Finite Group Databasebeta

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Dic₆₅₈₄ #39912035

• 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 855 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)(33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,172,173,174,175,176,177,178,179,180,181,182,183,184,185,186,187,188,189,190,191,192,193,194,195,196,197,198,199,200,201,202,203,204,205,206,207,208,209,210,211,212,213,214,215,216,217,218,219,220,221,222,223,224,225,226,227,228,229,230,231,232,233,234,235,236,237,238,239,240,241,242,243,244,245,246,247,248,249,250,251,252,253,254,255,256,257,258,259,260,261,262,263,264,265,266,267,268,269,270,271,272,273,274,275,276,277,278,279,280,281,282,283,284,285,286,287,288,289,290,291,292,293,294,295,296,297,298,299,300,301,302,303,304,305,306,307,308,309,310,311,312,313,314,315,316,317,318,319,320,321,322,323,324,325,326,327,328,329,330,331,332,333,334,335,336,337,338,339,340,341,342,343,344,345,346,347,348,349,350,351,352,353,354,355,356,357,358,359,360,361,362,363,364,365,366,367,368,369,370,371,372,373,374,375,376,377,378,379,380,381,382,383,384,385,386,387,388,389,390,391,392,393,394,395,396,397,398,399,400,401,402,403,404,405,406,407,408,409,410,411,412,413,414,415,416,417,418,419,420,421,422,423,424,425,426,427,428,429,430,431,432,433,434,435,436,437,438,439,440,441,442,443,444,445,446,447,448,449,450,451,452,453,454,455,456,457,458,459,460,461,462,463,464,465,466,467,468,469,470,471,472,473,474,475,476,477,478,479,480,481,482,483,484,485,486,487,488,489,490,491,492,493,494,495,496,497,498,499,500,501,502,503,504,505,506,507,508,509,510,511,512,513,514,515,516,517,518,519,520,521,522,523,524,525,526,527,528,529,530,531,532,533,534,535,536,537,538,539,540,541,542,543,544,545,546,547,548,549,550,551,552,553,554,555,556,557,558,559,560,561,562,563,564,565,566,567,568,569,570,571,572,573,574,575,576,577,578,579,580,581,582,583,584,585,586,587,588,589,590,591,592,593,594,595,596,597,598,599,600,601,602,603,604,605,606,607,608,609,610,611,612,613,614,615,616,617,618,619,620,621,622,623,624,625,626,627,628,629,630,631,632,633,634,635,636,637,638,639,640,641,642,643,644,645,646,647,648,649,650,651,652,653,654,655,656,657,658,659,660,661,662,663,664,665,666,667,668,669,670,671,672,673,674,675,676,677,678,679,680,681,682,683,684,685,686,687,688,689,690,691,692,693,694,695,696,697,698,699,700,701,702,703,704,705,706,707,708,709,710,711,712,713,714,715,716,717,718,719,720,721,722,723,724,725,726,727,728,729,730,731,732,733,734,735,736,737,738,739,740,741,742,743,744,745,746,747,748,749,750,751,752,753,754,755,756,757,758,759,760,761,762,763,764,765,766,767,768,769,770,771,772,773,774,775,776,777,778,779,780,781,782,783,784,785,786,787,788,789,790,791,792,793,794,795,796,797,798,799,800,801,802,803,804,805,806,807,808,809,810,811,812,813,814,815,816,817,818,819,820,821,822,823,824,825,826,827,828,829,830,831,832,833,834,835,836,837,838,839,840,841,842,843,844,845,846,847,848,849,850,851,852,853,854,855);(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)(34,855)(35,854)(36,853)(37,852)(38,851)(39,850)(40,849)(41,848)(42,847)(43,846)(44,845)(45,844)(46,843)(47,842)(48,841)(49,840)(50,839)(51,838)(52,837)(53,836)(54,835)(55,834)(56,833)(57,832)(58,831)(59,830)(60,829)(61,828)(62,827)(63,826)(64,825)(65,824)(66,823)(67,822)(68,821)(69,820)(70,819)(71,818)(72,817)(73,816)(74,815)(75,814)(76,813)(77,812)(78,811)(79,810)(80,809)(81,808)(82,807)(83,806