Finite Group Databasebeta

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D₁₃₂₁₅ #40996189

• metacyclic
• supersolvable
• metabelian
• solvable
• monomial
• stem
• Frobenius

Aliases

Splittings

Subgroups

16 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 2 generators on 889 points:

(1,2,3)(4,5,6,7,8)(9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,172,173,174,175,176,177,178,179,180,181,182,183,184,185,186,187,188,189,190,191,192,193,194,195,196,197,198,199,200,201,202,203,204,205,206,207,208,209,210,211,212,213,214,215,216,217,218,219,220,221,222,223,224,225,226,227,228,229,230,231,232,233,234,235,236,237,238,239,240,241,242,243,244,245,246,247,248,249,250,251,252,253,254,255,256,257,258,259,260,261,262,263,264,265,266,267,268,269,270,271,272,273,274,275,276,277,278,279,280,281,282,283,284,285,286,287,288,289,290,291,292,293,294,295,296,297,298,299,300,301,302,303,304,305,306,307,308,309,310,311,312,313,314,315,316,317,318,319,320,321,322,323,324,325,326,327,328,329,330,331,332,333,334,335,336,337,338,339,340,341,342,343,344,345,346,347,348,349,350,351,352,353,354,355,356,357,358,359,360,361,362,363,364,365,366,367,368,369,370,371,372,373,374,375,376,377,378,379,380,381,382,383,384,385,386,387,388,389,390,391,392,393,394,395,396,397,398,399,400,401,402,403,404,405,406,407,408,409,410,411,412,413,414,415,416,417,418,419,420,421,422,423,424,425,426,427,428,429,430,431,432,433,434,435,436,437,438,439,440,441,442,443,444,445,446,447,448,449,450,451,452,453,454,455,456,457,458,459,460,461,462,463,464,465,466,467,468,469,470,471,472,473,474,475,476,477,478,479,480,481,482,483,484,485,486,487,488,489,490,491,492,493,494,495,496,497,498,499,500,501,502,503,504,505,506,507,508,509,510,511,512,513,514,515,516,517,518,519,520,521,522,523,524,525,526,527,528,529,530,531,532,533,534,535,536,537,538,539,540,541,542,543,544,545,546,547,548,549,550,551,552,553,554,555,556,557,558,559,560,561,562,563,564,565,566,567,568,569,570,571,572,573,574,575,576,577,578,579,580,581,582,583,584,585,586,587,588,589,590,591,592,593,594,595,596,597,598,599,600,601,602,603,604,605,606,607,608,609,610,611,612,613,614,615,616,617,618,619,620,621,622,623,624,625,626,627,628,629,630,631,632,633,634,635,636,637,638,639,640,641,642,643,644,645,646,647,648,649,650,651,652,653,654,655,656,657,658,659,660,661,662,663,664,665,666,667,668,669,670,671,672,673,674,675,676,677,678,679,680,681,682,683,684,685,686,687,688,689,690,691,692,693,694,695,696,697,698,699,700,701,702,703,704,705,706,707,708,709,710,711,712,713,714,715,716,717,718,719,720,721,722,723,724,725,726,727,728,729,730,731,732,733,734,735,736,737,738,739,740,741,742,743,744,745,746,747,748,749,750,751,752,753,754,755,756,757,758,759,760,761,762,763,764,765,766,767,768,769,770,771,772,773,774,775,776,777,778,779,780,781,782,783,784,785,786,787,788,789,790,791,792,793,794,795,796,797,798,799,800,801,802,803,804,805,806,807,808,809,810,811,812,813,814,815,816,817,818,819,820,821,822,823,824,825,826,827,828,829,830,831,832,833,834,835,836,837,838,839,840,841,842,843,844,845,846,847,848,849,850,851,852,853,854,855,856,857,858,859,860,861,862,863,864,865,866,867,868,869,870,871,872,873,874,875,876,877,878,879,880,881,882,883,884,885,886,887,888,889);(2,3)(5,8)(6,7)(10,889)(11,888)(12,887)(13,886)(14,885)(15,884)(16,883)(17,882)(18,881)(19,880)(20,879)(21,878)(22,877)(23,876)(24,875)(25,874)(26,873)(27,872)(28,871)(29,870)(30,869)(31,868)(32,867)(33,866)(34,865)(35,864)(36,863)(37,862)(38,861)(39,860)(40,859)(41,858)(42,857)(43,856)(44,855)(45,854)(46,853)(47,852)(48,851)(49,850)(50,849)(51,848)(52,847)(53,846)(54,845)(55,844)(56,843)(57,842)(58,841)(59,840)(60,839)(61,838)(62,