Finite Group Databasebeta

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D₁₈₇₃₆ #49154000

• 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 1187 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16)(17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,172,173,174,175,176,177,178,179,180,181,182,183,184,185,186,187,188,189,190,191,192,193,194,195,196,197,198,199,200,201,202,203,204,205,206,207,208,209,210,211,212,213,214,215,216,217,218,219,220,221,222,223,224,225,226,227,228,229,230,231,232,233,234,235,236,237,238,239,240,241,242,243,244,245,246,247,248,249,250,251,252,253,254,255,256,257,258,259,260,261,262,263,264,265,266,267,268,269,270,271,272,273,274,275,276,277,278,279,280,281,282,283,284,285,286,287,288,289,290,291,292,293,294,295,296,297,298,299,300,301,302,303,304,305,306,307,308,309,310,311,312,313,314,315,316,317,318,319,320,321,322,323,324,325,326,327,328,329,330,331,332,333,334,335,336,337,338,339,340,341,342,343,344,345,346,347,348,349,350,351,352,353,354,355,356,357,358,359,360,361,362,363,364,365,366,367,368,369,370,371,372,373,374,375,376,377,378,379,380,381,382,383,384,385,386,387,388,389,390,391,392,393,394,395,396,397,398,399,400,401,402,403,404,405,406,407,408,409,410,411,412,413,414,415,416,417,418,419,420,421,422,423,424,425,426,427,428,429,430,431,432,433,434,435,436,437,438,439,440,441,442,443,444,445,446,447,448,449,450,451,452,453,454,455,456,457,458,459,460,461,462,463,464,465,466,467,468,469,470,471,472,473,474,475,476,477,478,479,480,481,482,483,484,485,486,487,488,489,490,491,492,493,494,495,496,497,498,499,500,501,502,503,504,505,506,507,508,509,510,511,512,513,514,515,516,517,518,519,520,521,522,523,524,525,526,527,528,529,530,531,532,533,534,535,536,537,538,539,540,541,542,543,544,545,546,547,548,549,550,551,552,553,554,555,556,557,558,559,560,561,562,563,564,565,566,567,568,569,570,571,572,573,574,575,576,577,578,579,580,581,582,583,584,585,586,587,588,589,590,591,592,593,594,595,596,597,598,599,600,601,602,603,604,605,606,607,608,609,610,611,612,613,614,615,616,617,618,619,620,621,622,623,624,625,626,627,628,629,630,631,632,633,634,635,636,637,638,639,640,641,642,643,644,645,646,647,648,649,650,651,652,653,654,655,656,657,658,659,660,661,662,663,664,665,666,667,668,669,670,671,672,673,674,675,676,677,678,679,680,681,682,683,684,685,686,687,688,689,690,691,692,693,694,695,696,697,698,699,700,701,702,703,704,705,706,707,708,709,710,711,712,713,714,715,716,717,718,719,720,721,722,723,724,725,726,727,728,729,730,731,732,733,734,735,736,737,738,739,740,741,742,743,744,745,746,747,748,749,750,751,752,753,754,755,756,757,758,759,760,761,762,763,764,765,766,767,768,769,770,771,772,773,774,775,776,777,778,779,780,781,782,783,784,785,786,787,788,789,790,791,792,793,794,795,796,797,798,799,800,801,802,803,804,805,806,807,808,809,810,811,812,813,814,815,816,817,818,819,820,821,822,823,824,825,826,827,828,829,830,831,832,833,834,835,836,837,838,839,840,841,842,843,844,845,846,847,848,849,850,851,852,853,854,855,856,857,858,859,860,861,862,863,864,865,866,867,868,869,870,871,872,873,874,875,876,877,878,879,880,881,882,883,884,885,886,887,888,889,890,891,892,893,894,895,896,897,898,899,900,901,902,903,904,905,906,907,908,909,910,911,912,913,914,915,916,917,918,919,920,921,922,923,924,925,926,927,928,929,930,931,932,933,934,935,936,937,938,939,940,941,942,943,944,945,946,947,948,949,