Finite Group Databasebeta

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Dic₈₈₃ #16812948

• metacyclic
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Splittings

Subgroups

6 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 2 generators on 887 points:

(1,2)(3,4)(5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,172,173,174,175,176,177,178,179,180,181,182,183,184,185,186,187,188,189,190,191,192,193,194,195,196,197,198,199,200,201,202,203,204,205,206,207,208,209,210,211,212,213,214,215,216,217,218,219,220,221,222,223,224,225,226,227,228,229,230,231,232,233,234,235,236,237,238,239,240,241,242,243,244,245,246,247,248,249,250,251,252,253,254,255,256,257,258,259,260,261,262,263,264,265,266,267,268,269,270,271,272,273,274,275,276,277,278,279,280,281,282,283,284,285,286,287,288,289,290,291,292,293,294,295,296,297,298,299,300,301,302,303,304,305,306,307,308,309,310,311,312,313,314,315,316,317,318,319,320,321,322,323,324,325,326,327,328,329,330,331,332,333,334,335,336,337,338,339,340,341,342,343,344,345,346,347,348,349,350,351,352,353,354,355,356,357,358,359,360,361,362,363,364,365,366,367,368,369,370,371,372,373,374,375,376,377,378,379,380,381,382,383,384,385,386,387,388,389,390,391,392,393,394,395,396,397,398,399,400,401,402,403,404,405,406,407,408,409,410,411,412,413,414,415,416,417,418,419,420,421,422,423,424,425,426,427,428,429,430,431,432,433,434,435,436,437,438,439,440,441,442,443,444,445,446,447,448,449,450,451,452,453,454,455,456,457,458,459,460,461,462,463,464,465,466,467,468,469,470,471,472,473,474,475,476,477,478,479,480,481,482,483,484,485,486,487,488,489,490,491,492,493,494,495,496,497,498,499,500,501,502,503,504,505,506,507,508,509,510,511,512,513,514,515,516,517,518,519,520,521,522,523,524,525,526,527,528,529,530,531,532,533,534,535,536,537,538,539,540,541,542,543,544,545,546,547,548,549,550,551,552,553,554,555,556,557,558,559,560,561,562,563,564,565,566,567,568,569,570,571,572,573,574,575,576,577,578,579,580,581,582,583,584,585,586,587,588,589,590,591,592,593,594,595,596,597,598,599,600,601,602,603,604,605,606,607,608,609,610,611,612,613,614,615,616,617,618,619,620,621,622,623,624,625,626,627,628,629,630,631,632,633,634,635,636,637,638,639,640,641,642,643,644,645,646,647,648,649,650,651,652,653,654,655,656,657,658,659,660,661,662,663,664,665,666,667,668,669,670,671,672,673,674,675,676,677,678,679,680,681,682,683,684,685,686,687,688,689,690,691,692,693,694,695,696,697,698,699,700,701,702,703,704,705,706,707,708,709,710,711,712,713,714,715,716,717,718,719,720,721,722,723,724,725,726,727,728,729,730,731,732,733,734,735,736,737,738,739,740,741,742,743,744,745,746,747,748,749,750,751,752,753,754,755,756,757,758,759,760,761,762,763,764,765,766,767,768,769,770,771,772,773,774,775,776,777,778,779,780,781,782,783,784,785,786,787,788,789,790,791,792,793,794,795,796,797,798,799,800,801,802,803,804,805,806,807,808,809,810,811,812,813,814,815,816,817,818,819,820,821,822,823,824,825,826,827,828,829,830,831,832,833,834,835,836,837,838,839,840,841,842,843,844,845,846,847,848,849,850,851,852,853,854,855,856,857,858,859,860,861,862,863,864,865,866,867,868,869,870,871,872,873,874,875,876,877,878,879,880,881,882,883,884,885,886,887);(1,3,2,4)(6,887)(7,886)(8,885)(9,884)(10,883)(11,882)(12,881)(13,880)(14,879)(15,878)(16,877)(17,876)(18,875)(19,874)(20,873)(21,872)(22,871)(23,870)(24,869)(25,868)(26,867)(27,866)(28,865)(29,864)(30,863)(31,862)(32,861)(33,860)(34,859)(35,858)(36,857)(37,856)(38,855)(39,854)(40,853)(41,852)(42,851)(43,850)(44,849)(45,848)(46,847)(47,846)(48,845)(49,844)(50,843)(51,842)(52,841)(53,840)(54,839)(55,838)(56,837)(57,