Finite Group Databasebeta

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D₇₈₉₃ #30628916

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

Polycyclic presentation:

2,3,877,3|b^3=d^2,b^a=b^2d,c^a=c^876,d^a=d^2

Conjugacy classes & character table

3948 conjugacy classes. The character table is too large to display.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15786, 6);