Finite Group Databasebeta

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D₇₉₄₇ #30629626

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

Aliases

Splittings

Subgroups

12 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 2 generators on 892 points:

(1,2,3,4,5,6,7,8,9)(10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,172,173,174,175,176,177,178,179,180,181,182,183,184,185,186,187,188,189,190,191,192,193,194,195,196,197,198,199,200,201,202,203,204,205,206,207,208,209,210,211,212,213,214,215,216,217,218,219,220,221,222,223,224,225,226,227,228,229,230,231,232,233,234,235,236,237,238,239,240,241,242,243,244,245,246,247,248,249,250,251,252,253,254,255,256,257,258,259,260,261,262,263,264,265,266,267,268,269,270,271,272,273,274,275,276,277,278,279,280,281,282,283,284,285,286,287,288,289,290,291,292,293,294,295,296,297,298,299,300,301,302,303,304,305,306,307,308,309,310,311,312,313,314,315,316,317,318,319,320,321,322,323,324,325,326,327,328,329,330,331,332,333,334,335,336,337,338,339,340,341,342,343,344,345,346,347,348,349,350,351,352,353,354,355,356,357,358,359,360,361,362,363,364,365,366,367,368,369,370,371,372,373,374,375,376,377,378,379,380,381,382,383,384,385,386,387,388,389,390,391,392,393,394,395,396,397,398,399,400,401,402,403,404,405,406,407,408,409,410,411,412,413,414,415,416,417,418,419,420,421,422,423,424,425,426,427,428,429,430,431,432,433,434,435,436,437,438,439,440,441,442,443,444,445,446,447,448,449,450,451,452,453,454,455,456,457,458,459,460,461,462,463,464,465,466,467,468,469,470,471,472,473,474,475,476,477,478,479,480,481,482,483,484,485,486,487,488,489,490,491,492,493,494,495,496,497,498,499,500,501,502,503,504,505,506,507,508,509,510,511,512,513,514,515,516,517,518,519,520,521,522,523,524,525,526,527,528,529,530,531,532,533,534,535,536,537,538,539,540,541,542,543,544,545,546,547,548,549,550,551,552,553,554,555,556,557,558,559,560,561,562,563,564,565,566,567,568,569,570,571,572,573,574,575,576,577,578,579,580,581,582,583,584,585,586,587,588,589,590,591,592,593,594,595,596,597,598,599,600,601,602,603,604,605,606,607,608,609,610,611,612,613,614,615,616,617,618,619,620,621,622,623,624,625,626,627,628,629,630,631,632,633,634,635,636,637,638,639,640,641,642,643,644,645,646,647,648,649,650,651,652,653,654,655,656,657,658,659,660,661,662,663,664,665,666,667,668,669,670,671,672,673,674,675,676,677,678,679,680,681,682,683,684,685,686,687,688,689,690,691,692,693,694,695,696,697,698,699,700,701,702,703,704,705,706,707,708,709,710,711,712,713,714,715,716,717,718,719,720,721,722,723,724,725,726,727,728,729,730,731,732,733,734,735,736,737,738,739,740,741,742,743,744,745,746,747,748,749,750,751,752,753,754,755,756,757,758,759,760,761,762,763,764,765,766,767,768,769,770,771,772,773,774,775,776,777,778,779,780,781,782,783,784,785,786,787,788,789,790,791,792,793,794,795,796,797,798,799,800,801,802,803,804,805,806,807,808,809,810,811,812,813,814,815,816,817,818,819,820,821,822,823,824,825,826,827,828,829,830,831,832,833,834,835,836,837,838,839,840,841,842,843,844,845,846,847,848,849,850,851,852,853,854,855,856,857,858,859,860,861,862,863,864,865,866,867,868,869,870,871,872,873,874,875,876,877,878,879,880,881,882,883,884,885,886,887,888,889,890,891,892);(2,9)(3,8)(4,7)(5,6)(11,892)(12,891)(13,890)(14,889)(15,888)(16,887)(17,886)(18,885)(19,884)(20,883)(21,882)(22,881)(23,880)(24,879)(25,878)(26,877)(27,876)(28,875)(29,874)(30,873)(31,872)(32,871)(33,870)(34,869)(35,868)(36,867)(37,866)(38,865)(39,864)(40,863)(41,862)(42,861)(43,860)(44,859)(45,858)(46,857)(47,856)(48,855)(49,854)(50,853)(51,852)(52,851)(53,850)(54,849)(55,848)(56,847)(57,846)(58,845)(59,844)(60,843)(61,842)(62,841)(63,840)(64,839)(65