Finite Group Databasebeta

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D₁₇₉₆₈ #49090528

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

Aliases

Splittings

Subgroups

28 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 2 generators on 1139 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16)(17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,172,173,174,175,176,177,178,179,180,181,182,183,184,185,186,187,188,189,190,191,192,193,194,195,196,197,198,199,200,201,202,203,204,205,206,207,208,209,210,211,212,213,214,215,216,217,218,219,220,221,222,223,224,225,226,227,228,229,230,231,232,233,234,235,236,237,238,239,240,241,242,243,244,245,246,247,248,249,250,251,252,253,254,255,256,257,258,259,260,261,262,263,264,265,266,267,268,269,270,271,272,273,274,275,276,277,278,279,280,281,282,283,284,285,286,287,288,289,290,291,292,293,294,295,296,297,298,299,300,301,302,303,304,305,306,307,308,309,310,311,312,313,314,315,316,317,318,319,320,321,322,323,324,325,326,327,328,329,330,331,332,333,334,335,336,337,338,339,340,341,342,343,344,345,346,347,348,349,350,351,352,353,354,355,356,357,358,359,360,361,362,363,364,365,366,367,368,369,370,371,372,373,374,375,376,377,378,379,380,381,382,383,384,385,386,387,388,389,390,391,392,393,394,395,396,397,398,399,400,401,402,403,404,405,406,407,408,409,410,411,412,413,414,415,416,417,418,419,420,421,422,423,424,425,426,427,428,429,430,431,432,433,434,435,436,437,438,439,440,441,442,443,444,445,446,447,448,449,450,451,452,453,454,455,456,457,458,459,460,461,462,463,464,465,466,467,468,469,470,471,472,473,474,475,476,477,478,479,480,481,482,483,484,485,486,487,488,489,490,491,492,493,494,495,496,497,498,499,500,501,502,503,504,505,506,507,508,509,510,511,512,513,514,515,516,517,518,519,520,521,522,523,524,525,526,527,528,529,530,531,532,533,534,535,536,537,538,539,540,541,542,543,544,545,546,547,548,549,550,551,552,553,554,555,556,557,558,559,560,561,562,563,564,565,566,567,568,569,570,571,572,573,574,575,576,577,578,579,580,581,582,583,584,585,586,587,588,589,590,591,592,593,594,595,596,597,598,599,600,601,602,603,604,605,606,607,608,609,610,611,612,613,614,615,616,617,618,619,620,621,622,623,624,625,626,627,628,629,630,631,632,633,634,635,636,637,638,639,640,641,642,643,644,645,646,647,648,649,650,651,652,653,654,655,656,657,658,659,660,661,662,663,664,665,666,667,668,669,670,671,672,673,674,675,676,677,678,679,680,681,682,683,684,685,686,687,688,689,690,691,692,693,694,695,696,697,698,699,700,701,702,703,704,705,706,707,708,709,710,711,712,713,714,715,716,717,718,719,720,721,722,723,724,725,726,727,728,729,730,731,732,733,734,735,736,737,738,739,740,741,742,743,744,745,746,747,748,749,750,751,752,753,754,755,756,757,758,759,760,761,762,763,764,765,766,767,768,769,770,771,772,773,774,775,776,777,778,779,780,781,782,783,784,785,786,787,788,789,790,791,792,793,794,795,796,797,798,799,800,801,802,803,804,805,806,807,808,809,810,811,812,813,814,815,816,817,818,819,820,821,822,823,824,825,826,827,828,829,830,831,832,833,834,835,836,837,838,839,840,841,842,843,844,845,846,847,848,849,850,851,852,853,854,855,856,857,858,859,860,861,862,863,864,865,866,867,868,869,870,871,872,873,874,875,876,877,878,879,880,881,882,883,884,885,886,887,888,889,890