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Dic5935 #37557606
Aliases
Splittings
Subgroups
12 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 2 generators on 1196 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);(1,3,2,4)(6,9)(7,8)(11,1196)(12,1195)(13,1194)(14,1193)(15,1192)(16,1191)(17,1190)(18,1189)(19,1188)(20,1187)(21,1186)(22,1185)(23,1184)(24,1183)(25,1182)(26,1181)(27,1180)(28,1179)(29,1178)(30,1177)(31,1176)(32,1175)(33,1174)(34,1173)(35,1172)(36,1171)(37,1170)(38,1169)(39,1168)(40,1167)(41,1166)(42,1165)(43,1164)(44,1163)(45,1162)(46,1161)(47,1160)(48,1159)(49,1158)(50,1157)(51,1156)(52,1155)(53,1154)(54,1153)(55,1152)(56,1151)(57,1150)(58,1149)(59,1148)(60,1147)(61,1146)(62,1145)(63,1144)(64,1143)(65,1142)(66,1141)(67,1140)(68,1139)(69,1138)(70,1137)(71,1136)(72,1135)(73,1134)(74,1133)(75,1132)(76,1131)(77,1130)(78,1129)(79,1128)(80,1127)(81,1126)(82,1125)(83,1124)(84,1123)(85,1122)(86,1121)(87,1120)(88,1119)(89,1118)(90,1117)(91,1116)(92,1115)(93,1114)(94,1113)(95,1112)(96,1111)(97,1110)(98,1109)(99,1108)(100,1107)(101,1106)(102,1105)(103,1104)(104,1103)(105,1102)(106,1101)(107,1100)(108,1099)(109,1098)(110,1097)(111,1096)(112,1095)(113,1094)(114,1093)(115,1092)(116,1091)(117,1090)(118,1089)(119,1088)(120,1087)(121,1086)(122,1085)(123,1084)(124,1083)(125,1082)(126,1081)(127,1080)(128,1079)(129,1078)(130,1077)(131,1076)(132,1075)(133,1074)(134,1073)(135,1072)(136,1071)(137,1070)(138,1069)(139,1068)(140,1067)(141,1066)(142,1065)(143,1064)(144,1063)(145,1062)(146,1061)(147,1060)(148,1059)(149,1058)(150,1057)(151,1056)(152,1055)(153,1054)(154,1053)(155,1052)(156,1051)(157,1050)(158,1049)(159,1048)(160,1047)(161,1046)(162,1045)(163,1044)(164,1043)(165,1042)(166,1041)(167,1040)(168,1039)(169,1038)(170,1037)(171,1036)(172,1035)(173,1034)(174,1033)(175,1032)(176,1031)(177,1030)(178,1029)(179,1028)(180,1027)(181,1026)(182,1025)(183,1024)(184,1023)(185,1022)(186,1021)(187,1020)(188,1019)(189,1018)(190,1017)(191,1016)(192,1015)(193,1014)(194,1013)(195,1012)(196,1011)(197,1010)(198,1009)(199,1008)(200,1007)(201,1006)(202,1005)(203,1004)(204,1003)(205,1002)(206,1001)(207,1000)(208,999)(209,998)(210,997)(211,996)(212,995)(213,994)(214,993)(215,992)(216,991)(217,990)(218,989)(219,988)(220,987)(221,986)(222,985)(223,984)(224,983)(225,982)(226,981)(227,980)(228,979)(229,978)(230,977)(231,976)(232,975)(233,974)(234,973)(235,972)(236,971)(237,970)(238,969)(239,968)(240,967)(241,966)(242,965)(243,964)(244,963)(245,962)(246,961)(247,960)(248,959)(249,958)(250,957)(251,956)(252,955)(253,954)(254,953)(255,952)(256,951)(257,950)(258,949)(259,948)(260,947)(261,946)(262,945)(263,944)(264,943)(265,942)(266,941)(267,940)(268,939)(269,938)(270,937)(271,936)(272,935)(273,934)(274,933)(275,932)(276,931)(277,930)(278,929)(279,928)(280,927)(281,926)(282,925)(283,924)(284,923)(285,922)(286,921)(287,920)(288,919)(289,918)(290,917)(291,916)(292,915)(293,914)(294,913)(295,912)(296,911)(297,910)(298,909)(299,908)(300,907)(301,906)(302,