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D7864 #30628461
Aliases
Splittings
Subgroups
22 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 2 generators on 991 points:
(1,2,3,4,5,6,7,8)(9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,172,173,174,175,176,177,178,179,180,181,182,183,184,185,186,187,188,189,190,191,192,193,194,195,196,197,198,199,200,201,202,203,204,205,206,207,208,209,210,211,212,213,214,215,216,217,218,219,220,221,222,223,224,225,226,227,228,229,230,231,232,233,234,235,236,237,238,239,240,241,242,243,244,245,246,247,248,249,250,251,252,253,254,255,256,257,258,259,260,261,262,263,264,265,266,267,268,269,270,271,272,273,274,275,276,277,278,279,280,281,282,283,284,285,286,287,288,289,290,291,292,293,294,295,296,297,298,299,300,301,302,303,304,305,306,307,308,309,310,311,312,313,314,315,316,317,318,319,320,321,322,323,324,325,326,327,328,329,330,331,332,333,334,335,336,337,338,339,340,341,342,343,344,345,346,347,348,349,350,351,352,353,354,355,356,357,358,359,360,361,362,363,364,365,366,367,368,369,370,371,372,373,374,375,376,377,378,379,380,381,382,383,384,385,386,387,388,389,390,391,392,393,394,395,396,397,398,399,400,401,402,403,404,405,406,407,408,409,410,411,412,413,414,415,416,417,418,419,420,421,422,423,424,425,426,427,428,429,430,431,432,433,434,435,436,437,438,439,440,441,442,443,444,445,446,447,448,449,450,451,452,453,454,455,456,457,458,459,460,461,462,463,464,465,466,467,468,469,470,471,472,473,474,475,476,477,478,479,480,481,482,483,484,485,486,487,488,489,490,491,492,493,494,495,496,497,498,499,500,501,502,503,504,505,506,507,508,509,510,511,512,513,514,515,516,517,518,519,520,521,522,523,524,525,526,527,528,529,530,531,532,533,534,535,536,537,538,539,540,541,542,543,544,545,546,547,548,549,550,551,552,553,554,555,556,557,558,559,560,561,562,563,564,565,566,567,568,569,570,571,572,573,574,575,576,577,578,579,580,581,582,583,584,585,586,587,588,589,590,591,592,593,594,595,596,597,598,599,600,601,602,603,604,605,606,607,608,609,610,611,612,613,614,615,616,617,618,619,620,621,622,623,624,625,626,627,628,629,630,631,632,633,634,635,636,637,638,639,640,641,642,643,644,645,646,647,648,649,650,651,652,653,654,655,656,657,658,659,660,661,662,663,664,665,666,667,668,669,670,671,672,673,674,675,676,677,678,679,680,681,682,683,684,685,686,687,688,689,690,691,692,693,694,695,696,697,698,699,700,701,702,703,704,705,706,707,708,709,710,711,712,713,714,715,716,717,718,719,720,721,722,723,724,725,726,727,728,729,730,731,732,733,734,735,736,737,738,739,740,741,742,743,744,745,746,747,748,749,750,751,752,753,754,755,756,757,758,759,760,761,762,763,764,765,766,767,768,769,770,771,772,773,774,775,776,777,778,779,780,781,782,783,784,785,786,787,788,789,790,791,792,793,794,795,796,797,798,799,800,801,802,803,804,805,806,807,808,809,810,811,812,813,814,815,816,817,818,819,820,821,822,823,824,825,826,827,828,829,830,831,832,833,834,835,836,837,838,839,840,841,842,843,844,845,846,847,848,849,850,851,852,853,854,855,856,857,858,859,860,861,862,863,864,865,866,867,868,869,870,871,872,873,874,875,876,877,878,879,880,881,882,883,884,885,886,887,888,889,890,891,892,893,894,895,896,897,898,899,900,901,902,903,904,905,906,907,908,909,910,911,912,913,914,915,916,917,918,919,920,921,922,923,924,925,926,927,928,929,930,931,932,933,934,935,936,937,938,939,940,941,942,943,944,945,946,947,948,949,950,951,952,953,954,955,956,957,958,959,960,961,962,963,964,965,966,967,968,969,970,971,972,973,974,975,976,977,978,979,980,981,982,983,984,985,986,987,988,989,990,991);(2,8)(3,7)(4,6)(10,991)(11,990)(12,989)(13,988)(14,987)(15,986)(16,985)(17,984)(18,983)(19,982)(20,981)(21,980)(22,979)(23,978)(24,977)(25,976)(26,975)(27,974)(28,973)(29,972)(30,971)(31,970)(32,969)(33,968)(34,967)(35,966)(36,965)(37,964)(38,963)(39,962)(40,961)(41,960)(42,959)(43,958)(44,957)(45,956)(46,955)(47,954)(48,953)(49,952)(50,951)(51,950)(52,949)(53,948)(54,947)(55,946)(56,945)(57,944)(58,943)(59,942)(60,941)(61,940)(62,939)(63,938)(64,937)(65,936)(66,935)(67,934)(68,933)(69,932)(70,931)(71,930)(72,929)(73,928)(74,927)(75,926)(76,925