950,951,952,953,954,955,956,957,958,959,960,961,962,963,964,965,966,967,968,969,970,971,972,973,974,975,976,977,978,979,980,981,982,983,984,985,986,987,988,989,990,991,992,993,994,995,996,997,998,999,1000,1001,1002,1003,1004,1005,1006,1007,1008,1009,1010,1011,1012,1013,1014,1015,1016,1017,1018,1019,1020,1021,1022,1023,1024,1025,1026,1027,1028,1029,1030,1031,1032,1033,1034,1035,1036,1037,1038,1039,1040,1041,1042,1043,1044,1045,1046,1047,1048,1049,1050,1051,1052,1053,1054,1055,1056,1057,1058,1059,1060,1061,1062,1063,1064,1065,1066,1067,1068,1069,1070,1071,1072,1073,1074,1075,1076,1077,1078,1079,1080,1081,1082,1083,1084,1085,1086,1087,1088,1089,1090,1091,1092,1093,1094,1095,1096,1097,1098,1099,1100,1101,1102,1103,1104,1105,1106,1107,1108,1109,1110,1111,1112,1113,1114,1115,1116,1117,1118,1119,1120,1121,1122,1123,1124,1125,1126,1127,1128,1129,1130,1131,1132,1133,1134,1135,1136,1137,1138,1139,1140,1141,1142,1143,1144,1145,1146,1147,1148,1149,1150,1151,1152,1153,1154,1155,1156,1157,1158,1159,1160,1161,1162,1163,1164,1165,1166,1167,1168,1169,1170,1171,1172,1173,1174,1175,1176,1177,1178,1179,1180,1181,1182,1183,1184,1185,1186,1187);(2,16)(3,15)(4,14)(5,13)(6,12)(7,11)(8,10)(18,1187)(19,1186)(20,1185)(21,1184)(22,1183)(23,1182)(24,1181)(25,1180)(26,1179)(27,1178)(28,1177)(29,1176)(30,1175)(31,1174)(32,1173)(33,1172)(34,1171)(35,1170)(36,1169)(37,1168)(38,1167)(39,1166)(40,1165)(41,1164)(42,1163)(43,1162)(44,1161)(45,1160)(46,1159)(47,1158)(48,1157)(49,1156)(50,1155)(51,1154)(52,1153)(53,1152)(54,1151)(55,1150)(56,1149)(57,1148)(58,1147)(59,1146)(60,1145)(61,1144)(62,1143)(63,1142)(64,1141)(65,1140)(66,1139)(67,1138)(68,1137)(69,1136)(70,1135)(71,1134)(72,1133)(73,1132)(74,1131)(75,1130)(76,1129)(77,1128)(78,1127)(79,1126)(80,1125)(81,1124)(82,1123)(83,1122)(84,1121)(85,1120)(86,1119)(87,1118)(88,1117)(89,1116)(90,1115)(91,1114)(92,1113)(93,1112)(94,1111)(95,1110)(96,1109)(97,1108)(98,1107)(99,1106)(100,1105)(101,1104)(102,1103)(103,1102)(104,1101)(105,1100)(106,1099)(107,1098)(108,1097)(109,1096)(110,1095)(111,1094)(112,1093)(113,1092)(114,1091)(115,1090)(116,1089)(117,1088)(118,1087)(119,1086)(120,1085)(121,1084)(122,1083)(123,1082)(124,1081)(125,1080)(126,1079)(127,1078)(128,1077)(129,1076)(130,1075)(131,1074)(132,1073)(133,1072)(134,1071)(135,1070)(136,1069)(137,1068)(138,1067)(139,1066)(140,1065)(141,1064)(142,1063)(143,1062)(144,1061)(145,1060)(146,1059)(147,1058)(148,1057)(149,1056)(150,1055)(151,1054)(152,1053)(153,1052)(154,1051)(155,1050)(156,1049)(157,1048)(158,1047)(159,1046)(160,1045)(161,1044)(162,1043)(163,1042)(164,1041)(165,1040)(166,1039)(167,1038)(168,1037)(169,1036)(170,1035)(171,1034)(172,1033)(173,1032)(174,1031)(175,1030)(176,1029)(177,1028)(178,1027)(179,1026)(180,1025)(181,1024)(182,1023)(183,1022)(184,1021)(185,1020)(186,1019)(187,1018)(188,1017)(189,1016)(190,1015)(191,1014)(192,1013)(193,1012)(194,1011)(195,1010)(196,1009)(197,1008)(198,1007)(199,1006)(200,1005)(201,1004)(202,1003)(203,1002)(204,1001)(205,1000)(206,999)(207,998)(208,997)(209,996)(210,995)(211,994)(212,993)(213,992)(214,991)(215,990)(216,989)(217,988)(218,987)(219,986)(220,985)(221,984)(222,983)(223,982)(224,981)(225,980)(226,979)(227,978)(228,977)(229,976)(230,975)(231,974)(232,973)(233,972)(234,971)(235,970)(236,969)(237,968)(238,967)(239,966)(240,965)(241,964)(242,963)(243,962)(244,961)(245,960)(246,959)(247,958)(248,957)(249,956)(250,955