Finite Group Databasebeta

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Dic₄₆₀₄ #32914067

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

Aliases

Splittings

Subgroups

18 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 2 generators on 1167 points:

(1,2,3,4,5,6,7,8)(9,16,15,14,13,12,11,10)(17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,172,173,174,175,176,177,178,179,180,181,182,183,184,185,186,187,188,189,190,191,192,193,194,195,196,197,198,199,200,201,202,203,204,205,206,207,208,209,210,211,212,213,214,215,216,217,218,219,220,221,222,223,224,225,226,227,228,229,230,231,232,233,234,235,236,237,238,239,240,241,242,243,244,245,246,247,248,249,250,251,252,253,254,255,256,257,258,259,260,261,262,263,264,265,266,267,268,269,270,271,272,273,274,275,276,277,278,279,280,281,282,283,284,285,286,287,288,289,290,291,292,293,294,295,296,297,298,299,300,301,302,303,304,305,306,307,308,309,310,311,312,313,314,315,316,317,318,319,320,321,322,323,324,325,326,327,328,329,330,331,332,333,334,335,336,337,338,339,340,341,342,343,344,345,346,347,348,349,350,351,352,353,354,355,356,357,358,359,360,361,362,363,364,365,366,367,368,369,370,371,372,373,374,375,376,377,378,379,380,381,382,383,384,385,386,387,388,389,390,391,392,393,394,395,396,397,398,399,400,401,402,403,404,405,406,407,408,409,410,411,412,413,414,415,416,417,418,419,420,421,422,423,424,425,426,427,428,429,430,431,432,433,434,435,436,437,438,439,440,441,442,443,444,445,446,447,448,449,450,451,452,453,454,455,456,457,458,459,460,461,462,463,464,465,466,467,468,469,470,471,472,473,474,475,476,477,478,479,480,481,482,483,484,485,486,487,488,489,490,491,492,493,494,495,496,497,498,499,500,501,502,503,504,505,506,507,508,509,510,511,512,513,514,515,516,517,518,519,520,521,522,523,524,525,526,527,528,529,530,531,532,533,534,535,536,537,538,539,540,541,542,543,544,545,546,547,548,549,550,551,552,553,554,555,556,557,558,559,560,561,562,563,564,565,566,567,568,569,570,571,572,573,574,575,576,577,578,579,580,581,582,583,584,585,586,587,588,589,590,591,592,593,594,595,596,597,598,599,600,601,602,603,604,605,606,607,608,609,610,611,612,613,614,615,616,617,618,619,620,621,622,623,624,625,626,627,628,629,630,631,632,633,634,635,636,637,638,639,640,641,642,643,644,645,646,647,648,649,650,651,652,653,654,655,656,657,658,659,660,661,662,663,664,665,666,667,668,669,670,671,672,673,674,675,676,677,678,679,680,681,682,683,684,685,686,687,688,689,690,691,692,693,694,695,696,697,698,699,700,701,702,703,704,705,706,707,708,709,710,711,712,713,714,715,716,717,718,719,720,721,722,723,724,725,726,727,728,729,730,731,732,733,734,735,736,737,738,739,740,741,742,743,744,745,746,747,748,749,750,751,752,753,754,755,756,757,758,759,760,761,762,763,764,765,766,767,768,769,770,771,772,773,774,775,776,777,778,779,780,781,782,783,784,785,786,787,788,789,790,791,792,793,794,795,796,797,798,799,800,801,802,803,804,805,806,807,808,809,810,811,812,813,814,815,816,817,818,819,820,821,822,823,824,825,826,827,828,829,830,831,832,833,834,835,836,837,838,839,840,841,842,843,844,845,846,847,848,849,850,851,852,853,854,855,856,857,858,859,860,861,862,863,864,865,866,867,868,869,870,871,872,873,874,875,876,877,878,879,880,881,882,883,884,885,886,887,888,889,890,891,892,893,894,895,896,897,898,899,900,901,902,903,904,905,906,907,908,909,910,911,912,913,914,915,916,917,918,919,920