836)(58,835)(59,834)(60,833)(61,832)(62,831)(63,830)(64,829)(65,828)(66,827)(67,826)(68,825)(69,824)(70,823)(71,822)(72,821)(73,820)(74,819)(75,818)(76,817)(77,816)(78,815)(79,814)(80,813)(81,812)(82,811)(83,810)(84,809)(85,808)(86,807)(87,806)(88,805)(89,804)(90,803)(91,802)(92,801)(93,800)(94,799)(95,798)(96,797)(97,796)(98,795)(99,794)(100,793)(101,792)(102,791)(103,790)(104,789)(105,788)(106,787)(107,786)(108,785)(109,784)(110,783)(111,782)(112,781)(113,780)(114,779)(115,778)(116,777)(117,776)(118,775)(119,774)(120,773)(121,772)(122,771)(123,770)(124,769)(125,768)(126,767)(127,766)(128,765)(129,764)(130,763)(131,762)(132,761)(133,760)(134,759)(135,758)(136,757)(137,756)(138,755)(139,754)(140,753)(141,752)(142,751)(143,750)(144,749)(145,748)(146,747)(147,746)(148,745)(149,744)(150,743)(151,742)(152,741)(153,740)(154,739)(155,738)(156,737)(157,736)(158,735)(159,734)(160,733)(161,732)(162,731)(163,730)(164,729)(165,728)(166,727)(167,726)(168,725)(169,724)(170,723)(171,722)(172,721)(173,720)(174,719)(175,718)(176,717)(177,716)(178,715)(179,714)(180,713)(181,712)(182,711)(183,710)(184,709)(185,708)(186,707)(187,706)(188,705)(189,704)(190,703)(191,702)(192,701)(193,700)(194,699)(195,698)(196,697)(197,696)(198,695)(199,694)(200,693)(201,692)(202,691)(203,690)(204,689)(205,688)(206,687)(207,686)(208,685)(209,684)(210,683)(211,682)(212,681)(213,680)(214,679)(215,678)(216,677)(217,676)(218,675)(219,674)(220,673)(221,672)(222,671)(223,670)(224,669)(225,668)(226,667)(227,666)(228,665)(229,664)(230,663)(231,662)(232,661)(233,660)(234,659)(235,658)(236,657)(237,656)(238,655)(239,654)(240,653)(241,652)(242,651)(243,650)(244,649)(245,648)(246,647)(247,646)(248,645)(249,644)(250,643)(251,642)(252,641)(253,640)(254,639)(255,638)(256,637)(257,636)(258,635)(259,634)(260,633)(261,632)(262,631)(263,630)(264,629)(265,628)(266,627)(267,626)(268,625)(269,624)(270,623)(271,622)(272,621)(273,620)(274,619)(275,618)(276,617)(277,616)(278,615)(279,614)(280,613)(281,612)(282,611)(283,610)(284,609)(285,608)(286,607)(287,606)(288,605)(289,604)(290,603)(291,602)(292,601)(293,600)(294,599)(295,598)(296,597)(297,596)(298,595)(299,594)(300,593)(301,592)(302,591)(303,590)(304,589)(305,588)(306,587)(307,586)(308,585)(309,584)(310,583)(311,582)(312,581)(313,580)(314,579)(315,578)(316,577)(317,576)(318,575)(319,574)(320,573)(321,572)(322,571)(323,570)(324,569)(325,568)(326,567)(327,566)(328,565)(329,564)(330,563)(331,562)(332,561)(333,560)(334,559)(335,558)(336,557)(337,556)(338,555)(339,554)(340,553)(341,552)(342,551)(343,550)(344,549)(345,548)(346,547)(347,546)(348,545)(349,544)(350,543)(351,542)(352,541)(353,540)(354,539)(355,538)(356,537)(357,536)(358,535)(359,534)(360,533)(361,532)(362,531)(363,530)(364,529)(365,528)(366,527)(367,526)(368,525)(369,524)(370,523)(371,522)(372,521)(373,520)(374,519)(375,518)(376,517)(377,516)(378,515)(379,514)(380,513)(381,512)(382,511)(383,510)(384,509)(385,508)(386,507)(387,506)(388,505)(389,504)(390,503)(391,502)(392,501)(393,500)(394,499)(395,498)(396,497)(397,496)(398,495)(399,494)(400,493)(401,492)(402,491)(403,490)(404,489)(405,488)(406,487)(407,486)(408,485)(409,484)(410,483)(411,482)(412,481)(413,480)(414,479)(415,478)(416,477)(417,476)(418,475)(419,474)(420,473)(421,472)(422,471)(423,470)(424,469)(425,468)(426,467)(427,466)(428,465)(429,464)(430,463)(431,462)(432,461)(433,460)(434,459)(435,458)(436,457)(437,456)(438,455)(439,454)(440,453)(441,452)(442,451)(443,450)(444,449)(445,448)(446,447)

Polycyclic presentation:

2^2,883|a^2=b,c^a=c^882

Conjugacy classes & character table

886 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3532, 1);