)(251,954)(252,953)(253,952)(254,951)(255,950)(256,949)(257,948)(258,947)(259,946)(260,945)(261,944)(262,943)(263,942)(264,941)(265,940)(266,939)(267,938)(268,937)(269,936)(270,935)(271,934)(272,933)(273,932)(274,931)(275,930)(276,929)(277,928)(278,927)(279,926)(280,925)(281,924)(282,923)(283,922)(284,921)(285,920)(286,919)(287,918)(288,917)(289,916)(290,915)(291,914)(292,913)(293,912)(294,911)(295,910)(296,909)(297,908)(298,907)(299,906)(300,905)(301,904)(302,903)(303,902)(304,901)(305,900)(306,899)(307,898)(308,897)(309,896)(310,895)(311,894)(312,893)(313,892)(314,891)(315,890)(316,889)(317,888)(318,887)(319,886)(320,885)(321,884)(322,883)(323,882)(324,881)(325,880)(326,879)(327,878)(328,877)(329,876)(330,875)(331,874)(332,873)(333,872)(334,871)(335,870)(336,869)(337,868)(338,867)(339,866)(340,865)(341,864)(342,863)(343,862)(344,861)(345,860)(346,859)(347,858)(348,857)(349,856)(350,855)(351,854)(352,853)(353,852)(354,851)(355,850)(356,849)(357,848)(358,847)(359,846)(360,845)(361,844)(362,843)(363,842)(364,841)(365,840)(366,839)(367,838)(368,837)(369,836)(370,835)(371,834)(372,833)(373,832)(374,831)(375,830)(376,829)(377,828)(378,827)(379,826)(380,825)(381,824)(382,823)(383,822)(384,821)(385,820)(386,819)(387,818)(388,817)(389,816)(390,815)(391,814)(392,813)(393,812)(394,811)(395,810)(396,809)(397,808)(398,807)(399,806)(400,805)(401,804)(402,803)(403,802)(404,801)(405,800)(406,799)(407,798)(408,797)(409,796)(410,795)(411,794)(412,793)(413,792)(414,791)(415,790)(416,789)(417,788)(418,787)(419,786)(420,785)(421,784)(422,783)(423,782)(424,781)(425,780)(426,779)(427,778)(428,777)(429,776)(430,775)(431,774)(432,773)(433,772)(434,771)(435,770)(436,769)(437,768)(438,767)(439,766)(440,765)(441,764)(442,763)(443,762)(444,761)(445,760)(446,759)(447,758)(448,757)(449,756)(450,755)(451,754)(452,753)(453,752)(454,751)(455,750)(456,749)(457,748)(458,747)(459,746)(460,745)(461,744)(462,743)(463,742)(464,741)(465,740)(466,739)(467,738)(468,737)(469,736)(470,735)(471,734)(472,733)(473,732)(474,731)(475,730)(476,729)(477,728)(478,727)(479,726)(480,725)(481,724)(482,723)(483,722)(484,721)(485,720)(486,719)(487,718)(488,717)(489,716)(490,715)(491,714)(492,713)(493,712)(494,711)(495,710)(496,709)(497,708)(498,707)(499,706)(500,705)(501,704)(502,703)(503,702)(504,701)(505,700)(506,699)(507,698)(508,697)(509,696)(510,695)(511,694)(512,693)(513,692)(514,691)(515,690)(516,689)(517,688)(518,687)(519,686)(520,685)(521,684)(522,683)(523,682)(524,681)(525,680)(526,679)(527,678)(528,677)(529,676)(530,675)(531,674)(532,673)(533,672)(534,671)(535,670)(536,669)(537,668)(538,667)(539,666)(540,665)(541,664)(542,663)(543,662)(544,661)(545,660)(546,659)(547,658)(548,657)(549,656)(550,655)(551,654)(552,653)(553,652)(554,651)(555,650)(556,649)(557,648)(558,647)(559,646)(560,645)(561,644)(562,643)(563,642)(564,641)(565,640)(566,639)(567,638)(568,637)(569,636)(570,635)(571,634)(572,633)(573,632)(574,631)(575,630)(576,629)(577,628)(578,627)(579,626)(580,625)(581,624)(582,623)(583,622)(584,621)(585,620)(586,619)(587,618)(588,617)(589,616)(590,615)(591,614)(592,613)(593,612)(594,611)(595,610)(596,609)(597,608)(598,607)(599,606)(600,605)(601,604)(602,603)

Polycyclic presentation:

2^5,1171|c^2=de,d^2=e,b^a=bc,c^a=cd,d^a=de,f^a=f^1170,c^b=cd,d^b=de,f^b=f^1170

Conjugacy classes & character table

9371 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(37472, 88);