Finite Group Databasebeta

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Dic₃₆₇₆ #28413632

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

Polycyclic presentation:

2^4,919|a^2=d,b^2=d,c^2=d,b^a=bc,c^a=cd,e^a=e^918,c^b=cd,e^b=e^918

Conjugacy classes & character table

3679 conjugacy classes. The character table is too large to display.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(14704, 31);