Finite Group Databasebeta

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D₁₅₁₅₂ #44476192

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

Aliases

Splittings

Subgroups

28 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 2 generators on 963 points:

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

Polycyclic presentation:

2^5,947|c^2=de,d^2=e,b^a=bc,c^a=cd,d^a=de,f^a=f^946,c^b=cd,d^b=de,f^b=f^946

Conjugacy classes & character table

7579 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30304, 88);