Finite Group Databasebeta

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Dic₇₇₃₆ #44526068

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

Aliases

Splittings

Subgroups

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 2 generators on 999 points:

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

Polycyclic presentation:

2^5,967|a^2=e,b^2=e,c^2=de,d^2=e,b^a=bc,c^a=cd,d^a=de,f^a=f^966,c^b=cd,d^b=de,f^b=f^966

Conjugacy classes & character table

7739 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30944, 93);