,891,892,893,894,895,896,897,898,899,900,901,902,903,904,905,906,907,908,909,910,911,912,913,914,915,916,917,918,919,920,921,922,923,924,925,926,927,928,929,930,931,932,933,934,935,936,937,938,939,940,941,942,943,944,945,946,947,948,949,950,951,952,953,954,955,956,957,958,959,960,961,962,963,964,965,966,967,968,969,970,971,972,973,974,975,976,977,978,979,980,981,982,983,984,985,986,987,988,989,990,991,992,993,994,995,996,997,998,999,1000,1001,1002,1003,1004,1005,1006,1007,1008,1009,1010,1011,1012,1013,1014,1015,1016,1017,1018,1019,1020,1021,1022,1023,1024,1025,1026,1027,1028,1029,1030,1031,1032,1033,1034,1035,1036,1037,1038,1039,1040,1041,1042,1043,1044,1045,1046,1047,1048,1049,1050,1051,1052,1053,1054,1055,1056,1057,1058,1059,1060,1061,1062,1063,1064,1065,1066,1067,1068,1069,1070,1071,1072,1073,1074,1075,1076,1077,1078,1079,1080,1081,1082,1083,1084,1085,1086,1087,1088,1089,1090,1091,1092,1093,1094,1095,1096,1097,1098,1099,1100,1101,1102,1103,1104,1105,1106,1107,1108,1109,1110,1111,1112,1113,1114,1115,1116,1117,1118,1119,1120,1121,1122,1123,1124,1125,1126,1127,1128,1129,1130,1131,1132,1133,1134,1135,1136,1137,1138,1139);(2,16)(3,15)(4,14)(5,13)(6,12)(7,11)(8,10)(18,1139)(19,1138)(20,1137)(21,1136)(22,1135)(23,1134)(24,1133)(25,1132)(26,1131)(27,1130)(28,1129)(29,1128)(30,1127)(31,1126)(32,1125)(33,1124)(34,1123)(35,1122)(36,1121)(37,1120)(38,1119)(39,1118)(40,1117)(41,1116)(42,1115)(43,1114)(44,1113)(45,1112)(46,1111)(47,1110)(48,1109)(49,1108)(50,1107)(51,1106)(52,1105)(53,1104)(54,1103)(55,1102)(56,1101)(57,1100)(58,1099)(59,1098)(60,1097)(61,1096)(62,1095)(63,1094)(64,1093)(65,1092)(66,1091)(67,1090)(68,1089)(69,1088)(70,1087)(71,1086)(72,1085)(73,1084)(74,1083)(75,1082)(76,1081)(77,1080)(78,1079)(79,1078)(80,1077)(81,1076)(82,1075)(83,1074)(84,1073)(85,1072)(86,1071)(87,1070)(88,1069)(89,1068)(90,1067)(91,1066)(92,1065)(93,1064)(94,1063)(95,1062)(96,1061)(97,1060)(98,1059)(99,1058)(100,1057)(101,1056)(102,1055)(103,1054)(104,1053)(105,1052)(106,1051)(107,1050)(108,1049)(109,1048)(110,1047)(111,1046)(112,1045)(113,1044)(114,1043)(115,1042)(116,1041)(117,1040)(118,1039)(119,1038)(120,1037)(121,1036)(122,1035)(123,1034)(124,1033)(125,1032)(126,1031)(127,1030)(128,1029)(129,1028)(130,1027)(131,1026)(132,1025)(133,1024)(134,1023)(135,1022)(136,1021)(137,1020)(138,1019)(139,1018)(140,1017)(141,1016)(142,1015)(143,1014)(144,1013)(145,1012)(146,1011)(147,1010)(148,1009)(149,1008)(150,1007)(151,1006)(152,1005)(153,1004)(154,1003)(155,1002)(156,1001)(157,1000)(158,999)(159,998)(160,997)(161,996)(162,995)(163,994)(164,993)(165,992)(166,991)(167,990)(168,989)(169,988)(170,987)(171,986)(172,985)(173,984)(174,983)(175,982)(176,981)(177,980)(178,979)(179,978)(180,977)(181,976)(182,975)(183,974)(184,973)(185,972)(186,971)(187,970)(188,969)(189,968)(190,967)(191,966)(192,965)(193,964)(194,963)(195,962)(196,961)(197,960)(198,959)(199,958)(200,957)(201,956)(202,955)(203,954)(204,953)(205,952)(206,951)(207,950)(208,949)(209,948)(210,947)(211,946)(212,945)(213,944)(214,943)(215,942)(216,941)(217,940)(218,939)(219,938)(220,937)(221,936)(222,935)(223,934)(224,933)(225,932)(226,931)(227,930)(228,929)(229,928)(230,927)(231,926)(232,925)(233,924)(234,923)(235,922)(236,921)(237,920)(238,919)(239,918)(240,917)(241,916