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D8488 #30684102
Aliases
Splittings
Subgroups
22 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 2 generators on 1069 points:
(1,2,3,4,5,6,7,8)(9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,172,173,174,175,176,177,178,179,180,181,182,183,184,185,186,187,188,189,190,191,192,193,194,195,196,197,198,199,200,201,202,203,204,205,206,207,208,209,210,211,212,213,214,215,216,217,218,219,220,221,222,223,224,225,226,227,228,229,230,231,232,233,234,235,236,237,238,239,240,241,242,243,244,245,246,247,248,249,250,251,252,253,254,255,256,257,258,259,260,261,262,263,264,265,266,267,268,269,270,271,272,273,274,275,276,277,278,279,280,281,282,283,284,285,286,287,288,289,290,291,292,293,294,295,296,297,298,299,300,301,302,303,304,305,306,307,308,309,310,311,312,313,314,315,316,317,318,319,320,321,322,323,324,325,326,327,328,329,330,331,332,333,334,335,336,337,338,339,340,341,342,343,344,345,346,347,348,349,350,351,352,353,354,355,356,357,358,359,360,361,362,363,364,365,366,367,368,369,370,371,372,373,374,375,376,377,378,379,380,381,382,383,384,385,386,387,388,389,390,391,392,393,394,395,396,397,398,399,400,401,402,403,404,405,406,407,408,409,410,411,412,413,414,415,416,417,418,419,420,421,422,423,424,425,426,427,428,429,430,431,432,433,434,435,436,437,438,439,440,441,442,443,444,445,446,447,448,449,450,451,452,453,454,455,456,457,458,459,460,461,462,463,464,465,466,467,468,469,470,471,472,473,474,475,476,477,478,479,480,481,482,483,484,485,486,487,488,489,490,491,492,493,494,495,496,497,498,499,500,501,502,503,504,505,506,507,508,509,510,511,512,513,514,515,516,517,518,519,520,521,522,523,524,525,526,527,528,529,530,531,532,533,534,535,536,537,538,539,540,541,542,543,544,545,546,547,548,549,550,551,552,553,554,555,556,557,558,559,560,561,562,563,564,565,566,567,568,569,570,571,572,573,574,575,576,577,578,579,580,581,582,583,584,585,586,587,588,589,590,591,592,593,594,595,596,597,598,599,600,601,602,603,604,605,606,607,608,609,610,611,612,613,614,615,616,617,618,619,620,621,622,623,624,625,626,627,628,629,630,631,632,633,634,635,636,637,638,639,640,641,642,643,644,645,646,647,648,649,650,651,652,653,654,655,656,657,658,659,660,661,662,663,664,665,666,667,668,669,670,671,672,673,674,675,676,677,678,679,680,681,682,683,684,685,686,687,688,689,690,691,692,693,694,695,696,697,698,699,700,701,702,703,704,705,706,707,708,709,710,711,712,713,714,715,716,717,718,719,720,721,722,723,724,725,726,727,728,729,730,731,732,733,734,735,736,737,738,739,740,741,742,743,744,745,746,747,748,749,750,751,752,753,754,755,756,757,758,759,760,761,762,763,764,765,766,767,768,769,770,771,772,773,774,775,776,777,778,779,780,781,782,783,784,785,786,787,788,789,790,791,792,793,794,795,796,797,798,799,800,801,802,803,804,805,806,807,808,809,810,811,812,813,814,815,816,817,818,819,820,821,822,823,824,825,826,827,828,829,830,831,832,833,834,835,836,837,838,839,840,841,842,843,844,845,846,847,848,849,850,851,852,853,854,855,