Finite Group Databasebeta

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Dic₈₄₈₈ #46800577

• 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 1093 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)(33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,172,173,174,175,176,177,178,179,180,181,182,183,184,185,186,187,188,189,190,191,192,193,194,195,196,197,198,199,200,201,202,203,204,205,206,207,208,209,210,211,212,213,214,215,216,217,218,219,220,221,222,223,224,225,226,227,228,229,230,231,232,233,234,235,236,237,238,239,240,241,242,243,244,245,246,247,248,249,250,251,252,253,254,255,256,257,258,259,260,261,262,263,264,265,266,267,268,269,270,271,272,273,274,275,276,277,278,279,280,281,282,283,284,285,286,287,288,289,290,291,292,293,294,295,296,297,298,299,300,301,302,303,304,305,306,307,308,309,310,311,312,313,314,315,316,317,318,319,320,321,322,323,324,325,326,327,328,329,330,331,332,333,334,335,336,337,338,339,340,341,342,343,344,345,346,347,348,349,350,351,352,353,354,355,356,357,358,359,360,361,362,363,364,365,366,367,368,369,370,371,372,373,374,375,376,377,378,379,380,381,382,383,384,385,386,387,388,389,390,391,392,393,394,395,396,397,398,399,400,401,402,403,404,405,406,407,408,409,410,411,412,413,414,415,416,417,418,419,420,421,422,423,424,425,426,427,428,429,430,431,432,433,434,435,436,437,438,439,440,441,442,443,444,445,446,447,448,449,450,451,452,453,454,455,456,457,458,459,460,461,462,463,464,465,466,467,468,469,470,471,472,473,474,475,476,477,478,479,480,481,482,483,484,485,486,487,488,489,490,491,492,493,494,495,496,497,498,499,500,501,502,503,504,505,506,507,508,509,510,511,512,513,514,515,516,517,518,519,520,521,522,523,524,525,526,527,528,529,530,531,532,533,534,535,536,537,538,539,540,541,542,543,544,545,546,547,548,549,550,551,552,553,554,555,556,557,558,559,560,561,562,563,564,565,566,567,568,569,570,571,572,573,574,575,576,577,578,579,580,581,582,583,584,585,586,587,588,589,590,591,592,593,594,595,596,597,598,599,600,601,602,603,604,605,606,607,608,609,610,611,612,613,614,615,616,617,618,619,620,621,622,623,624,625,626,627,628,629,630,631,632,633,634,635,636,637,638,639,640,641,642,643,644,645,646,647,648,649,650,651,652,653,654,655,656,657,658,659,660,661,662,663,664,665,666,667,668,669,670,671,672,673,674,675,676,677,678,679,680,681,682,683,684,685,686,687,688,689,690,691,692,693,694,695,696,697,698,699,700,701,702,703,704,705,706,707,708,709,710,711,712,713,714,715,716,717,718,719,720,721,722,723,724,725,726,727,728,729,730,731,732,733,734,735,736,737,738,739,740,741,742,743,744,745,746,747,748,749,750,751,752,753,754,755,756,757,758,759,760,761,762,763,764,765,766,767,768,769,770,771,772,773,774,775,776,777,778,779,780,781,782,783,784,785,786,787,788,789,790,791,792,793,794,795,796,797,798,799,800,801,802,803,804,805,806,807,808,809,810,811,812,813,814,815,816,817,818,819,820,821,822,823,824,825,826,827,828,829,830,831,832,833,834,835,836,837,838,839,840,841,842,843,844,845,846,847,848,849,850,851,852,853,854,855,856,857,858,859,860,861,862,863,864,865