Finite Group Databasebeta

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Dic₈₄₀₈ #46777626

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

Aliases

Splittings

Subgroups

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 2 generators on 1083 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16)(17,32,31,30,29,28,27,26,25,24,23,22,21,20,19,18)(33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,172,173,174,175,176,177,178,179,180,181,182,183,184,185,186,187,188,189,190,191,192,193,194,195,196,197,198,199,200,201,202,203,204,205,206,207,208,209,210,211,212,213,214,215,216,217,218,219,220,221,222,223,224,225,226,227,228,229,230,231,232,233,234,235,236,237,238,239,240,241,242,243,244,245,246,247,248,249,250,251,252,253,254,255,256,257,258,259,260,261,262,263,264,265,266,267,268,269,270,271,272,273,274,275,276,277,278,279,280,281,282,283,284,285,286,287,288,289,290,291,292,293,294,295,296,297,298,299,300,301,302,303,304,305,306,307,308,309,310,311,312,313,314,315,316,317,318,319,320,321,322,323,324,325,326,327,328,329,330,331,332,333,334,335,336,337,338,339,340,341,342,343,344,345,346,347,348,349,350,351,352,353,354,355,356,357,358,359,360,361,362,363,364,365,366,367,368,369,370,371,372,373,374,375,376,377,378,379,380,381,382,383,384,385,386,387,388,389,390,391,392,393,394,395,396,397,398,399,400,401,402,403,404,405,406,407,408,409,410,411,412,413,414,415,416,417,418,419,420,421,422,423,424,425,426,427,428,429,430,431,432,433,434,435,436,437,438,439,440,441,442,443,444,445,446,447,448,449,450,451,452,453,454,455,456,457,458,459,460,461,462,463,464,465,466,467,468,469,470,471,472,473,474,475,476,477,478,479,480,481,482,483,484,485,486,487,488,489,490,491,492,493,494,495,496,497,498,499,500,501,502,503,504,505,506,507,508,509,510,511,512,513,514,515,516,517,518,519,520,521,522,523,524,525,526,527,528,529,530,531,532,533,534,535,536,537,538,539,540,541,542,543,544,545,546,547,548,549,550,551,552,553,554,555,556,557,558,559,560,561,562,563,564,565,566,567,568,569,570,571,572,573,574,575,576,577,578,579,580,581,582,583,584,585,586,587,588,589,590,591,592,593,594,595,596,597,598,599,600,601,602,603,604,605,606,607,608,609,610,611,612,613,614,615,616,617,618,619,620,621,622,623,624,625,626,627,628,629,630,631,632,633,634,635,636,637,638,639,640,641,642,643,644,645,646,647,648,649,650,651,652,653,654,655,656,657,658,659,660,661,662,663,664,665,666,667,668,669,670,671,672,673,674,675,676,677,678,679,680,681,682,683,684,685,686,687,688,689,690,691,692,693,694,695,696,697,698,699,700,701,702,703,704,705,706,707,708,709,710,711,712,713,714,715,716,717,718,719,720,721,722,723,724,725,726,727,728,729,730,731,732,733,734,735,736,737,738,739,740,741,742,743,744,745,746,747,748,749,750,751,752,753,754,755,756,757,758,759,760,761,762,763,764,765,766,767,768,769,770,771,772,773,774,775,776,777,778,779,780,781,782,783,784,785,786,787,788,789,790,791,792,793,794,795,796,797,798,799,800,801,802,803,804,805,806,807,808,809,810,811,812,813,814,815,816,817,818,819,820,821,822,823,824,825,826,827,828,829,830,831,832,833,834