Finite Group Databasebeta

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D₁₈₈₉₆ #49180345

• 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 1197 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16)(17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,172,173,174,175,176,177,178,179,180,181,182,183,184,185,186,187,188,189,190,191,192,193,194,195,196,197,198,199,200,201,202,203,204,205,206,207,208,209,210,211,212,213,214,215,216,217,218,219,220,221,222,223,224,225,226,227,228,229,230,231,232,233,234,235,236,237,238,239,240,241,242,243,244,245,246,247,248,249,250,251,252,253,254,255,256,257,258,259,260,261,262,263,264,265,266,267,268,269,270,271,272,273,274,275,276,277,278,279,280,281,282,283,284,285,286,287,288,289,290,291,292,293,294,295,296,297,298,299,300,301,302,303,304,305,306,307,308,309,310,311,312,313,314,315,316,317,318,319,320,321,322,323,324,325,326,327,328,329,330,331,332,333,334,335,336,337,338,339,340,341,342,343,344,345,346,347,348,349,350,351,352,353,354,355,356,357,358,359,360,361,362,363,364,365,366,367,368,369,370,371,372,373,374,375,376,377,378,379,380,381,382,383,384,385,386,387,388,389,390,391,392,393,394,395,396,397,398,399,400,401,402,403,404,405,406,407,408,409,410,411,412,413,414,415,416,417,418,419,420,421,422,423,424,425,426,427,428,429,430,431,432,433,434,435,436,437,438,439,440,441,442,443,444,445,446,447,448,449,450,451,452,453,454,455,456,457,458,459,460,461,462,463,464,465,466,467,468,469,470,471,472,473,474,475,476,477,478,479,480,481,482,483,484,485,486,487,488,489,490,491,492,493,494,495,496,497,498,499,500,501,502,503,504,505,506,507,508,509,510,511,512,513,514,515,516,517,518,519,520,521,522,523,524,525,526,527,528,529,530,531,532,533,534,535,536,537,538,539,540,541,542,543,544,545,546,547,548,549,550,551,552,553,554,555,556,557,558,559,560,561,562,563,564,565,566,567,568,569,570,571,572,573,574,575,576,577,578,579,580,581,582,583,584,585,586,587,588,589,590,591,592,593,594,595,596,597,598,599,600,601,602,603,604,605,606,607,608,609,610,611,612,613,614,615,616,617,618,619,620,621,622,623,624,625,626,627,628,629,630,631,632,633,634,635,636,637,638,639,640,641,642,643,644,645,646,647,648,649,650,651,652,653,654,655,656,657,658,659,660,661,662,663,664,665,666,667,668,669,670,671,672,673,674,675,676,677,678,679,680,681,682,683,684,685,686,687,688,689,690,691,692,693,694,695,696,697,698,699,700,701,702,703,704,705,706,707,708,709,710,711,712,713,714,715,716,717,718,719,720,721,722,723,724,725,726,727,728,729,730,731,732,733,734,735,736,737,738,739,740,741,742,743,744,745,746,747,748,749,750,751,752,753,754,755,756,757,758,759,760,761,762,763,764,765,766,767,768,769,770,771,772,773,774,775,776,777,778,779,780,781,782,783,784,785,786,787,788,789,790,791,792,793,794,795,796,797,798,799,800,801,802,803,804,805,806,807,808,809,810,811,812,813,814,815,816,817,818,819,820,821,822,823,824,825,826,827,828,829,830,831,832,833,834,835,836,837,838,839,840,841,842,843,844,845,846,847,848,849,850,851,852,853,854,855,856,857,858,859,860,861,862,863,864,865,866,867,868,869,870,871,872,873,874,875,876,877,878,879,880,881,882,883,884,885,886,887,888,889,890,891,892,893,894,895,896,897,898,899,900,901,902,903,904,905,906,907,908,909,910,911,912,913,914,915,916,917,918,919,920,921,922,923,924,925,926,927,928,929,930,931,932,933,934,935,936,937,938,939,940,941,942,943,944,945,946,947,948,949,950,951,952,953,954,955,956,957,958