Finite Group Databasebeta

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D₁₂₅₉₂ #38737909

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

Polycyclic presentation:

2^5,787|c^2=de,d^2=e,b^a=bc,c^a=cd,d^a=de,f^a=f^786,c^b=cd,d^b=de,f^b=f^786

Conjugacy classes & character table

6299 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(25184, 88);