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Dic₆₀₀₈ #37562385

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

Polycyclic presentation:

2^5,751|a^2=e,b^2=e,c^2=de,d^2=e,b^a=bc,c^a=cd,d^a=de,f^a=f^750,c^b=cd,d^b=de,f^b=f^750

Conjugacy classes & character table

6011 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24032, 93);