Finite Group Databasebeta

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Dic₄₀₃₆ #30633323

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

Polycyclic presentation:

2^4,1009|a^2=d,b^2=d,c^2=d,b^a=bc,c^a=cd,e^a=e^1008,c^b=cd,e^b=e^1008

Conjugacy classes & character table

4039 conjugacy classes. The character table is too large to display.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16144, 31);