,835,836,837,838,839,840,841,842,843,844,845,846,847,848,849,850,851,852,853,854,855,856,857,858,859,860,861,862,863,864,865,866,867,868,869,870,871,872,873,874,875,876,877,878,879,880,881,882,883,884,885,886,887,888,889,890,891,892,893,894,895,896,897,898,899,900,901,902,903,904,905,906,907,908,909,910,911,912,913,914,915,916,917,918,919,920,921,922,923,924,925,926,927,928,929,930,931,932,933,934,935,936,937,938,939,940,941,942,943,944,945,946,947,948,949,950,951,952,953,954,955,956,957,958,959,960,961,962,963,964,965,966,967,968,969,970,971,972,973,974,975,976,977,978,979,980,981,982,983,984,985,986,987,988,989,990,991,992,993,994,995,996,997,998,999,1000,1001,1002,1003,1004,1005,1006,1007,1008,1009,1010,1011,1012,1013,1014,1015,1016,1017,1018,1019,1020,1021,1022,1023,1024,1025,1026,1027,1028,1029,1030,1031,1032,1033,1034,1035,1036,1037,1038,1039,1040,1041,1042,1043,1044,1045,1046,1047,1048,1049,1050,1051,1052,1053,1054,1055,1056,1057,1058,1059,1060,1061,1062,1063,1064,1065,1066,1067,1068,1069,1070,1071,1072,1073,1074,1075,1076,1077,1078,1079,1080,1081,1082,1083);(1,17,9,25)(2,18,10,26)(3,19,11,27)(4,20,12,28)(5,21,13,29)(6,22,14,30)(7,23,15,31)(8,24,16,32)(34,1083)(35,1082)(36,1081)(37,1080)(38,1079)(39,1078)(40,1077)(41,1076)(42,1075)(43,1074)(44,1073)(45,1072)(46,1071)(47,1070)(48,1069)(49,1068)(50,1067)(51,1066)(52,1065)(53,1064)(54,1063)(55,1062)(56,1061)(57,1060)(58,1059)(59,1058)(60,1057)(61,1056)(62,1055)(63,1054)(64,1053)(65,1052)(66,1051)(67,1050)(68,1049)(69,1048)(70,1047)(71,1046)(72,1045)(73,1044)(74,1043)(75,1042)(76,1041)(77,1040)(78,1039)(79,1038)(80,1037)(81,1036)(82,1035)(83,1034)(84,1033)(85,1032)(86,1031)(87,1030)(88,1029)(89,1028)(90,1027)(91,1026)(92,1025)(93,1024)(94,1023)(95,1022)(96,1021)(97,1020)(98,1019)(99,1018)(100,1017)(101,1016)(102,1015)(103,1014)(104,1013)(105,1012)(106,1011)(107,1010)(108,1009)(109,1008)(110,1007)(111,1006)(112,1005)(113,1004)(114,1003)(115,1002)(116,1001)(117,1000)(118,999)(119,998)(120,997)(121,996)(122,995)(123,994)(124,993)(125,992)(126,991)(127,990)(128,989)(129,988)(130,987)(131,986)(132,985)(133,984)(134,983)(135,982)(136,981)(137,980)(138,979)(139,978)(140,977)(141,976)(142,975)(143,974)(144,973)(145,972)(146,971)(147,970)(148,969)(149,968)(150,967)(151,966)(152,965)(153,964)(154,963)(155,962)(156,961)(157,960)(158,959)(159,958)(160,957)(161,956)(162,955)(163,954)(164,953)(165,952)(166,951)(167,950)(168,949)(169,948)(170,947)(171,946)(172,945)(173,944)(174,943)(175,942)(176,941)(177,940)(178,939)(179,938)(180,937)(181,936)(182,935)(183,934)(184,933)(185,932)(186,931)(187,930)(188,929)(189,928)(190,927)(191,926)(192,925)(193,924)(194,923)(195,922)(196,921)(197,920)(198,919)(199,918)(200,917)(201,916)(202,915)(203,914)(204,913)(205,912)(206,911)(207,910)(208,909)(209,908)(210,907)(211,906)(212,905)(213,904)(214,903)(215,902)(216,901)(217,900)(218,899)(219,898)(220,897)(221,896)(222,895)(223,894)(224,893)(225,892)(226,891)(227,890)(228,889)(229,888)(230,887)(231,886)(232,885)(233,884)(234,883)(235,882)(236,881)(237,880)(238,879)(239,878)(240,877)(241,876)(242,875