)(77,924)(78,923)(79,922)(80,921)(81,920)(82,919)(83,918)(84,917)(85,916)(86,915)(87,914)(88,913)(89,912)(90,911)(91,910)(92,909)(93,908)(94,907)(95,906)(96,905)(97,904)(98,903)(99,902)(100,901)(101,900)(102,899)(103,898)(104,897)(105,896)(106,895)(107,894)(108,893)(109,892)(110,891)(111,890)(112,889)(113,888)(114,887)(115,886)(116,885)(117,884)(118,883)(119,882)(120,881)(121,880)(122,879)(123,878)(124,877)(125,876)(126,875)(127,874)(128,873)(129,872)(130,871)(131,870)(132,869)(133,868)(134,867)(135,866)(136,865)(137,864)(138,863)(139,862)(140,861)(141,860)(142,859)(143,858)(144,857)(145,856)(146,855)(147,854)(148,853)(149,852)(150,851)(151,850)(152,849)(153,848)(154,847)(155,846)(156,845)(157,844)(158,843)(159,842)(160,841)(161,840)(162,839)(163,838)(164,837)(165,836)(166,835)(167,834)(168,833)(169,832)(170,831)(171,830)(172,829)(173,828)(174,827)(175,826)(176,825)(177,824)(178,823)(179,822)(180,821)(181,820)(182,819)(183,818)(184,817)(185,816)(186,815)(187,814)(188,813)(189,812)(190,811)(191,810)(192,809)(193,808)(194,807)(195,806)(196,805)(197,804)(198,803)(199,802)(200,801)(201,800)(202,799)(203,798)(204,797)(205,796)(206,795)(207,794)(208,793)(209,792)(210,791)(211,790)(212,789)(213,788)(214,787)(215,786)(216,785)(217,784)(218,783)(219,782)(220,781)(221,780)(222,779)(223,778)(224,777)(225,776)(226,775)(227,774)(228,773)(229,772)(230,771)(231,770)(232,769)(233,768)(234,767)(235,766)(236,765)(237,764)(238,763)(239,762)(240,761)(241,760)(242,759)(243,758)(244,757)(245,756)(246,755)(247,754)(248,753)(249,752)(250,751)(251,750)(252,749)(253,748)(254,747)(255,746)(256,745)(257,744)(258,743)(259,742)(260,741)(261,740)(262,739)(263,738)(264,737)(265,736)(266,735)(267,734)(268,733)(269,732)(270,731)(271,730)(272,729)(273,728)(274,727)(275,726)(276,725)(277,724)(278,723)(279,722)(280,721)(281,720)(282,719)(283,718)(284,717)(285,716)(286,715)(287,714)(288,713)(289,712)(290,711)(291,710)(292,709)(293,708)(294,707)(295,706)(296,705)(297,704)(298,703)(299,702)(300,701)(301,700)(302,699)(303,698)(304,697)(305,696)(306,695)(307,694)(308,693)(309,692)(310,691)(311,690)(312,689)(313,688)(314,687)(315,686)(316,685)(317,684)(318,683)(319,682)(320,681)(321,680)(322,679)(323,678)(324,677)(325,676)(326,675)(327,674)(328,673)(329,672)(330,671)(331,670)(332,669)(333,668)(334,667)(335,666)(336,665)(337,664)(338,663)(339,662)(340,661)(341,660)(342,659)(343,658)(344,657)(345,656)(346,655)(347,654)(348,653)(349,652)(350,651)(351,650)(352,649)(353,648)(354,647)(355,646)(356,645)(357,644)(358,643)(359,642)(360,641)(361,640)(362,639)(363,638)(364,637)(365,636)(366,635)(367,634)(368,633)(369,632)(370,631)(371,630)(372,629)(373,628)(374,627)(375,626)(376,625)(377,624)(378,623)(379,622)(380,621)(381,620)(382,619)(383,618)(384,617)(385,616)(386,615)(387,614)(388,613)(389,612)(390,611)(391,610)(392,609)(393,608)(394,607)(395,606)(396,605)(397,604)(398,603)(399,602)(400,601)(401,600)(402,599)(403,598)(404,597)(405,596)(406,595)(407,594)(408,593)(409,592)(410,591)(411,590)(412,589)(413,588)(414,587)(415,586)(416,585)(417,584)(418,583)(419,582)(420,581)(421,580)(422,579)(423,578)(424,577)(425,576)(426,575)(427,574)(428,573)(429,572)(430,571)(431,570)(432,569)(433,568)(434,567)(435,566)(436,565)(437,564)(438,563)(439,562)(440,561)(441,560)(442,559)(443,558)(444,557)(445,556)(446,555)(447,554)(448,553)(449,552)(450,551)(451,550)(452,549)(453,548)(454,547)(455,546)(456,545)(457,544)(458,543)(459,542)(460,541)(461,540)(462,539)(463,538)(464,537)(465,536)(466,535)(467,534)(468,533)(469,532)(470,531)(471,530)(472,529)(473,528)(474,527)(475,526)(476,525)(477,524)(478,523)(479,522)(480,521)(481,520)(482,519)(483,518)(484,517)(485,516)(486,515)(487,514)(488,513)(489,512)(490,511)(491,510)(492,509)(493,508)(494,507)(495,506)(496,505)(497,504)(498,503)(499,502)(500,501)
Polycyclic presentation:
2^4,983|c^2=d,b^a=bc,c^a=cd,e^a=e^982,c^b=cd,e^b=e^982
Conjugacy classes & character table
3935 conjugacy classes. The character table is too large to display.
Relationships
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15728, 26);
Finite Group Databasebeta