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D8312 #30659013
Aliases
Splittings
Subgroups
22 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 2 generators on 1047 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);(2,8)(3,7)(4,6)(10,1047)(11,1046)(12,1045)(13,1044)(14,1043)(15,1042)(16,1041)(17,1040)(18,1039)(19,1038)(20,1037)(21,1036)(22,1035)(23,1034)(24,1033)(25,1032)(26,1031)(27,1030)(28,1029)(29,1028)(30,1027)(31,1026)(32,1025)(33,1024)(34,1023)(35,1022)(36,1021)(37,1020)(38,1019)(39,1018)(40,1017)(41,1016)(42,1015)(43,1014)(44,1013)(45,1012)(46,1011)(47,1010)(48,1009)(49,1008)(50,1007)(51,1006)(52,1005)(53,1004)(54,1003)(55,1002)(56,1001)(57,1000)(58,999)(59,998)(60,997)(61,996)(62,995)(63,994)(64,993)(65,992)(66,991)(67,990)(68,989)(69,988)(70,987)(71,986)(72,985)(73,984)(74,983)(75,982)(76,981)(77,980)(78,979)(79,978)(80,977)(81,976)(82,975)(83,974)(84,973)(85,972)(86,971)(87,970)(88,969)(89,968)(90,967)(91,966)(92,965)(93,964)(94,963)(95,962)(96,961)(97,960)(98,959)(99,958)(100,957)(101,956)(102,955)(103,954)(104,953)(105,952)(106,951)(107,950)(108,949)(109,948)(110,947)(111,946)(112,945)(113,944)(114,943)(115,942)(116,941)(117,940)(118,939)(119,938)(120,937)(121,936)(122,935)(123,934)(124,933)(125,932)(126,931)(127,930)(128,929)(129,928)(130,927)(131,926)(132,925)(133,924)(134,923)(135,922)(136,921)(137,920)(138,919)(139,918)(140,917)(141,916)(142,915)(143,914)(144,913)(145,912)(146,911)(147,910)(148,909)(149,908)(150,907)(151,906)(152,905)(153,904)(154,903)(155,902)(156,901)(157,900)(158,899)(159,898)(160,897)(161,896)(162,895)(163,894)(164,893)(165,892)(166,891)(167,890)(168,889)(169,888)(170,887)(171,886)(172,885)(173,884)(174,883)(175,882)(176,881)(177,880)(178,879)(179,878)(180,877)(181,876)(182,875)(183,874)(184,873)(185,872)(186,871)(187,870)(188,869)(189,868)(190,867)(191,866)(192,865)(193,864)(194,863)(195,862)(196,861)(197,860)(198,859)(199,858)(200,857)(201,856)(202,855)(203,854)(204,853)(205,852)(206,851)(207,850)(208,849)(209,848)(210,847)(211,846)(212,845)(213,844)(214,843)(215,842)(216,841)(217,840)(218,839)(219,838)(220,837)(221,836)(222,835)(223,834)(224,833)(225,832)(226,831)(227,830)(228,829)(229,828)(230,827)(231,826)(232,825)(233,824)(234,823)(235,822)(236,821)(237,820)(238,819)(239,818)(240,817)(241,816)(242,815)(243,814)(244,813)(245,812)(246,811)(247,810)(248,809)(249,808)(250,807)(251,806)(252,805)(253,804)(254,803)(255,802)(256,801)(257,800)(258,799)(259,798)(260,797)(261,796)(262,795)(263,794)(264,793)(265,792)(266,791)(267,790)(268,789)(269,788)(270,787)(271,786)(272,785)(273,784)(274,783)(275,782)(276,781)(277,780)(278,779)(279,778)(280,777)(281,776)(282,775)(283,774)(284,773)(285,772)(286,771)(287,770)(288,769)(289,768)(290,767)(291,766)(292,765)(293,764)(294,763)(295,762)(296,761)(297,760)(298,759)(299,758)(300,757)(301,756)(302,755)(303,754)(304,753)(305,752)(306,751)(307,750)(308,749)(309,748)(310,747)(311,746)(312,745)(313,744)(314,743)(315,742)(316,741)(317,740)(318,739)(319,738)(320,737)(321,736)(322,735)(323,734)(324,733)(325,732)(326,731)(327,730)(328,729)(329,728)(330,727)(331,726)(332,725)(333,724)(334,723)(335,722)(336,721)(337,720)(338,719)(339,718)(340,717)(341,716)(342,715)(343,714)(344,713)(345,712)(346,711)(347,710)(348,709)(349,708)(350,707)(351,706)(352,705)(353,704)(354,703)(355,702)(356,701)(357,700)(358,699)(359,698)(360,697)(361,696)(362,695)(363,694)(364,693)(365,692)(366,691)(367,690)(368,689)(369,688)(370,687)(371,686)(372,685)(373,684)(374,683)(375,682)(376,681)(377,680)(378,679)(379,678)(380,677)(381,676)(382,675)(383,674)(384,673)(385,672)(386,671)(387,670)(388,669)(389,668)(390,667)(391,666)(392,665)(393,664)(394,663)(395,662)(396,661)(397,660)(398,659)(399,658)(400,657)(401,656)(402,655)(403,654)(404,653)(405,652)(406,651)(407,650)(408,649)(409,648)(410,647)(411,646)(412,645)(413,644)(414,643)(415,642)(416,641)(417,640)(418,639)(419,638)(420,637)(421,636)(422,635)(423,634)(424,633)(425,632)(426,631)(427,630)(428,629)(429,628)(430,627)(431,626)(432,625)(433,624)(434,623)(435,622)(436,621)(437,620)(438,619)(439,618)(440,617)(441,616)(442,615)(443,614)(444,613)(445,612)(446,611)(447,610)(448,609)(449,608)(450,607)(451,606)(452,605)(453,604)(454,603)(455,602)(456,601)(457,600)(458,599)(459,598)(460,597)(461,596)(462,595)(463,594)(464,593)(465,592)(466,591)(467,590)(468,589)(469,588)(470,587)(471,586)(472,585)(473,584)(474,583)(475,582)(476,581)(477,580)(478,579)(479,578)(480,577)(481,576)(482,575)(483,574)(484,573)(485,572)(486,571)(487,570)(488,569)(489,568)(490,567)(491,566)(492,565)(493,564)(494,563)(495,562)(496,561)(497,560)(498,559)(499,558)(500,557)(501,556)(502,555)(503,554)(504,553)(505,552)(506,551)(507,550)(508,549)(509,548)(510,547)(511,546)(512,545)(513,544)(514,543)(515,542)(516,541)(517,540)(518,539)(519,538)(520,537)(521,536)(522,535)(523,534)(524,533)(525,532)(526,531)(527,530)(528,529)
Polycyclic presentation:
2^4,1039|c^2=d,b^a=bc,c^a=cd,e^a=e^1038,c^b=cd,e^b=e^1038
Conjugacy classes & character table
4159 conjugacy classes. The character table is too large to display.
Relationships
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16624, 26);
Finite Group Databasebeta