905)(303,904)(304,903)(305,902)(306,901)(307,900)(308,899)(309,898)(310,897)(311,896)(312,895)(313,894)(314,893)(315,892)(316,891)(317,890)(318,889)(319,888)(320,887)(321,886)(322,885)(323,884)(324,883)(325,882)(326,881)(327,880)(328,879)(329,878)(330,877)(331,876)(332,875)(333,874)(334,873)(335,872)(336,871)(337,870)(338,869)(339,868)(340,867)(341,866)(342,865)(343,864)(344,863)(345,862)(346,861)(347,860)(348,859)(349,858)(350,857)(351,856)(352,855)(353,854)(354,853)(355,852)(356,851)(357,850)(358,849)(359,848)(360,847)(361,846)(362,845)(363,844)(364,843)(365,842)(366,841)(367,840)(368,839)(369,838)(370,837)(371,836)(372,835)(373,834)(374,833)(375,832)(376,831)(377,830)(378,829)(379,828)(380,827)(381,826)(382,825)(383,824)(384,823)(385,822)(386,821)(387,820)(388,819)(389,818)(390,817)(391,816)(392,815)(393,814)(394,813)(395,812)(396,811)(397,810)(398,809)(399,808)(400,807)(401,806)(402,805)(403,804)(404,803)(405,802)(406,801)(407,800)(408,799)(409,798)(410,797)(411,796)(412,795)(413,794)(414,793)(415,792)(416,791)(417,790)(418,789)(419,788)(420,787)(421,786)(422,785)(423,784)(424,783)(425,782)(426,781)(427,780)(428,779)(429,778)(430,777)(431,776)(432,775)(433,774)(434,773)(435,772)(436,771)(437,770)(438,769)(439,768)(440,767)(441,766)(442,765)(443,764)(444,763)(445,762)(446,761)(447,760)(448,759)(449,758)(450,757)(451,756)(452,755)(453,754)(454,753)(455,752)(456,751)(457,750)(458,749)(459,748)(460,747)(461,746)(462,745)(463,744)(464,743)(465,742)(466,741)(467,740)(468,739)(469,738)(470,737)(471,736)(472,735)(473,734)(474,733)(475,732)(476,731)(477,730)(478,729)(479,728)(480,727)(481,726)(482,725)(483,724)(484,723)(485,722)(486,721)(487,720)(488,719)(489,718)(490,717)(491,716)(492,715)(493,714)(494,713)(495,712)(496,711)(497,710)(498,709)(499,708)(500,707)(501,706)(502,705)(503,704)(504,703)(505,702)(506,701)(507,700)(508,699)(509,698)(510,697)(511,696)(512,695)(513,694)(514,693)(515,692)(516,691)(517,690)(518,689)(519,688)(520,687)(521,686)(522,685)(523,684)(524,683)(525,682)(526,681)(527,680)(528,679)(529,678)(530,677)(531,676)(532,675)(533,674)(534,673)(535,672)(536,671)(537,670)(538,669)(539,668)(540,667)(541,666)(542,665)(543,664)(544,663)(545,662)(546,661)(547,660)(548,659)(549,658)(550,657)(551,656)(552,655)(553,654)(554,653)(555,652)(556,651)(557,650)(558,649)(559,648)(560,647)(561,646)(562,645)(563,644)(564,643)(565,642)(566,641)(567,640)(568,639)(569,638)(570,637)(571,636)(572,635)(573,634)(574,633)(575,632)(576,631)(577,630)(578,629)(579,628)(580,627)(581,626)(582,625)(583,624)(584,623)(585,622)(586,621)(587,620)(588,619)(589,618)(590,617)(591,616)(592,615)(593,614)(594,613)(595,612)(596,611)(597,610)(598,609)(599,608)(600,607)(601,606)(602,605)(603,604)
Polycyclic presentation:
2,5,1187,2|a^2=d,b^a=b^4,c^a=c^1186
Conjugacy classes & character table
5938 conjugacy classes. The character table is too large to display.
Relationships
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23740, 4);
Finite Group Databasebeta