)(242,915)(243,914)(244,913)(245,912)(246,911)(247,910)(248,909)(249,908)(250,907)(251,906)(252,905)(253,904)(254,903)(255,902)(256,901)(257,900)(258,899)(259,898)(260,897)(261,896)(262,895)(263,894)(264,893)(265,892)(266,891)(267,890)(268,889)(269,888)(270,887)(271,886)(272,885)(273,884)(274,883)(275,882)(276,881)(277,880)(278,879)(279,878)(280,877)(281,876)(282,875)(283,874)(284,873)(285,872)(286,871)(287,870)(288,869)(289,868)(290,867)(291,866)(292,865)(293,864)(294,863)(295,862)(296,861)(297,860)(298,859)(299,858)(300,857)(301,856)(302,855)(303,854)(304,853)(305,852)(306,851)(307,850)(308,849)(309,848)(310,847)(311,846)(312,845)(313,844)(314,843)(315,842)(316,841)(317,840)(318,839)(319,838)(320,837)(321,836)(322,835)(323,834)(324,833)(325,832)(326,831)(327,830)(328,829)(329,828)(330,827)(331,826)(332,825)(333,824)(334,823)(335,822)(336,821)(337,820)(338,819)(339,818)(340,817)(341,816)(342,815)(343,814)(344,813)(345,812)(346,811)(347,810)(348,809)(349,808)(350,807)(351,806)(352,805)(353,804)(354,803)(355,802)(356,801)(357,800)(358,799)(359,798)(360,797)(361,796)(362,795)(363,794)(364,793)(365,792)(366,791)(367,790)(368,789)(369,788)(370,787)(371,786)(372,785)(373,784)(374,783)(375,782)(376,781)(377,780)(378,779)(379,778)(380,777)(381,776)(382,775)(383,774)(384,773)(385,772)(386,771)(387,770)(388,769)(389,768)(390,767)(391,766)(392,765)(393,764)(394,763)(395,762)(396,761)(397,760)(398,759)(399,758)(400,757)(401,756)(402,755)(403,754)(404,753)(405,752)(406,751)(407,750)(408,749)(409,748)(410,747)(411,746)(412,745)(413,744)(414,743)(415,742)(416,741)(417,740)(418,739)(419,738)(420,737)(421,736)(422,735)(423,734)(424,733)(425,732)(426,731)(427,730)(428,729)(429,728)(430,727)(431,726)(432,725)(433,724)(434,723)(435,722)(436,721)(437,720)(438,719)(439,718)(440,717)(441,716)(442,715)(443,714)(444,713)(445,712)(446,711)(447,710)(448,709)(449,708)(450,707)(451,706)(452,705)(453,704)(454,703)(455,702)(456,701)(457,700)(458,699)(459,698)(460,697)(461,696)(462,695)(463,694)(464,693)(465,692)(466,691)(467,690)(468,689)(469,688)(470,687)(471,686)(472,685)(473,684)(474,683)(475,682)(476,681)(477,680)(478,679)(479,678)(480,677)(481,676)(482,675)(483,674)(484,673)(485,672)(486,671)(487,670)(488,669)(489,668)(490,667)(491,666)(492,665)(493,664)(494,663)(495,662)(496,661)(497,660)(498,659)(499,658)(500,657)(501,656)(502,655)(503,654)(504,653)(505,652)(506,651)(507,650)(508,649)(509,648)(510,647)(511,646)(512,645)(513,644)(514,643)(515,642)(516,641)(517,640)(518,639)(519,638)(520,637)(521,636)(522,635)(523,634)(524,633)(525,632)(526,631)(527,630)(528,629)(529,628)(530,627)(531,626)(532,625)(533,624)(534,623)(535,622)(536,621)(537,620)(538,619)(539,618)(540,617)(541,616)(542,615)(543,614)(544,613)(545,612)(546,611)(547,610)(548,609)(549,608)(550,607)(551,606)(552,605)(553,604)(554,603)(555,602)(556,601)(557,600)(558,599)(559,598)(560,597)(561,596)(562,595)(563,594)(564,593)(565,592)(566,591)(567,590)(568,589)(569,588)(570,587)(571,586)(572,585)(573,584)(574,583)(575,582)(576,581)(577,580)(578,579)

Polycyclic presentation:

2^5,1123|c^2=de,d^2=e,b^a=bc,c^a=cd,d^a=de,f^a=f^1122,c^b=cd,d^b=de,f^b=f^1122

Conjugacy classes & character table

8987 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(35936, 88);