,838)(66,837)(67,836)(68,835)(69,834)(70,833)(71,832)(72,831)(73,830)(74,829)(75,828)(76,827)(77,826)(78,825)(79,824)(80,823)(81,822)(82,821)(83,820)(84,819)(85,818)(86,817)(87,816)(88,815)(89,814)(90,813)(91,812)(92,811)(93,810)(94,809)(95,808)(96,807)(97,806)(98,805)(99,804)(100,803)(101,802)(102,801)(103,800)(104,799)(105,798)(106,797)(107,796)(108,795)(109,794)(110,793)(111,792)(112,791)(113,790)(114,789)(115,788)(116,787)(117,786)(118,785)(119,784)(120,783)(121,782)(122,781)(123,780)(124,779)(125,778)(126,777)(127,776)(128,775)(129,774)(130,773)(131,772)(132,771)(133,770)(134,769)(135,768)(136,767)(137,766)(138,765)(139,764)(140,763)(141,762)(142,761)(143,760)(144,759)(145,758)(146,757)(147,756)(148,755)(149,754)(150,753)(151,752)(152,751)(153,750)(154,749)(155,748)(156,747)(157,746)(158,745)(159,744)(160,743)(161,742)(162,741)(163,740)(164,739)(165,738)(166,737)(167,736)(168,735)(169,734)(170,733)(171,732)(172,731)(173,730)(174,729)(175,728)(176,727)(177,726)(178,725)(179,724)(180,723)(181,722)(182,721)(183,720)(184,719)(185,718)(186,717)(187,716)(188,715)(189,714)(190,713)(191,712)(192,711)(193,710)(194,709)(195,708)(196,707)(197,706)(198,705)(199,704)(200,703)(201,702)(202,701)(203,700)(204,699)(205,698)(206,697)(207,696)(208,695)(209,694)(210,693)(211,692)(212,691)(213,690)(214,689)(215,688)(216,687)(217,686)(218,685)(219,684)(220,683)(221,682)(222,681)(223,680)(224,679)(225,678)(226,677)(227,676)(228,675)(229,674)(230,673)(231,672)(232,671)(233,670)(234,669)(235,668)(236,667)(237,666)(238,665)(239,664)(240,663)(241,662)(242,661)(243,660)(244,659)(245,658)(246,657)(247,656)(248,655)(249,654)(250,653)(251,652)(252,651)(253,650)(254,649)(255,648)(256,647)(257,646)(258,645)(259,644)(260,643)(261,642)(262,641)(263,640)(264,639)(265,638)(266,637)(267,636)(268,635)(269,634)(270,633)(271,632)(272,631)(273,630)(274,629)(275,628)(276,627)(277,626)(278,625)(279,624)(280,623)(281,622)(282,621)(283,620)(284,619)(285,618)(286,617)(287,616)(288,615)(289,614)(290,613)(291,612)(292,611)(293,610)(294,609)(295,608)(296,607)(297,606)(298,605)(299,604)(300,603)(301,602)(302,601)(303,600)(304,599)(305,598)(306,597)(307,596)(308,595)(309,594)(310,593)(311,592)(312,591)(313,590)(314,589)(315,588)(316,587)(317,586)(318,585)(319,584)(320,583)(321,582)(322,581)(323,580)(324,579)(325,578)(326,577)(327,576)(328,575)(329,574)(330,573)(331,572)(332,571)(333,570)(334,569)(335,568)(336,567)(337,566)(338,565)(339,564)(340,563)(341,562)(342,561)(343,560)(344,559)(345,558)(346,557)(347,556)(348,555)(349,554)(350,553)(351,552)(352,551)(353,550)(354,549)(355,548)(356,547)(357,546)(358,545)(359,544)(360,543)(361,542)(362,541)(363,540)(364,539)(365,538)(366,537)(367,536)(368,535)(369,534)(370,533)(371,532)(372,531)(373,530)(374,529)(375,528)(376,527)(377,526)(378,525)(379,524)(380,523)(381,522)(382,521)(383,520)(384,519)(385,518)(386,517)(387,516)(388,515)(389,514)(390,513)(391,512)(392,511)(393,510)(394,509)(395,508)(396,507)(397,506)(398,505)(399,504)(400,503)(401,502)(402,501)(403,500)(404,499)(405,498)(406,497)(407,496)(408,495)(409,494)(410,493)(411,492)(412,491)(413,490)(414,489)(415,488)(416,487)(417,486)(418,485)(419,484)(420,483)(421,482)(422,481)(423,480)(424,479)(425,478)(426,477)(427,476)(428,475)(429,474)(430,473)(431,472)(432,471)(433,470)(434,469)(435,468)(436,467)(437,466)(438,465)(439,464)(440,463)(441,462)(442,461)(443,460)(444,459)(445,458)(446,457)(447,456)(448,455)(449,454)(450,453)(451,452)

Polycyclic presentation:

2,3,883,3|b^3=d^2,b^a=b^2d,c^a=c^882,d^a=d^2

Conjugacy classes & character table

3975 conjugacy classes. The character table is too large to display.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15894, 6);