Finite Group Databasebeta

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Dic₄₁₉₆ #30680907

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

Polycyclic presentation:

2^4,1049|a^2=d,b^2=d,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, 31);