)(84,805)(85,804)(86,803)(87,802)(88,801)(89,800)(90,799)(91,798)(92,797)(93,796)(94,795)(95,794)(96,793)(97,792)(98,791)(99,790)(100,789)(101,788)(102,787)(103,786)(104,785)(105,784)(106,783)(107,782)(108,781)(109,780)(110,779)(111,778)(112,777)(113,776)(114,775)(115,774)(116,773)(117,772)(118,771)(119,770)(120,769)(121,768)(122,767)(123,766)(124,765)(125,764)(126,763)(127,762)(128,761)(129,760)(130,759)(131,758)(132,757)(133,756)(134,755)(135,754)(136,753)(137,752)(138,751)(139,750)(140,749)(141,748)(142,747)(143,746)(144,745)(145,744)(146,743)(147,742)(148,741)(149,740)(150,739)(151,738)(152,737)(153,736)(154,735)(155,734)(156,733)(157,732)(158,731)(159,730)(160,729)(161,728)(162,727)(163,726)(164,725)(165,724)(166,723)(167,722)(168,721)(169,720)(170,719)(171,718)(172,717)(173,716)(174,715)(175,714)(176,713)(177,712)(178,711)(179,710)(180,709)(181,708)(182,707)(183,706)(184,705)(185,704)(186,703)(187,702)(188,701)(189,700)(190,699)(191,698)(192,697)(193,696)(194,695)(195,694)(196,693)(197,692)(198,691)(199,690)(200,689)(201,688)(202,687)(203,686)(204,685)(205,684)(206,683)(207,682)(208,681)(209,680)(210,679)(211,678)(212,677)(213,676)(214,675)(215,674)(216,673)(217,672)(218,671)(219,670)(220,669)(221,668)(222,667)(223,666)(224,665)(225,664)(226,663)(227,662)(228,661)(229,660)(230,659)(231,658)(232,657)(233,656)(234,655)(235,654)(236,653)(237,652)(238,651)(239,650)(240,649)(241,648)(242,647)(243,646)(244,645)(245,644)(246,643)(247,642)(248,641)(249,640)(250,639)(251,638)(252,637)(253,636)(254,635)(255,634)(256,633)(257,632)(258,631)(259,630)(260,629)(261,628)(262,627)(263,626)(264,625)(265,624)(266,623)(267,622)(268,621)(269,620)(270,619)(271,618)(272,617)(273,616)(274,615)(275,614)(276,613)(277,612)(278,611)(279,610)(280,609)(281,608)(282,607)(283,606)(284,605)(285,604)(286,603)(287,602)(288,601)(289,600)(290,599)(291,598)(292,597)(293,596)(294,595)(295,594)(296,593)(297,592)(298,591)(299,590)(300,589)(301,588)(302,587)(303,586)(304,585)(305,584)(306,583)(307,582)(308,581)(309,580)(310,579)(311,578)(312,577)(313,576)(314,575)(315,574)(316,573)(317,572)(318,571)(319,570)(320,569)(321,568)(322,567)(323,566)(324,565)(325,564)(326,563)(327,562)(328,561)(329,560)(330,559)(331,558)(332,557)(333,556)(334,555)(335,554)(336,553)(337,552)(338,551)(339,550)(340,549)(341,548)(342,547)(343,546)(344,545)(345,544)(346,543)(347,542)(348,541)(349,540)(350,539)(351,538)(352,537)(353,536)(354,535)(355,534)(356,533)(357,532)(358,531)(359,530)(360,529)(361,528)(362,527)(363,526)(364,525)(365,524)(366,523)(367,522)(368,521)(369,520)(370,519)(371,518)(372,517)(373,516)(374,515)(375,514)(376,513)(377,512)(378,511)(379,510)(380,509)(381,508)(382,507)(383,506)(384,505)(385,504)(386,503)(387,502)(388,501)(389,500)(390,499)(391,498)(392,497)(393,496)(394,495)(395,494)(396,493)(397,492)(398,491)(399,490)(400,489)(401,488)(402,487)(403,486)(404,485)(405,484)(406,483)(407,482)(408,481)(409,480)(410,479)(411,478)(412,477)(413,476)(414,475)(415,474)(416,473)(417,472)(418,471)(419,470)(420,469)(421,468)(422,467)(423,466)(424,465)(425,464)(426,463)(427,462)(428,461)(429,460)(430,459)(431,458)(432,457)(433,456)(434,455)(435,454)(436,453)(437,452)(438,451)(439,450)(440,449)(441,448)(442,447)(443,446)(444,445)

Polycyclic presentation:

2^5,823|a^2=e,b^2=e,c^2=de,d^2=e,b^a=bc,c^a=cd,d^a=de,f^a=f^822,c^b=cd,d^b=de,f^b=f^822

Conjugacy classes & character table

6587 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26336, 93);