856,857,858,859,860,861,862,863,864,865,866,867,868,869,870,871,872,873,874,875,876,877,878,879,880,881,882,883,884,885,886,887,888,889,890,891,892,893,894,895,896,897,898,899,900,901,902,903,904,905,906,907,908,909,910,911,912,913,914,915,916,917,918,919,920,921,922,923,924,925,926,927,928,929,930,931,932,933,934,935,936,937,938,939,940,941,942,943,944,945,946,947,948,949,950,951,952,953,954,955,956,957,958,959,960,961,962,963,964,965,966,967,968,969,970,971,972,973,974,975,976,977,978,979,980,981,982,983,984,985,986,987,988,989,990,991,992,993,994,995,996,997,998,999,1000,1001,1002,1003,1004,1005,1006,1007,1008,1009,1010,1011,1012,1013,1014,1015,1016,1017,1018,1019,1020,1021,1022,1023,1024,1025,1026,1027,1028,1029,1030,1031,1032,1033,1034,1035,1036,1037,1038,1039,1040,1041,1042,1043,1044,1045,1046,1047,1048,1049,1050,1051,1052,1053,1054,1055,1056,1057,1058,1059,1060,1061,1062,1063,1064,1065,1066,1067,1068,1069);(2,8)(3,7)(4,6)(10,1069)(11,1068)(12,1067)(13,1066)(14,1065)(15,1064)(16,1063)(17,1062)(18,1061)(19,1060)(20,1059)(21,1058)(22,1057)(23,1056)(24,1055)(25,1054)(26,1053)(27,1052)(28,1051)(29,1050)(30,1049)(31,1048)(32,1047)(33,1046)(34,1045)(35,1044)(36,1043)(37,1042)(38,1041)(39,1040)(40,1039)(41,1038)(42,1037)(43,1036)(44,1035)(45,1034)(46,1033)(47,1032)(48,1031)(49,1030)(50,1029)(51,1028)(52,1027)(53,1026)(54,1025)(55,1024)(56,1023)(57,1022)(58,1021)(59,1020)(60,1019)(61,1018)(62,1017)(63,1016)(64,1015)(65,1014)(66,1013)(67,1012)(68,1011)(69,1010)(70,1009)(71,1008)(72,1007)(73,1006)(74,1005)(75,1004)(76,1003)(77,1002)(78,1001)(79,1000)(80,999)(81,998)(82,997)(83,996)(84,995)(85,994)(86,993)(87,992)(88,991)(89,990)(90,989)(91,988)(92,987)(93,986)(94,985)(95,984)(96,983)(97,982)(98,981)(99,980)(100,979)(101,978)(102,977)(103,976)(104,975)(105,974)(106,973)(107,972)(108,971)(109,970)(110,969)(111,968)(112,967)(113,966)(114,965)(115,964)(116,963)(117,962)(118,961)(119,960)(120,959)(121,958)(122,957)(123,956)(124,955)(125,954)(126,953)(127,952)(128,951)(129,950)(130,949)(131,948)(132,947)(133,946)(134,945)(135,944)(136,943)(137,942)(138,941)(139,940)(140,939)(141,938)(142,937)(143,936)(144,935)(145,934)(146,933)(147,932)(148,931)(149,930)(150,929)(151,928)(152,927)(153,926)(154,925)(155,924)(156,923)(157,922)(158,921)(159,920)(160,919)(161,918)(162,917)(163,916)(164,915)(165,914)(166,913)(167,912)(168,911)(169,910)(170,909)(171,908)(172,907)(173,906)(174,905)(175,904)(176,903)(177,902)(178,901)(179,900)(180,899)(181,898)(182,897)(183,896)(184,895)(185,894)(186,893)(187,892)(188,891)(189,890)(190,889)(191,888)(192,887)(193,886)(194,885)(195,884)(196,883)(197,882)(198,881)(199,880)(200,879)(201,878)(202,877)(203,876)(204,875)(205,874)(206,873)(207,872)(208,871)(209,870)(210,869)(211,868)(212,867)(213,866)(214,865)(215,864)(216,863)(217,862)(218,861)(219,860)(220,859)(221,858)(222,857)(223,856)(224,855)(225,854)(226,853)(227,852)(228,851)(229,850)(230,849)(231,848)(232,847)(233,846)(234,845)(235,844)(236,843)(237,842)(238,841)(239,840)