Finite Group Databasebeta

?

← Prev (#49089248) Next (#49089250) →

D₁₇₉₁₃ #49089249

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

Polycyclic presentation:

2,3,7,853|b^a=b^2,c^a=c^6,d^a=d^852

Conjugacy classes & character table

8958 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(35826, 12);