Finite Group Databasebeta

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Dic₄₂₅₂ #30684381

• metacyclic
• supersolvable
• metabelian
• solvable
• monomial
• stem

Aliases

Splittings

Subgroups

18 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 2 generators on 1079 points:

(1,2,3,4,5,6,7,8)(9,16,15,14,13,12,11,10)(17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,172,173,174,175,176,177,178,179,180,181,182,183,184,185,186,187,188,189,190,191,192,193,194,195,196,197,198,199,200,201,202,203,204,205,206,207,208,209,210,211,212,213,214,215,216,217,218,219,220,221,222,223,224,225,226,227,228,229,230,231,232,233,234,235,236,237,238,239,240,241,242,243,244,245,246,247,248,249,250,251,252,253,254,255,256,257,258,259,260,261,262,263,264,265,266,267,268,269,270,271,272,273,274,275,276,277,278,279,280,281,282,283,284,285,286,287,288,289,290,291,292,293,294,295,296,297,298,299,300,301,302,303,304,305,306,307,308,309,310,311,312,313,314,315,316,317,318,319,320,321,322,323,324,325,326,327,328,329,330,331,332,333,334,335,336,337,338,339,340,341,342,343,344,345,346,347,348,349,350,351,352,353,354,355,356,357,358,359,360,361,362,363,364,365,366,367,368,369,370,371,372,373,374,375,376,377,378,379,380,381,382,383,384,385,386,387,388,389,390,391,392,393,394,395,396,397,398,399,400,401,402,403,404,405,406,407,408,409,410,411,412,413,414,415,416,417,418,419,420,421,422,423,424,425,426,427,428,429,430,431,432,433,434,435,436,437,438,439,440,441,442,443,444,445,446,447,448,449,450,451,452,453,454,455,456,457,458,459,460,461,462,463,464,465,466,467,468,469,470,471,472,473,474,475,476,477,478,479,480,481,482,483,484,485,486,487,488,489,490,491,492,493,494,495,496,497,498,499,500,501,502,503,504,505,506,507,508,509,510,511,512,513,514,515,516,517,518,519,520,521,522,523,524,525,526,527,528,529,530,531,532,533,534,535,536,537,538,539,540,541,542,543,544,545,546,547,548,549,550,551,552,553,554,555,556,557,558,559,560,561,562,563,564,565,566,567,568,569,570,571,572,573,574,575,576,577,578,579,580,581,582,583,584,585,586,587,588,589,590,591,592,593,594,595,596,597,598,599,600,601,602,603,604,605,606,607,608,609,610,611,612,613,614,615,616,617,618,619,620,621,622,623,624,625,626,627,628,629,630,631,632,633,634,635,636,637,638,639,640,641,642,643,644,645,646,647,648,649,650,651,652,653,654,655,656,657,658,659,660,661,662,663,664,665,666,667,668,669,670,671,672,673,674,675,676,677,678,679,680,681,682,683,684,685,686,687,688,689,690,691,692,693,694,695,696,697,698,699,700,701,702,703,704,705,706,707,708,709,710,711,712,713,714,715,716,717,718,719,720,721,722,723,724,725,726,727,728,729,730,731,732,733,734,735,736,737,738,739,740,741,742,743,744,745,746,747,748,749,750,751,752,753,754,755,756,757,758,759,760,761,762,763,764,765,766,767,768,769,770,771,772,773,774,775,776,777,778,779,780,781,782,783,784,785,786,787,788,789,790,791,792,793,794,795,796,797,798,799,800,801,802,803,804,805,806,807,808,809,810,811,812,813,814,815,816,817,818,819,820,821,822,823,824,825,826,827,828,829,830,831,832,833,834,835,836,837,838,839,840