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D8072 #30633318
Aliases
Splittings
Subgroups
22 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 2 generators on 1017 points:
(1,2,3,4,5,6,7,8)(9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,172,173,174,175,176,177,178,179,180,181,182,183,184,185,186,187,188,189,190,191,192,193,194,195,196,197,198,199,200,201,202,203,204,205,206,207,208,209,210,211,212,213,214,215,216,217,218,219,220,221,222,223,224,225,226,227,228,229,230,231,232,233,234,235,236,237,238,239,240,241,242,243,244,245,246,247,248,249,250,251,252,253,254,255,256,257,258,259,260,261,262,263,264,265,266,267,268,269,270,271,272,273,274,275,276,277,278,279,280,281,282,283,284,285,286,287,288,289,290,291,292,293,294,295,296,297,298,299,300,301,302,303,304,305,306,307,308,309,310,311,312,313,314,315,316,317,318,319,320,321,322,323,324,325,326,327,328,329,330,331,332,333,334,335,336,337,338,339,340,341,342,343,344,345,346,347,348,349,350,351,352,353,354,355,356,357,358,359,360,361,362,363,364,365,366,367,368,369,370,371,372,373,374,375,376,377,378,379,380,381,382,383,384,385,386,387,388,389,390,391,392,393,394,395,396,397,398,399,400,401,402,403,404,405,406,407,408,409,410,411,412,413,414,415,416,417,418,419,420,421,422,423,424,425,426,427,428,429,430,431,432,433,434,435,436,437,438,439,440,441,442,443,444,445,446,447,448,449,450,451,452,453,454,455,456,457,458,459,460,461,462,463,464,465,466,467,468,469,470,471,472,473,474,475,476,477,478,479,480,481,482,483,484,485,486,487,488,489,490,491,492,493,494,495,496,497,498,499,500,501,502,503,504,505,506,507,508,509,510,511,512,513,514,515,516,517,518,519,520,521,522,523,524,525,526,527,528,529,530,531,532,533,534,535,536,537,538,539,540,541,542,543,544,545,546,547,548,549,550,551,552,553,554,555,556,557,558,559,560,561,562,563,564,565,566,567,568,569,570,571,572,573,574,575,576,577,578,579,580,581,582,583,584,585,586,587,588,589,590,591,592,593,594,595,596,597,598,599,600,601,602,603,604,605,606,607,608,609,610,611,612,613,614,615,616,617,618,619,620,621,622,623,624,625,626,627,628,629,630,631,632,633,634,635,636,637,638,639,640,641,642,643,644,645,646,647,648,649,650,651,652,653,654,655,656,657,658,659,660,661,662,663,664,665,666,667,668,669,670,671,672,673,674,675,676,677,678,679,680,681,682,683,684,685,686,687,688,689,690,691,692,693,694,695,696,697,698,699,700,701,702,703,704,705,706,707,708,709,710,711,712,713,714,715,716,717,718,719,720,721,722,723,724,725,726,727,728,729,730,731,732,733,734,735,736,737,738,739,740,741,742,743,744,745,746,747,748,749,750,751,752,753,754,755,756,757,758,759,760,761,762,763,764,765,766,767,768,769,770,771,772,773,774,775,776,777,778,779,780,781,782,783,784,785,786,787,788,789,790,791,792,793,794,795,796,797,798,799,800,801,802,803,804,805,806,807,808,809,810,811,812,813,814,815,816,817,818,819,820,821,822,823,824,825,826,827,828,829,830,831,832,833,834,835,836,837,838,839,840,841,842,843,844,845,846,847,848,849,850,851,852,853,854,855,856,857,858,859,860,861,862,863,864,865,866,867,868,869,870,871,872,873,874,875,876,877,878,879,880,881,882,883,884,885,886,887,888,889,890,891,892,893,894,895,896,897,898,899,900,901,902,903,904,905,906,907,908,909,910,911,912,913,914,915,916,917,918,919,920,921,922,923,924,925,926,927,928,929,930,931,932,933,934,935,936,937,938,939,940,941,942,943,944,945,946,947,948,949,950,951,952,953,954,955,956,957,958,959,960,961,962,963,964,965,966,967,968,969,970,971,972,973,974,975,976,977,978,979,980,981,982,983,984,985,986,987,988,989,990,991,992,993,994,995,996,997,998,999,1000,1001,1002,1003,1004,1005,1006,1007,1008,1009,1010,1011,1012,1013,1014,1015,1016,1017);(2,8)(3,7)(4,6)(10,1017)(11,1016)(12,1015)(13,1014)(14,1013)(15,1012)(16,1011)(17,1010)(18,1009)(19,1008)(20,1007)(21,1006)(22,1005)(23,1004)(24,1003)(25,1002)(26,1001)(27,1000)(28,999)(29,998)(30,997)(31,996)(32,995)(33,994)(34,993)(35,992)(36,991)(37,990)(38,989)(39,988)(40,987)(41,986)(42,985)(43,984)(44,983)(45,982)(46,981)(47,980)(48,979)(49,978)(50,977)(51,976)(52,975)(53,974)(54,973)(55,972)(56,971)(57,970)(58,969)(59,968)(60,967)(61,966)(62,965)(63,964)(64,963)(65,962)(66,961)(67,960)(68,959)(69,958)(70,957)(71,956)(72,955)(73,954)(74,953)(75