic presentation:
2,967|b^a=b^966
Conjugacy classes & character table
485 conjugacy classes — view the full character table.
Relationships
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1934, 1);
Finite Group Databasebeta