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D8392 #30680902
Aliases
Splittings
Subgroups
22 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 2 generators on 1057 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);(2,8)(3,7)(4,6)(10,1057)(11,1056)(12,1055)(13,1054)(14,1053)(15,1052)(16,1051)(17,1050)(18,1049)(19,1048)(20,1047)(21,1046)(22,1045)(23,1044)(24,1043)(25,1042)(26,1041)(27,1040)(28,1039)(29,1038)(30,1037)(31,1036)(32,1035)(33,1034)(34,1033)(35,1032)(36,1031)(37,1030)(38,1029)(39,1028)(40,1027)(41,1026)(42,1025)(43,1024)(44,1023)(45,1022)(46,1021)(47,1020)(48,1019)(49,1018)(50,1017)(51,1016)(52,1015)(53,1014)(54,1013)(55,1012)(56,1011)(57,1010)(58,1009)(59,1008)(60,1007)(61,1006)(62,1005)(63,1004)(64,1003)(65,1002)(66,1001)(67,1000)(68,999)(69,998)(70,997)(71,996)(72,995)(73,994)(74,993)(75,992)(76,991)(77,990)(78,989)(79,988)(80,987)(81,986)(82,985)(83,984)(84,983)(85,982)(86,981)(87,980)(88,979)(89,978)(90,977)(91,976)(92,975)(93,974)(94,973)(95,972)(96,971)(97,970)(98,969)(99,968)(100,967)(101,966)(102,965)(103,964)(104,963)(105,962)(106,961)(107,960)(108,959)(109,958)(110,957)(111,956)(112,955)(113,954)(114,953)(115,952)(116,951)(117,950)(118,949)(119,948)(120,947)(121,946)(122,945)(123,944)(124,943)(125,942)(126,941)(127,940)(128,939)(129,938)(130,937)(131,936)(132,935)(133,934)(134,933)(135,932)(136,931)(137,930)(138,929)(139,928)(140,927)(141,926)(142,925)(143,924)(144,923)(145,922)(146,921)(147,920)(148,919)(149,918)(150,917)(151,916)(152,915)(153,914)(154,913)(155,912)(156,911)(157,910)(158,909)(159,908)(160,907)(161,906)(162,905)(163,904)(164,903)(165,902)(166,901)(167,900)(168,899)(169,898)(170,897)(171,896)(172,895)(173,894)(174,893)(175,892)(176,891)(177,890)(178,889)(179,888)(180,887)(181,886)(182,885)(183,884)(184,883)(185,882)(186,881)(187,880)(188,879)(189,878)(190,877)(191,876)(192,875)(193,874)(194,873)(195,872)(196,871)(197,870)(198,869)(199,868)(200,867)(201,866)(202,865)(203,864)(204,863)(205,862)(206,861)(207,860)(208,859)(209,858)(210,857)(211,856)(212,855)(213,854)(214,853)(215,852)(216,851)(217,850)(218,849)(219,848)(220,847)(221,846)(222,845)(223,844)(224,843)(225,842)(226,841)(227,840)(228,839)(229,838)(230,837)(231,836)(232,835)(233,834)(234,833)(235,832)(236,831)(237,830)(238,829)(239,828)(240,827)(241,826)(242,825)(243,824)(244,823)(245,822)(246,821)(247,820)(248,819)(249,818)(250,817)(251,816)(252,815)(253,814)(254,813)(255,812)(256,811)(257,810)(258,809)(259,808)(260,807)(261,806)(262,805)(263,804)(264,803)(265,802)(266,801)(267,800)(268,799)(269,798)(270,797)(271,796)(272,795)(273,794)(274,793)(275,792)(276,791)(277,790)(278,789)(279,788)(280,787)(281,786)(282,785)(283,784)(284,783)(285,782)(286,781)(287,780)(288,779)(289,778)(290,777)(291,776)(292,775)(293,774)(294,773)(295,772)(296,771)(297,770)(298,769)(299,768)(300,767)(301,766)(302,765)(303,764)(304,763)(305,762)(306,761)(307,760)(308,759)(309,758)(310,757)(311,756)(312,755)(313,754)(314,753)(315,752)(316,751)(317,750)(318,749)(319,748)(320,747)(321,746)(322,745)(323,744)(324,743)(325,742)(326,741)(327,740)(328,739)(329,738)(330,737)(331,736)(332,735)(333,734)(334,733)(335,732)(336,731)(337,730)(338,729)(339,728)(340,727)(341,726)(342,725)(343,724)(344,723)(345,722)(346,721)(347,720)(348,719)(349,718)(350,717)(351,716)(352,715)(353,714)(354,713)(355,712)(356,711)(357,710)(358,709)(359,708)(360,707)(361,706)(362,705)(363,704)(364,703)(365,702)(366,701)(367,700)(368,699)(369,698)(370,697)(371,696)(372,695)(373,694)(374,693)(375,692)(376,691)(377,690)(378,689)(379,688)(380,687)(381,686)(382,685)(383,684)(384,683)(385,682)(386,681)(387,680)(388,679)(389,678)(390,677)(391,676)(392,675)(393,674)(394,673)(395,672)(396,671)(397,670)(398,669)(399,668)(400,667)(401,666)(402,665)(403,664)(404,663)(405,662)(406,661)(407,660)(408,659)(409,658)(410,657)(411,656)(412,655)(413,654)(414,653)(415,652)(416,651)(417,650)(418,649)(419,648)(420,647)(421,646)(422,645)(423,644)(424,643)(425,642)(426,641)(427,640)(428,639)(429,638)(430,637)(431,636)(432,635)(433,634)(434,633)(435,632)(436,631)(437,630)(438,629)(439,628)(440,627)(441,626)(442,625)(443,624)(444,623)(445,622)(446,621)(447,620)(448,619)(449,618)(450,617)(451,616)(452,615)(453,614)(454,613)(455,612)(456,611)(457,610)(458,609)(459,608)(460,607)(461,606)(462,605)(463,604)(464,603)(465,602)(466,601)(467,600)(468,599)(469,598)(470,597)(471,596)(472,595)(473,594)(474,593)(475,592)(476,591)(477,590)(478,589)(479,588)(480,587)(481,586)(482,585)(483,584)(484,583)(485,582)(486,581)(487,580)(488,579)(489,578)(490,577)(491,576)(492,575)(493,574)(494,573)(495,572)(496,571)(497,570)(498,569)(499,568)(500,567)(501,566)(502,565)(503,564)(504,563)(505,562)(506,561)(507,560)(508,559)(509,558)(510,557)(511,556)(512,555)(513,554)(514,553)(515,552)(516,551)(517,550)(518,549)(519,548)(520,547)(521,546)(522,545)(523,544)(524,543)(525,542)(526,541)(527,540)(528,539)(529,538)(530,537)(531,536)(532,535)(533,534)
Polycyclic presentation:
2^4,1049|c^2=d,b^a=bc,c^a=cd,e^a=e^1048,c^b=cd,e^b=e^1048
Conjugacy classes & character table
4199 conjugacy classes. The character table is too large to display.
Relationships
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16784, 26);
Finite Group Databasebeta