837)(63,836)(64,835)(65,834)(66,833)(67,832)(68,831)(69,830)(70,829)(71,828)(72,827)(73,826)(74,825)(75,824)(76,823)(77,822)(78,821)(79,820)(80,819)(81,818)(82,817)(83,816)(84,815)(85,814)(86,813)(87,812)(88,811)(89,810)(90,809)(91,808)(92,807)(93,806)(94,805)(95,804)(96,803)(97,802)(98,801)(99,800)(100,799)(101,798)(102,797)(103,796)(104,795)(105,794)(106,793)(107,792)(108,791)(109,790)(110,789)(111,788)(112,787)(113,786)(114,785)(115,784)(116,783)(117,782)(118,781)(119,780)(120,779)(121,778)(122,777)(123,776)(124,775)(125,774)(126,773)(127,772)(128,771)(129,770)(130,769)(131,768)(132,767)(133,766)(134,765)(135,764)(136,763)(137,762)(138,761)(139,760)(140,759)(141,758)(142,757)(143,756)(144,755)(145,754)(146,753)(147,752)(148,751)(149,750)(150,749)(151,748)(152,747)(153,746)(154,745)(155,744)(156,743)(157,742)(158,741)(159,740)(160,739)(161,738)(162,737)(163,736)(164,735)(165,734)(166,733)(167,732)(168,731)(169,730)(170,729)(171,728)(172,727)(173,726)(174,725)(175,724)(176,723)(177,722)(178,721)(179,720)(180,719)(181,718)(182,717)(183,716)(184,715)(185,714)(186,713)(187,712)(188,711)(189,710)(190,709)(191,708)(192,707)(193,706)(194,705)(195,704)(196,703)(197,702)(198,701)(199,700)(200,699)(201,698)(202,697)(203,696)(204,695)(205,694)(206,693)(207,692)(208,691)(209,690)(210,689)(211,688)(212,687)(213,686)(214,685)(215,684)(216,683)(217,682)(218,681)(219,680)(220,679)(221,678)(222,677)(223,676)(224,675)(225,674)(226,673)(227,672)(228,671)(229,670)(230,669)(231,668)(232,667)(233,666)(234,665)(235,664)(236,663)(237,662)(238,661)(239,660)(240,659)(241,658)(242,657)(243,656)(244,655)(245,654)(246,653)(247,652)(248,651)(249,650)(250,649)(251,648)(252,647)(253,646)(254,645)(255,644)(256,643)(257,642)(258,641)(259,640)(260,639)(261,638)(262,637)(263,636)(264,635)(265,634)(266,633)(267,632)(268,631)(269,630)(270,629)(271,628)(272,627)(273,626)(274,625)(275,624)(276,623)(277,622)(278,621)(279,620)(280,619)(281,618)(282,617)(283,616)(284,615)(285,614)(286,613)(287,612)(288,611)(289,610)(290,609)(291,608)(292,607)(293,606)(294,605)(295,604)(296,603)(297,602)(298,601)(299,600)(300,599)(301,598)(302,597)(303,596)(304,595)(305,594)(306,593)(307,592)(308,591)(309,590)(310,589)(311,588)(312,587)(313,586)(314,585)(315,584)(316,583)(317,582)(318,581)(319,580)(320,579)(321,578)(322,577)(323,576)(324,575)(325,574)(326,573)(327,572)(328,571)(329,570)(330,569)(331,568)(332,567)(333,566)(334,565)(335,564)(336,563)(337,562)(338,561)(339,560)(340,559)(341,558)(342,557)(343,556)(344,555)(345,554)(346,553)(347,552)(348,551)(349,550)(350,549)(351,548)(352,547)(353,546)(354,545)(355,544)(356,543)(357,542)(358,541)(359,540)(360,539)(361,538)(362,537)(363,536)(364,535)(365,534)(366,533)(367,532)(368,531)(369,530)(370,529)(371,528)(372,527)(373,526)(374,525)(375,524)(376,523)(377,522)(378,521)(379,520)(380,519)(381,518)(382,517)(383,516)(384,515)(385,514)(386,513)(387,512)(388,511)(389,510)(390,509)(391,508)(392,507)(393,506)(394,505)(395,504)(396,503)(397,502)(398,501)(399,500)(400,499)(401,498)(402,497)(403,496)(404,495)(405,494)(406,493)(407,492)(408,491)(409,490)(410,489)(411,488)(412,487)(413,486)(414,485)(415,484)(416,483)(417,482)(418,481)(419,480)(420,479)(421,478)(422,477)(423,476)(424,475)(425,474)(426,473)(427,472)(428,471)(429,470)(430,469)(431,468)(432,467)(433,466)(434,465)(435,464)(436,463)(437,462)(438,461)(439,460)(440,459)(441,458)(442,457)(443,456)(444,455)(445,454)(446,453)(447,452)(448,451)(449,450)

Polycyclic presentation:

2,3,5,881|b^a=b^2,c^a=c^4,d^a=d^880

Conjugacy classes & character table

6609 conjugacy classes. The character table is too large to display.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26430, 9);