,841,842,843,844,845,846,847,848,849,850,851,852,853,854,855,856,857,858,859,860,861,862,863,864,865,866,867,868,869,870,871,872,873,874,875,876,877,878,879,880,881,882,883,884,885,886,887,888,889,890,891,892,893,894,895,896,897,898,899,900,901,902,903,904,905,906,907,908,909,910,911,912,913,914,915,916,917,918,919,920,921,922,923,924,925,926,927,928,929,930,931,932,933,934,935,936,937,938,939,940,941,942,943,944,945,946,947,948,949,950,951,952,953,954,955,956,957,958,959,960,961,962,963,964,965,966,967,968,969,970,971,972,973,974,975,976,977,978,979,980,981,982,983,984,985,986,987,988,989,990,991,992,993,994,995,996,997,998,999,1000,1001,1002,1003,1004,1005,1006,1007,1008,1009,1010,1011,1012,1013,1014,1015,1016,1017,1018,1019,1020,1021,1022,1023,1024,1025,1026,1027,1028,1029,1030,1031,1032,1033,1034,1035,1036,1037,1038,1039,1040,1041,1042,1043,1044,1045,1046,1047,1048,1049,1050,1051,1052,1053,1054,1055,1056,1057,1058,1059,1060,1061,1062,1063,1064,1065,1066,1067,1068,1069,1070,1071,1072,1073,1074,1075,1076,1077,1078,1079);(1,9,5,13)(2,10,6,14)(3,11,7,15)(4,12,8,16)(18,1079)(19,1078)(20,1077)(21,1076)(22,1075)(23,1074)(24,1073)(25,1072)(26,1071)(27,1070)(28,1069)(29,1068)(30,1067)(31,1066)(32,1065)(33,1064)(34,1063)(35,1062)(36,1061)(37,1060)(38,1059)(39,1058)(40,1057)(41,1056)(42,1055)(43,1054)(44,1053)(45,1052)(46,1051)(47,1050)(48,1049)(49,1048)(50,1047)(51,1046)(52,1045)(53,1044)(54,1043)(55,1042)(56,1041)(57,1040)(58,1039)(59,1038)(60,1037)(61,1036)(62,1035)(63,1034)(64,1033)(65,1032)(66,1031)(67,1030)(68,1029)(69,1028)(70,1027)(71,1026)(72,1025)(73,1024)(74,1023)(75,1022)(76,1021)(77,1020)(78,1019)(79,1018)(80,1017)(81,1016)(82,1015)(83,1014)(84,1013)(85,1012)(86,1011)(87,1010)(88,1009)(89,1008)(90,1007)(91,1006)(92,1005)(93,1004)(94,1003)(95,1002)(96,1001)(97,1000)(98,999)(99,998)(100,997)(101,996)(102,995)(103,994)(104,993)(105,992)(106,991)(107,990)(108,989)(109,988)(110,987)(111,986)(112,985)(113,984)(114,983)(115,982)(116,981)(117,980)(118,979)(119,978)(120,977)(121,976)(122,975)(123,974)(124,973)(125,972)(126,971)(127,970)(128,969)(129,968)(130,967)(131,966)(132,965)(133,964)(134,963)(135,962)(136,961)(137,960)(138,959)(139,958)(140,957)(141,956)(142,955)(143,954)(144,953)(145,952)(146,951)(147,950)(148,949)(149,948)(150,947)(151,946)(152,945)(153,944)(154,943)(155,942)(156,941)(157,940)(158,939)(159,938)(160,937)(161,936)(162,935)(163,934)(164,933)(165,932)(166,931)(167,930)(168,929)(169,928)(170,927)(171,926)(172,925)(173,924)(174,923)(175,922)(176,921)(177,920)(178,919)(179,918)(180,917)(181,916)(182,915)(183,914)(184,913)(185,912)(186,911)(187,910)(188,909)(189,908)(190,907)(191,906)(192,905)(193,904)(194,903)(195,902)(196,901)(197,900)(198,899)(199,898)(200,897)(201,896)(202,895)(203,894)(204,893)(205,892)(206,891)(207,890)(208,889)(209,888)(210,887)(211,886)(212,885)(213,884)(214,883)(215,882)(216,881)(217,880)(218,879)(219,878)(220,877)(221,876)(222,875)(223,874)(224,873)(225,872)(226,871)(227,870)(228,869)(229,868)(230,867)(231,866)(232,865)(233,864)(234,863)(235,862)(236,861)(237,860)(238