,952)(76,951)(77,950)(78,949)(79,948)(80,947)(81,946)(82,945)(83,944)(84,943)(85,942)(86,941)(87,940)(88,939)(89,938)(90,937)(91,936)(92,935)(93,934)(94,933)(95,932)(96,931)(97,930)(98,929)(99,928)(100,927)(101,926)(102,925)(103,924)(104,923)(105,922)(106,921)(107,920)(108,919)(109,918)(110,917)(111,916)(112,915)(113,914)(114,913)(115,912)(116,911)(117,910)(118,909)(119,908)(120,907)(121,906)(122,905)(123,904)(124,903)(125,902)(126,901)(127,900)(128,899)(129,898)(130,897)(131,896)(132,895)(133,894)(134,893)(135,892)(136,891)(137,890)(138,889)(139,888)(140,887)(141,886)(142,885)(143,884)(144,883)(145,882)(146,881)(147,880)(148,879)(149,878)(150,877)(151,876)(152,875)(153,874)(154,873)(155,872)(156,871)(157,870)(158,869)(159,868)(160,867)(161,866)(162,865)(163,864)(164,863)(165,862)(166,861)(167,860)(168,859)(169,858)(170,857)(171,856)(172,855)(173,854)(174,853)(175,852)(176,851)(177,850)(178,849)(179,848)(180,847)(181,846)(182,845)(183,844)(184,843)(185,842)(186,841)(187,840)(188,839)(189,838)(190,837)(191,836)(192,835)(193,834)(194,833)(195,832)(196,831)(197,830)(198,829)(199,828)(200,827)(201,826)(202,825)(203,824)(204,823)(205,822)(206,821)(207,820)(208,819)(209,818)(210,817)(211,816)(212,815)(213,814)(214,813)(215,812)(216,811)(217,810)(218,809)(219,808)(220,807)(221,806)(222,805)(223,804)(224,803)(225,802)(226,801)(227,800)(228,799)(229,798)(230,797)(231,796)(232,795)(233,794)(234,793)(235,792)(236,791)(237,790)(238,789)(239,788)(240,787)(241,786)(242,785)(243,784)(244,783)(245,782)(246,781)(247,780)(248,779)(249,778)(250,777)(251,776)(252,775)(253,774)(254,773)(255,772)(256,771)(257,770)(258,769)(259,768)(260,767)(261,766)(262,765)(263,764)(264,763)(265,762)(266,761)(267,760)(268,759)(269,758)(270,757)(271,756)(272,755)(273,754)(274,753)(275,752)(276,751)(277,750)(278,749)(279,748)(280,747)(281,746)(282,745)(283,744)(284,743)(285,742)(286,741)(287,740)(288,739)(289,738)(290,737)(291,736)(292,735)(293,734)(294,733)(295,732)(296,731)(297,730)(298,729)(299,728)(300,727)(301,726)(302,725)(303,724)(304,723)(305,722)(306,721)(307,720)(308,719)(309,718)(310,717)(311,716)(312,715)(313,714)(314,713)(315,712)(316,711)(317,710)(318,709)(319,708)(320,707)(321,706)(322,705)(323,704)(324,703)(325,702)(326,701)(327,700)(328,699)(329,698)(330,697)(331,696)(332,695)(333,694)(334,693)(335,692)(336,691)(337,690)(338,689)(339,688)(340,687)(341,686)(342,685)(343,684)(344,683)(345,682)(346,681)(347,680)(348,679)(349,678)(350,677)(351,676)(352,675)(353,674)(354,673)(355,672)(356,671)(357,670)(358,669)(359,668)(360,667)(361,666)(362,665)(363,664)(364,663)(365,662)(366,661)(367,660)(368,659)(369,658)(370,657)(371,656)(372,655)(373,654)(374,653)(375,652)(376,651)(377,650)(378,649)(379,648)(380,647)(381,646)(382,645)(383,644)(384,643)(385,642)(386,641)(387,640)(388,639)(389,638)(390,637)(391,636)(392,635)(393,634)(394,633)(395,632)(396,631)(397,630)(398,629)(399,628)(400,627)(401,626)(402,625)(403,624)(404,623)(405,622)(406,621)(407,620)(408,619)(409,618)(410,617)(411,616)(412,615)(413,614)(414,613)(415,612)(416,611)(417,610)(418,609)(419,608)(420,607)(421,606)(422,605)(423,604)(424,603)(425,602)(426,601)(427,600)(428,599)(429,598)(430,597)(431,596)(432,595)(433,594)(434,593)(435,592)(436,591)(437,590)(438,589)(439,588)(440,587)(441,586)(442,585)(443,584)(444,583)(445,582)(446,581)(447,580)(448,579)(449,578)(450,577)(451,576)(452,575)(453,574)(454,573)(455,572)(456,571)(457,570)(458,569)(459,568)(460,567)(461,566)(462,565)(463,564)(464,563)(465,562)(466,561)(467,560)(468,559)(469,558)(470,557)(471,556)(472,555)(473,554)(474,553)(475,552)(476,551)(477,550)(478,549)(479,548)(480,547)(481,546)(482,545)(483,544)(484,543)(485,542)(486,541)(487,540)(488,539)(489,538)(490,537)(491,536)(492,535)(493,534)(494,533)(495,532)(496,531)(497,530)(498,529)(499,528)(500,527)(501,526)(502,525)(503,524)(504,523)(505,522)(506,521)(507,520)(508,519)(509,518)(510,517)(511,516)(512,515)(513,514)
Polycyclic presentation:
2^4,1009|c^2=d,b^a=bc,c^a=cd,e^a=e^1008,c^b=cd,e^b=e^1008
Conjugacy classes & character table
4039 conjugacy classes. The character table is too large to display.
Relationships
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16144, 26);
Finite Group Databasebeta