(240,839)(241,838)(242,837)(243,836)(244,835)(245,834)(246,833)(247,832)(248,831)(249,830)(250,829)(251,828)(252,827)(253,826)(254,825)(255,824)(256,823)(257,822)(258,821)(259,820)(260,819)(261,818)(262,817)(263,816)(264,815)(265,814)(266,813)(267,812)(268,811)(269,810)(270,809)(271,808)(272,807)(273,806)(274,805)(275,804)(276,803)(277,802)(278,801)(279,800)(280,799)(281,798)(282,797)(283,796)(284,795)(285,794)(286,793)(287,792)(288,791)(289,790)(290,789)(291,788)(292,787)(293,786)(294,785)(295,784)(296,783)(297,782)(298,781)(299,780)(300,779)(301,778)(302,777)(303,776)(304,775)(305,774)(306,773)(307,772)(308,771)(309,770)(310,769)(311,768)(312,767)(313,766)(314,765)(315,764)(316,763)(317,762)(318,761)(319,760)(320,759)(321,758)(322,757)(323,756)(324,755)(325,754)(326,753)(327,752)(328,751)(329,750)(330,749)(331,748)(332,747)(333,746)(334,745)(335,744)(336,743)(337,742)(338,741)(339,740)(340,739)(341,738)(342,737)(343,736)(344,735)(345,734)(346,733)(347,732)(348,731)(349,730)(350,729)(351,728)(352,727)(353,726)(354,725)(355,724)(356,723)(357,722)(358,721)(359,720)(360,719)(361,718)(362,717)(363,716)(364,715)(365,714)(366,713)(367,712)(368,711)(369,710)(370,709)(371,708)(372,707)(373,706)(374,705)(375,704)(376,703)(377,702)(378,701)(379,700)(380,699)(381,698)(382,697)(383,696)(384,695)(385,694)(386,693)(387,692)(388,691)(389,690)(390,689)(391,688)(392,687)(393,686)(394,685)(395,684)(396,683)(397,682)(398,681)(399,680)(400,679)(401,678)(402,677)(403,676)(404,675)(405,674)(406,673)(407,672)(408,671)(409,670)(410,669)(411,668)(412,667)(413,666)(414,665)(415,664)(416,663)(417,662)(418,661)(419,660)(420,659)(421,658)(422,657)(423,656)(424,655)(425,654)(426,653)(427,652)(428,651)(429,650)(430,649)(431,648)(432,647)(433,646)(434,645)(435,644)(436,643)(437,642)(438,641)(439,640)(440,639)(441,638)(442,637)(443,636)(444,635)(445,634)(446,633)(447,632)(448,631)(449,630)(450,629)(451,628)(452,627)(453,626)(454,625)(455,624)(456,623)(457,622)(458,621)(459,620)(460,619)(461,618)(462,617)(463,616)(464,615)(465,614)(466,613)(467,612)(468,611)(469,610)(470,609)(471,608)(472,607)(473,606)(474,605)(475,604)(476,603)(477,602)(478,601)(479,600)(480,599)(481,598)(482,597)(483,596)(484,595)(485,594)(486,593)(487,592)(488,591)(489,590)(490,589)(491,588)(492,587)(493,586)(494,585)(495,584)(496,583)(497,582)(498,581)(499,580)(500,579)(501,578)(502,577)(503,576)(504,575)(505,574)(506,573)(507,572)(508,571)(509,570)(510,569)(511,568)(512,567)(513,566)(514,565)(515,564)(516,563)(517,562)(518,561)(519,560)(520,559)(521,558)(522,557)(523,556)(524,555)(525,554)(526,553)(527,552)(528,551)(529,550)(530,549)(531,548)(532,547)(533,546)(534,545)(535,544)(536,543)(537,542)(538,541)(539,540)
Polycyclic presentation:
2^4,1061|c^2=d,b^a=bc,c^a=cd,e^a=e^1060,c^b=cd,e^b=e^1060
Conjugacy classes & character table
4247 conjugacy classes. The character table is too large to display.
Relationships
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16976, 26);
Finite Group Databasebeta