,859)(239,858)(240,857)(241,856)(242,855)(243,854)(244,853)(245,852)(246,851)(247,850)(248,849)(249,848)(250,847)(251,846)(252,845)(253,844)(254,843)(255,842)(256,841)(257,840)(258,839)(259,838)(260,837)(261,836)(262,835)(263,834)(264,833)(265,832)(266,831)(267,830)(268,829)(269,828)(270,827)(271,826)(272,825)(273,824)(274,823)(275,822)(276,821)(277,820)(278,819)(279,818)(280,817)(281,816)(282,815)(283,814)(284,813)(285,812)(286,811)(287,810)(288,809)(289,808)(290,807)(291,806)(292,805)(293,804)(294,803)(295,802)(296,801)(297,800)(298,799)(299,798)(300,797)(301,796)(302,795)(303,794)(304,793)(305,792)(306,791)(307,790)(308,789)(309,788)(310,787)(311,786)(312,785)(313,784)(314,783)(315,782)(316,781)(317,780)(318,779)(319,778)(320,777)(321,776)(322,775)(323,774)(324,773)(325,772)(326,771)(327,770)(328,769)(329,768)(330,767)(331,766)(332,765)(333,764)(334,763)(335,762)(336,761)(337,760)(338,759)(339,758)(340,757)(341,756)(342,755)(343,754)(344,753)(345,752)(346,751)(347,750)(348,749)(349,748)(350,747)(351,746)(352,745)(353,744)(354,743)(355,742)(356,741)(357,740)(358,739)(359,738)(360,737)(361,736)(362,735)(363,734)(364,733)(365,732)(366,731)(367,730)(368,729)(369,728)(370,727)(371,726)(372,725)(373,724)(374,723)(375,722)(376,721)(377,720)(378,719)(379,718)(380,717)(381,716)(382,715)(383,714)(384,713)(385,712)(386,711)(387,710)(388,709)(389,708)(390,707)(391,706)(392,705)(393,704)(394,703)(395,702)(396,701)(397,700)(398,699)(399,698)(400,697)(401,696)(402,695)(403,694)(404,693)(405,692)(406,691)(407,690)(408,689)(409,688)(410,687)(411,686)(412,685)(413,684)(414,683)(415,682)(416,681)(417,680)(418,679)(419,678)(420,677)(421,676)(422,675)(423,674)(424,673)(425,672)(426,671)(427,670)(428,669)(429,668)(430,667)(431,666)(432,665)(433,664)(434,663)(435,662)(436,661)(437,660)(438,659)(439,658)(440,657)(441,656)(442,655)(443,654)(444,653)(445,652)(446,651)(447,650)(448,649)(449,648)(450,647)(451,646)(452,645)(453,644)(454,643)(455,642)(456,641)(457,640)(458,639)(459,638)(460,637)(461,636)(462,635)(463,634)(464,633)(465,632)(466,631)(467,630)(468,629)(469,628)(470,627)(471,626)(472,625)(473,624)(474,623)(475,622)(476,621)(477,620)(478,619)(479,618)(480,617)(481,616)(482,615)(483,614)(484,613)(485,612)(486,611)(487,610)(488,609)(489,608)(490,607)(491,606)(492,605)(493,604)(494,603)(495,602)(496,601)(497,600)(498,599)(499,598)(500,597)(501,596)(502,595)(503,594)(504,593)(505,592)(506,591)(507,590)(508,589)(509,588)(510,587)(511,586)(512,585)(513,584)(514,583)(515,582)(516,581)(517,580)(518,579)(519,578)(520,577)(521,576)(522,575)(523,574)(524,573)(525,572)(526,571)(527,570)(528,569)(529,568)(530,567)(531,566)(532,565)(533,564)(534,563)(535,562)(536,561)(537,560)(538,559)(539,558)(540,557)(541,556)(542,555)(543,554)(544,553)(545,552)(546,551)(547,550)(548,549)

Polycyclic presentation:

2^4,1063|a^2=d,b^2=d,c^2=d,b^a=bc,c^a=cd,e^a=e^1062,c^b=cd,e^b=e^1062

Conjugacy classes & character table

4255 conjugacy classes. The character table is too large to display.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17008, 31);