Finite Group Databasebeta

?

← Prev (#37564328) Next (#37564330) →

D₁₂₁₁₂ #37564329

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

Polycyclic presentation:

2^5,757|c^2=de,d^2=e,b^a=bc,c^a=cd,d^a=de,f^a=f^756,c^b=cd,d^b=de,f^b=f^756

Conjugacy classes & character table

6059 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24224, 88);