,921,922,923,924,925,926,927,928,929,930,931,932,933,934,935,936,937,938,939,940,941,942,943,944,945,946,947,948,949,950,951,952,953,954,955,956,957,958,959,960,961,962,963,964,965,966,967,968,969,970,971,972,973,974,975,976,977,978,979,980,981,982,983,984,985,986,987,988,989,990,991,992,993,994,995,996,997,998,999,1000,1001,1002,1003,1004,1005,1006,1007,1008,1009,1010,1011,1012,1013,1014,1015,1016,1017,1018,1019,1020,1021,1022,1023,1024,1025,1026,1027,1028,1029,1030,1031,1032,1033,1034,1035,1036,1037,1038,1039,1040,1041,1042,1043,1044,1045,1046,1047,1048,1049,1050,1051,1052,1053,1054,1055,1056,1057,1058,1059,1060,1061,1062,1063,1064,1065,1066,1067,1068,1069,1070,1071,1072,1073,1074,1075,1076,1077,1078,1079,1080,1081,1082,1083,1084,1085,1086,1087,1088,1089,1090,1091,1092,1093,1094,1095,1096,1097,1098,1099,1100,1101,1102,1103,1104,1105,1106,1107,1108,1109,1110,1111,1112,1113,1114,1115,1116,1117,1118,1119,1120,1121,1122,1123,1124,1125,1126,1127,1128,1129,1130,1131,1132,1133,1134,1135,1136,1137,1138,1139,1140,1141,1142,1143,1144,1145,1146,1147,1148,1149,1150,1151,1152,1153,1154,1155,1156,1157,1158,1159,1160,1161,1162,1163,1164,1165,1166,1167);(1,9,5,13)(2,10,6,14)(3,11,7,15)(4,12,8,16)(18,1167)(19,1166)(20,1165)(21,1164)(22,1163)(23,1162)(24,1161)(25,1160)(26,1159)(27,1158)(28,1157)(29,1156)(30,1155)(31,1154)(32,1153)(33,1152)(34,1151)(35,1150)(36,1149)(37,1148)(38,1147)(39,1146)(40,1145)(41,1144)(42,1143)(43,1142)(44,1141)(45,1140)(46,1139)(47,1138)(48,1137)(49,1136)(50,1135)(51,1134)(52,1133)(53,1132)(54,1131)(55,1130)(56,1129)(57,1128)(58,1127)(59,1126)(60,1125)(61,1124)(62,1123)(63,1122)(64,1121)(65,1120)(66,1119)(67,1118)(68,1117)(69,1116)(70,1115)(71,1114)(72,1113)(73,1112)(74,1111)(75,1110)(76,1109)(77,1108)(78,1107)(79,1106)(80,1105)(81,1104)(82,1103)(83,1102)(84,1101)(85,1100)(86,1099)(87,1098)(88,1097)(89,1096)(90,1095)(91,1094)(92,1093)(93,1092)(94,1091)(95,1090)(96,1089)(97,1088)(98,1087)(99,1086)(100,1085)(101,1084)(102,1083)(103,1082)(104,1081)(105,1080)(106,1079)(107,1078)(108,1077)(109,1076)(110,1075)(111,1074)(112,1073)(113,1072)(114,1071)(115,1070)(116,1069)(117,1068)(118,1067)(119,1066)(120,1065)(121,1064)(122,1063)(123,1062)(124,1061)(125,1060)(126,1059)(127,1058)(128,1057)(129,1056)(130,1055)(131,1054)(132,1053)(133,1052)(134,1051)(135,1050)(136,1049)(137,1048)(138,1047)(139,1046)(140,1045)(141,1044)(142,1043)(143,1042)(144,1041)(145,1040)(146,1039)(147,1038)(148,1037)(149,1036)(150,1035)(151,1034)(152,1033)(153,1032)(154,1031)(155,1030)(156,1029)(157,1028)(158,1027)(159,1026)(160,1025)(161,1024)(162,1023)(163,1022)(164,1021)(165,1020)(166,1019)(167,1018)(168,1017)(169,1016)(170,1015)(171,1014)(172,1013)(173,1012)(174,1011)(175,1010)(176,1009)(177,1008)(178,1007)(179,1006)(180,1005)(181,1004)(182,1003)(183,1002)(184,1001)(185,1000)(186,999)(187,998)(188,997)(189,996)(190,995)(191,994)(192,993)(193,992)(194,991)(195,990)(196,989)(197,988)(198,987)(199,986)(200,985)(201,984)(202,983)(203,982)(204,981)(205,980)(206,979)(207,978)(208,977)(209,976)(210,975)(211,974)(212,973)(213,972)(214,971)(215,970)(216,969)(217,968)(218,967)(219,966)(220,965)(221,964)(222,963)(223,962)(224,961)(225,960)(226,959)(227,958)(228,957)(229,956)(230,955)(231,954)(232,953)(233,952)(234,951)(235,950)(236,949)(237,948)(238,947)(239,946)(240,945)(241,944)(242,943)(243,942)(244,941)(245,940)(246,939)(247,938)(248,937