)(243,874)(244,873)(245,872)(246,871)(247,870)(248,869)(249,868)(250,867)(251,866)(252,865)(253,864)(254,863)(255,862)(256,861)(257,860)(258,859)(259,858)(260,857)(261,856)(262,855)(263,854)(264,853)(265,852)(266,851)(267,850)(268,849)(269,848)(270,847)(271,846)(272,845)(273,844)(274,843)(275,842)(276,841)(277,840)(278,839)(279,838)(280,837)(281,836)(282,835)(283,834)(284,833)(285,832)(286,831)(287,830)(288,829)(289,828)(290,827)(291,826)(292,825)(293,824)(294,823)(295,822)(296,821)(297,820)(298,819)(299,818)(300,817)(301,816)(302,815)(303,814)(304,813)(305,812)(306,811)(307,810)(308,809)(309,808)(310,807)(311,806)(312,805)(313,804)(314,803)(315,802)(316,801)(317,800)(318,799)(319,798)(320,797)(321,796)(322,795)(323,794)(324,793)(325,792)(326,791)(327,790)(328,789)(329,788)(330,787)(331,786)(332,785)(333,784)(334,783)(335,782)(336,781)(337,780)(338,779)(339,778)(340,777)(341,776)(342,775)(343,774)(344,773)(345,772)(346,771)(347,770)(348,769)(349,768)(350,767)(351,766)(352,765)(353,764)(354,763)(355,762)(356,761)(357,760)(358,759)(359,758)(360,757)(361,756)(362,755)(363,754)(364,753)(365,752)(366,751)(367,750)(368,749)(369,748)(370,747)(371,746)(372,745)(373,744)(374,743)(375,742)(376,741)(377,740)(378,739)(379,738)(380,737)(381,736)(382,735)(383,734)(384,733)(385,732)(386,731)(387,730)(388,729)(389,728)(390,727)(391,726)(392,725)(393,724)(394,723)(395,722)(396,721)(397,720)(398,719)(399,718)(400,717)(401,716)(402,715)(403,714)(404,713)(405,712)(406,711)(407,710)(408,709)(409,708)(410,707)(411,706)(412,705)(413,704)(414,703)(415,702)(416,701)(417,700)(418,699)(419,698)(420,697)(421,696)(422,695)(423,694)(424,693)(425,692)(426,691)(427,690)(428,689)(429,688)(430,687)(431,686)(432,685)(433,684)(434,683)(435,682)(436,681)(437,680)(438,679)(439,678)(440,677)(441,676)(442,675)(443,674)(444,673)(445,672)(446,671)(447,670)(448,669)(449,668)(450,667)(451,666)(452,665)(453,664)(454,663)(455,662)(456,661)(457,660)(458,659)(459,658)(460,657)(461,656)(462,655)(463,654)(464,653)(465,652)(466,651)(467,650)(468,649)(469,648)(470,647)(471,646)(472,645)(473,644)(474,643)(475,642)(476,641)(477,640)(478,639)(479,638)(480,637)(481,636)(482,635)(483,634)(484,633)(485,632)(486,631)(487,630)(488,629)(489,628)(490,627)(491,626)(492,625)(493,624)(494,623)(495,622)(496,621)(497,620)(498,619)(499,618)(500,617)(501,616)(502,615)(503,614)(504,613)(505,612)(506,611)(507,610)(508,609)(509,608)(510,607)(511,606)(512,605)(513,604)(514,603)(515,602)(516,601)(517,600)(518,599)(519,598)(520,597)(521,596)(522,595)(523,594)(524,593)(525,592)(526,591)(527,590)(528,589)(529,588)(530,587)(531,586)(532,585)(533,584)(534,583)(535,582)(536,581)(537,580)(538,579)(539,578)(540,577)(541,576)(542,575)(543,574)(544,573)(545,572)(546,571)(547,570)(548,569)(549,568)(550,567)(551,566)(552,565)(553,564)(554,563)(555,562)(556,561)(557,560)(558,559)

Polycyclic presentation:

2^5,1051|a^2=e,b^2=e,c^2=de,d^2=e,b^a=bc,c^a=cd,d^a=de,f^a=f^1050,c^b=cd,d^b=de,f^b=f^1050

Conjugacy classes & character table

8411 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33632, 93);