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Dic₅₈₁₆ #37551495

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

Polycyclic presentation:

2^5,727|a^2=e,b^2=e,c^2=de,d^2=e,b^a=bc,c^a=cd,d^a=de,f^a=f^726,c^b=cd,d^b=de,f^b=f^726

Conjugacy classes & character table

5819 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23264, 93);