,959,960,961,962,963,964,965,966,967,968,969,970,971,972,973,974,975,976,977,978,979,980,981,982,983,984,985,986,987,988,989,990,991,992,993,994,995,996,997,998,999,1000,1001,1002,1003,1004,1005,1006,1007,1008,1009,1010,1011,1012,1013,1014,1015,1016,1017,1018,1019,1020,1021,1022,1023,1024,1025,1026,1027,1028,1029,1030,1031,1032,1033,1034,1035,1036,1037,1038,1039,1040,1041,1042,1043,1044,1045,1046,1047,1048,1049,1050,1051,1052,1053,1054,1055,1056,1057,1058,1059,1060,1061,1062,1063,1064,1065,1066,1067,1068,1069,1070,1071,1072,1073,1074,1075,1076,1077,1078,1079,1080,1081,1082,1083,1084,1085,1086,1087,1088,1089,1090,1091,1092,1093,1094,1095,1096,1097,1098,1099,1100,1101,1102,1103,1104,1105,1106,1107,1108,1109,1110,1111,1112,1113,1114,1115,1116,1117,1118,1119,1120,1121,1122,1123,1124,1125,1126,1127,1128,1129,1130,1131,1132,1133,1134,1135,1136,1137,1138,1139,1140,1141,1142,1143,1144,1145,1146,1147,1148,1149,1150,1151,1152,1153,1154,1155,1156,1157,1158,1159,1160,1161,1162,1163,1164,1165,1166,1167,1168,1169,1170,1171,1172,1173,1174,1175,1176,1177,1178,1179,1180,1181,1182,1183,1184,1185,1186,1187,1188,1189,1190,1191,1192,1193,1194,1195,1196,1197);(2,16)(3,15)(4,14)(5,13)(6,12)(7,11)(8,10)(18,1197)(19,1196)(20,1195)(21,1194)(22,1193)(23,1192)(24,1191)(25,1190)(26,1189)(27,1188)(28,1187)(29,1186)(30,1185)(31,1184)(32,1183)(33,1182)(34,1181)(35,1180)(36,1179)(37,1178)(38,1177)(39,1176)(40,1175)(41,1174)(42,1173)(43,1172)(44,1171)(45,1170)(46,1169)(47,1168)(48,1167)(49,1166)(50,1165)(51,1164)(52,1163)(53,1162)(54,1161)(55,1160)(56,1159)(57,1158)(58,1157)(59,1156)(60,1155)(61,1154)(62,1153)(63,1152)(64,1151)(65,1150)(66,1149)(67,1148)(68,1147)(69,1146)(70,1145)(71,1144)(72,1143)(73,1142)(74,1141)(75,1140)(76,1139)(77,1138)(78,1137)(79,1136)(80,1135)(81,1134)(82,1133)(83,1132)(84,1131)(85,1130)(86,1129)(87,1128)(88,1127)(89,1126)(90,1125)(91,1124)(92,1123)(93,1122)(94,1121)(95,1120)(96,1119)(97,1118)(98,1117)(99,1116)(100,1115)(101,1114)(102,1113)(103,1112)(104,1111)(105,1110)(106,1109)(107,1108)(108,1107)(109,1106)(110,1105)(111,1104)(112,1103)(113,1102)(114,1101)(115,1100)(116,1099)(117,1098)(118,1097)(119,1096)(120,1095)(121,1094)(122,1093)(123,1092)(124,1091)(125,1090)(126,1089)(127,1088)(128,1087)(129,1086)(130,1085)(131,1084)(132,1083)(133,1082)(134,1081)(135,1080)(136,1079)(137,1078)(138,1077)(139,1076)(140,1075)(141,1074)(142,1073)(143,1072)(144,1071)(145,1070)(146,1069)(147,1068)(148,1067)(149,1066)(150,1065)(151,1064)(152,1063)(153,1062)(154,1061)(155,1060)(156,1059)(157,1058)(158,1057)(159,1056)(160,1055)(161,1054)(162,1053)(163,1052)(164,1051)(165,1050)(166,1049)(167,1048)(168,1047)(169,1046)(170,1045)(171,1044)(172,1043)(173,1042)(174,1041)(175,1040)(176,1039)(177,1038)(178,1037)(179,1036)(180,1035)(181,1034)(182,1033)(183,1032)(184,1031)(185,1030)(186,1029)(187,1028)(188,1027)(189,1026)(190,1025)(191,1024)(192,1023)(193,1022)(194,1021)(195,1020)(196,1019)(197,1018)(198,1017)(199,1016)(200,1015)(201,1014)(202,1013)(203,1012)(204,1011)(205,1010)(206,1009)(207,1008)(208,1007)(209,1006)(210,1005)(211,1004)(212,1003)(213,1002)(214,1001)(215,1000)(216,999)(217,998)(218,997)(219,996)(220,995)(221,994)(222,993)(223,992)(224,991)(225,990)(226,989)(227,988)(228,987)(229,986)(230,985)(231,984)(232,983)(233,982)(234,981)(235,980)(236,979)(237,978)(238,977)(239,976)(240,975)(241,974)(242,973)(243,972)(244,971)(245,970)(246,969)(247,968)(248,967)(249,966)(250,965)(251,964)