Finite Group Databasebeta

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Dic₃₇₁₆ #28415441

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

Polycyclic presentation:

2^4,929|a^2=d,b^2=d,c^2=d,b^a=bc,c^a=cd,e^a=e^928,c^b=cd,e^b=e^928

Conjugacy classes & character table

3719 conjugacy classes. The character table is too large to display.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(14864, 31);