,866,867,868,869,870,871,872,873,874,875,876,877,878,879,880,881,882,883,884,885,886,887,888,889,890,891,892,893,894,895,896,897,898,899,900,901,902,903,904,905,906,907,908,909,910,911,912,913,914,915,916,917,918,919,920,921,922,923,924,925,926,927,928,929,930,931,932,933,934,935,936,937,938,939,940,941,942,943,944,945,946,947,948,949,950,951,952,953,954,955,956,957,958,959,960,961,962,963,964,965,966,967,968,969,970,971,972,973,974,975,976,977,978,979,980,981,982,983,984,985,986,987,988,989,990,991,992,993,994,995,996,997,998,999,1000,1001,1002,1003,1004,1005,1006,1007,1008,1009,1010,1011,1012,1013,1014,1015,1016,1017,1018,1019,1020,1021,1022,1023,1024,1025,1026,1027,1028,1029,1030,1031,1032,1033,1034,1035,1036,1037,1038,1039,1040,1041,1042,1043,1044,1045,1046,1047,1048,1049,1050,1051,1052,1053,1054,1055,1056,1057,1058,1059,1060,1061,1062,1063,1064,1065,1066,1067,1068,1069,1070,1071,1072,1073,1074,1075,1076,1077,1078,1079,1080,1081,1082,1083,1084,1085,1086,1087,1088,1089,1090,1091,1092,1093);(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)(34,1093)(35,1092)(36,1091)(37,1090)(38,1089)(39,1088)(40,1087)(41,1086)(42,1085)(43,1084)(44,1083)(45,1082)(46,1081)(47,1080)(48,1079)(49,1078)(50,1077)(51,1076)(52,1075)(53,1074)(54,1073)(55,1072)(56,1071)(57,1070)(58,1069)(59,1068)(60,1067)(61,1066)(62,1065)(63,1064)(64,1063)(65,1062)(66,1061)(67,1060)(68,1059)(69,1058)(70,1057)(71,1056)(72,1055)(73,1054)(74,1053)(75,1052)(76,1051)(77,1050)(78,1049)(79,1048)(80,1047)(81,1046)(82,1045)(83,1044)(84,1043)(85,1042)(86,1041)(87,1040)(88,1039)(89,1038)(90,1037)(91,1036)(92,1035)(93,1034)(94,1033)(95,1032)(96,1031)(97,1030)(98,1029)(99,1028)(100,1027)(101,1026)(102,1025)(103,1024)(104,1023)(105,1022)(106,1021)(107,1020)(108,1019)(109,1018)(110,1017)(111,1016)(112,1015)(113,1014)(114,1013)(115,1012)(116,1011)(117,1010)(118,1009)(119,1008)(120,1007)(121,1006)(122,1005)(123,1004)(124,1003)(125,1002)(126,1001)(127,1000)(128,999)(129,998)(130,997)(131,996)(132,995)(133,994)(134,993)(135,992)(136,991)(137,990)(138,989)(139,988)(140,987)(141,986)(142,985)(143,984)(144,983)(145,982)(146,981)(147,980)(148,979)(149,978)(150,977)(151,976)(152,975)(153,974)(154,973)(155,972)(156,971)(157,970)(158,969)(159,968)(160,967)(161,966)(162,965)(163,964)(164,963)(165,962)(166,961)(167,960)(168,959)(169,958)(170,957)(171,956)(172,955)(173,954)(174,953)(175,952)(176,951)(177,950)(178,949)(179,948)(180,947)(181,946)(182,945)(183,944)(184,943)(185,942)(186,941)(187,940)(188,939)(189,938)(190,937)(191,936)(192,935)(193,934)(194,933)(195,932)(196,931)(197,930)(198,929)(199,928)(200,927)(201,926)(202,925)(203,924)(204,923)(205,922)(206,921)(207,920)(208,919)(209,918)(210,917)(211,916)(212,915)(213,914)(214,913)(215,912)(216,911)(217,910)(218,909)(219,908)(220,907)(221,906)(222,905)(223,904)(224,903)(225,902)(226,901)(227,900)(228,899)(229,898)(230,897)(231,896)(232,895)(233,894)(234,893)(235,892)(236,891)(237,890)(238,889)(239,888)(240,887)(241,886)(242,885)(243,884)(244,883)(245,882)(246,881)(247,880)(248,879)(249,878)(250,877