(252,963)(253,962)(254,961)(255,960)(256,959)(257,958)(258,957)(259,956)(260,955)(261,954)(262,953)(263,952)(264,951)(265,950)(266,949)(267,948)(268,947)(269,946)(270,945)(271,944)(272,943)(273,942)(274,941)(275,940)(276,939)(277,938)(278,937)(279,936)(280,935)(281,934)(282,933)(283,932)(284,931)(285,930)(286,929)(287,928)(288,927)(289,926)(290,925)(291,924)(292,923)(293,922)(294,921)(295,920)(296,919)(297,918)(298,917)(299,916)(300,915)(301,914)(302,913)(303,912)(304,911)(305,910)(306,909)(307,908)(308,907)(309,906)(310,905)(311,904)(312,903)(313,902)(314,901)(315,900)(316,899)(317,898)(318,897)(319,896)(320,895)(321,894)(322,893)(323,892)(324,891)(325,890)(326,889)(327,888)(328,887)(329,886)(330,885)(331,884)(332,883)(333,882)(334,881)(335,880)(336,879)(337,878)(338,877)(339,876)(340,875)(341,874)(342,873)(343,872)(344,871)(345,870)(346,869)(347,868)(348,867)(349,866)(350,865)(351,864)(352,863)(353,862)(354,861)(355,860)(356,859)(357,858)(358,857)(359,856)(360,855)(361,854)(362,853)(363,852)(364,851)(365,850)(366,849)(367,848)(368,847)(369,846)(370,845)(371,844)(372,843)(373,842)(374,841)(375,840)(376,839)(377,838)(378,837)(379,836)(380,835)(381,834)(382,833)(383,832)(384,831)(385,830)(386,829)(387,828)(388,827)(389,826)(390,825)(391,824)(392,823)(393,822)(394,821)(395,820)(396,819)(397,818)(398,817)(399,816)(400,815)(401,814)(402,813)(403,812)(404,811)(405,810)(406,809)(407,808)(408,807)(409,806)(410,805)(411,804)(412,803)(413,802)(414,801)(415,800)(416,799)(417,798)(418,797)(419,796)(420,795)(421,794)(422,793)(423,792)(424,791)(425,790)(426,789)(427,788)(428,787)(429,786)(430,785)(431,784)(432,783)(433,782)(434,781)(435,780)(436,779)(437,778)(438,777)(439,776)(440,775)(441,774)(442,773)(443,772)(444,771)(445,770)(446,769)(447,768)(448,767)(449,766)(450,765)(451,764)(452,763)(453,762)(454,761)(455,760)(456,759)(457,758)(458,757)(459,756)(460,755)(461,754)(462,753)(463,752)(464,751)(465,750)(466,749)(467,748)(468,747)(469,746)(470,745)(471,744)(472,743)(473,742)(474,741)(475,740)(476,739)(477,738)(478,737)(479,736)(480,735)(481,734)(482,733)(483,732)(484,731)(485,730)(486,729)(487,728)(488,727)(489,726)(490,725)(491,724)(492,723)(493,722)(494,721)(495,720)(496,719)(497,718)(498,717)(499,716)(500,715)(501,714)(502,713)(503,712)(504,711)(505,710)(506,709)(507,708)(508,707)(509,706)(510,705)(511,704)(512,703)(513,702)(514,701)(515,700)(516,699)(517,698)(518,697)(519,696)(520,695)(521,694)(522,693)(523,692)(524,691)(525,690)(526,689)(527,688)(528,687)(529,686)(530,685)(531,684)(532,683)(533,682)(534,681)(535,680)(536,679)(537,678)(538,677)(539,676)(540,675)(541,674)(542,673)(543,672)(544,671)(545,670)(546,669)(547,668)(548,667)(549,666)(550,665)(551,664)(552,663)(553,662)(554,661)(555,660)(556,659)(557,658)(558,657)(559,656)(560,655)(561,654)(562,653)(563,652)(564,651)(565,650)(566,649)(567,648)(568,647)(569,646)(570,645)(571,644)(572,643)(573,642)(574,641)(575,640)(576,639)(577,638)(578,637)(579,636)(580,635)(581,634)(582,633)(583,632)(584,631)(585,630)(586,629)(587,628)(588,627)(589,626)(590,625)(591,624)(592,623)(593,622)(594,621)(595,620)(596,619)(597,618)(598,617)(599,616)(600,615)(601,614)(602,613)(603,612)(604,611)(605,610)(606,609)(607,608)

Polycyclic presentation:

2^5,1181|c^2=de,d^2=e,b^a=bc,c^a=cd,d^a=de,f^a=f^1180,c^b=cd,d^b=de,f^b=f^1180

Conjugacy classes & character table

9451 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(37792, 88);