Finite Group Databasebeta

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Dic₅₉₄₄ #37557926

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

Polycyclic presentation:

2^5,743|a^2=e,b^2=e,c^2=de,d^2=e,b^a=bc,c^a=cd,d^a=de,f^a=f^742,c^b=cd,d^b=de,f^b=f^742

Conjugacy classes & character table

5947 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23776, 93);