)(251,876)(252,875)(253,874)(254,873)(255,872)(256,871)(257,870)(258,869)(259,868)(260,867)(261,866)(262,865)(263,864)(264,863)(265,862)(266,861)(267,860)(268,859)(269,858)(270,857)(271,856)(272,855)(273,854)(274,853)(275,852)(276,851)(277,850)(278,849)(279,848)(280,847)(281,846)(282,845)(283,844)(284,843)(285,842)(286,841)(287,840)(288,839)(289,838)(290,837)(291,836)(292,835)(293,834)(294,833)(295,832)(296,831)(297,830)(298,829)(299,828)(300,827)(301,826)(302,825)(303,824)(304,823)(305,822)(306,821)(307,820)(308,819)(309,818)(310,817)(311,816)(312,815)(313,814)(314,813)(315,812)(316,811)(317,810)(318,809)(319,808)(320,807)(321,806)(322,805)(323,804)(324,803)(325,802)(326,801)(327,800)(328,799)(329,798)(330,797)(331,796)(332,795)(333,794)(334,793)(335,792)(336,791)(337,790)(338,789)(339,788)(340,787)(341,786)(342,785)(343,784)(344,783)(345,782)(346,781)(347,780)(348,779)(349,778)(350,777)(351,776)(352,775)(353,774)(354,773)(355,772)(356,771)(357,770)(358,769)(359,768)(360,767)(361,766)(362,765)(363,764)(364,763)(365,762)(366,761)(367,760)(368,759)(369,758)(370,757)(371,756)(372,755)(373,754)(374,753)(375,752)(376,751)(377,750)(378,749)(379,748)(380,747)(381,746)(382,745)(383,744)(384,743)(385,742)(386,741)(387,740)(388,739)(389,738)(390,737)(391,736)(392,735)(393,734)(394,733)(395,732)(396,731)(397,730)(398,729)(399,728)(400,727)(401,726)(402,725)(403,724)(404,723)(405,722)(406,721)(407,720)(408,719)(409,718)(410,717)(411,716)(412,715)(413,714)(414,713)(415,712)(416,711)(417,710)(418,709)(419,708)(420,707)(421,706)(422,705)(423,704)(424,703)(425,702)(426,701)(427,700)(428,699)(429,698)(430,697)(431,696)(432,695)(433,694)(434,693)(435,692)(436,691)(437,690)(438,689)(439,688)(440,687)(441,686)(442,685)(443,684)(444,683)(445,682)(446,681)(447,680)(448,679)(449,678)(450,677)(451,676)(452,675)(453,674)(454,673)(455,672)(456,671)(457,670)(458,669)(459,668)(460,667)(461,666)(462,665)(463,664)(464,663)(465,662)(466,661)(467,660)(468,659)(469,658)(470,657)(471,656)(472,655)(473,654)(474,653)(475,652)(476,651)(477,650)(478,649)(479,648)(480,647)(481,646)(482,645)(483,644)(484,643)(485,642)(486,641)(487,640)(488,639)(489,638)(490,637)(491,636)(492,635)(493,634)(494,633)(495,632)(496,631)(497,630)(498,629)(499,628)(500,627)(501,626)(502,625)(503,624)(504,623)(505,622)(506,621)(507,620)(508,619)(509,618)(510,617)(511,616)(512,615)(513,614)(514,613)(515,612)(516,611)(517,610)(518,609)(519,608)(520,607)(521,606)(522,605)(523,604)(524,603)(525,602)(526,601)(527,600)(528,599)(529,598)(530,597)(531,596)(532,595)(533,594)(534,593)(535,592)(536,591)(537,590)(538,589)(539,588)(540,587)(541,586)(542,585)(543,584)(544,583)(545,582)(546,581)(547,580)(548,579)(549,578)(550,577)(551,576)(552,575)(553,574)(554,573)(555,572)(556,571)(557,570)(558,569)(559,568)(560,567)(561,566)(562,565)(563,564)

Polycyclic presentation:

2^5,1061|a^2=e,b^2=e,c^2=de,d^2=e,b^a=bc,c^a=cd,d^a=de,f^a=f^1060,c^b=cd,d^b=de,f^b=f^1060

Conjugacy classes & character table

8491 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33952, 93);