)(249,936)(250,935)(251,934)(252,933)(253,932)(254,931)(255,930)(256,929)(257,928)(258,927)(259,926)(260,925)(261,924)(262,923)(263,922)(264,921)(265,920)(266,919)(267,918)(268,917)(269,916)(270,915)(271,914)(272,913)(273,912)(274,911)(275,910)(276,909)(277,908)(278,907)(279,906)(280,905)(281,904)(282,903)(283,902)(284,901)(285,900)(286,899)(287,898)(288,897)(289,896)(290,895)(291,894)(292,893)(293,892)(294,891)(295,890)(296,889)(297,888)(298,887)(299,886)(300,885)(301,884)(302,883)(303,882)(304,881)(305,880)(306,879)(307,878)(308,877)(309,876)(310,875)(311,874)(312,873)(313,872)(314,871)(315,870)(316,869)(317,868)(318,867)(319,866)(320,865)(321,864)(322,863)(323,862)(324,861)(325,860)(326,859)(327,858)(328,857)(329,856)(330,855)(331,854)(332,853)(333,852)(334,851)(335,850)(336,849)(337,848)(338,847)(339,846)(340,845)(341,844)(342,843)(343,842)(344,841)(345,840)(346,839)(347,838)(348,837)(349,836)(350,835)(351,834)(352,833)(353,832)(354,831)(355,830)(356,829)(357,828)(358,827)(359,826)(360,825)(361,824)(362,823)(363,822)(364,821)(365,820)(366,819)(367,818)(368,817)(369,816)(370,815)(371,814)(372,813)(373,812)(374,811)(375,810)(376,809)(377,808)(378,807)(379,806)(380,805)(381,804)(382,803)(383,802)(384,801)(385,800)(386,799)(387,798)(388,797)(389,796)(390,795)(391,794)(392,793)(393,792)(394,791)(395,790)(396,789)(397,788)(398,787)(399,786)(400,785)(401,784)(402,783)(403,782)(404,781)(405,780)(406,779)(407,778)(408,777)(409,776)(410,775)(411,774)(412,773)(413,772)(414,771)(415,770)(416,769)(417,768)(418,767)(419,766)(420,765)(421,764)(422,763)(423,762)(424,761)(425,760)(426,759)(427,758)(428,757)(429,756)(430,755)(431,754)(432,753)(433,752)(434,751)(435,750)(436,749)(437,748)(438,747)(439,746)(440,745)(441,744)(442,743)(443,742)(444,741)(445,740)(446,739)(447,738)(448,737)(449,736)(450,735)(451,734)(452,733)(453,732)(454,731)(455,730)(456,729)(457,728)(458,727)(459,726)(460,725)(461,724)(462,723)(463,722)(464,721)(465,720)(466,719)(467,718)(468,717)(469,716)(470,715)(471,714)(472,713)(473,712)(474,711)(475,710)(476,709)(477,708)(478,707)(479,706)(480,705)(481,704)(482,703)(483,702)(484,701)(485,700)(486,699)(487,698)(488,697)(489,696)(490,695)(491,694)(492,693)(493,692)(494,691)(495,690)(496,689)(497,688)(498,687)(499,686)(500,685)(501,684)(502,683)(503,682)(504,681)(505,680)(506,679)(507,678)(508,677)(509,676)(510,675)(511,674)(512,673)(513,672)(514,671)(515,670)(516,669)(517,668)(518,667)(519,666)(520,665)(521,664)(522,663)(523,662)(524,661)(525,660)(526,659)(527,658)(528,657)(529,656)(530,655)(531,654)(532,653)(533,652)(534,651)(535,650)(536,649)(537,648)(538,647)(539,646)(540,645)(541,644)(542,643)(543,642)(544,641)(545,640)(546,639)(547,638)(548,637)(549,636)(550,635)(551,634)(552,633)(553,632)(554,631)(555,630)(556,629)(557,628)(558,627)(559,626)(560,625)(561,624)(562,623)(563,622)(564,621)(565,620)(566,619)(567,618)(568,617)(569,616)(570,615)(571,614)(572,613)(573,612)(574,611)(575,610)(576,609)(577,608)(578,607)(579,606)(580,605)(581,604)(582,603)(583,602)(584,601)(585,600)(586,599)(587,598)(588,597)(589,596)(590,595)(591,594)(592,593)

Polycyclic presentation:

2^4,1151|a^2=d,b^2=d,c^2=d,b^a=bc,c^a=cd,e^a=e^1150,c^b=cd,e^b=e^1150

Conjugacy classes & character table

4607 conjugacy classes. The character table is too large to display.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18416, 31);