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Dic3711 #28415328
Aliases
Splittings
Subgroups
12 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 2 generators on 1244 points:
(1,2)(3,4)(5,6,7)(8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,172,173,174,175,176,177,178,179,180,181,182,183,184,185,186,187,188,189,190,191,192,193,194,195,196,197,198,199,200,201,202,203,204,205,206,207,208,209,210,211,212,213,214,215,216,217,218,219,220,221,222,223,224,225,226,227,228,229,230,231,232,233,234,235,236,237,238,239,240,241,242,243,244,245,246,247,248,249,250,251,252,253,254,255,256,257,258,259,260,261,262,263,264,265,266,267,268,269,270,271,272,273,274,275,276,277,278,279,280,281,282,283,284,285,286,287,288,289,290,291,292,293,294,295,296,297,298,299,300,301,302,303,304,305,306,307,308,309,310,311,312,313,314,315,316,317,318,319,320,321,322,323,324,325,326,327,328,329,330,331,332,333,334,335,336,337,338,339,340,341,342,343,344,345,346,347,348,349,350,351,352,353,354,355,356,357,358,359,360,361,362,363,364,365,366,367,368,369,370,371,372,373,374,375,376,377,378,379,380,381,382,383,384,385,386,387,388,389,390,391,392,393,394,395,396,397,398,399,400,401,402,403,404,405,406,407,408,409,410,411,412,413,414,415,416,417,418,419,420,421,422,423,424,425,426,427,428,429,430,431,432,433,434,435,436,437,438,439,440,441,442,443,444,445,446,447,448,449,450,451,452,453,454,455,456,457,458,459,460,461,462,463,464,465,466,467,468,469,470,471,472,473,474,475,476,477,478,479,480,481,482,483,484,485,486,487,488,489,490,491,492,493,494,495,496,497,498,499,500,501,502,503,504,505,506,507,508,509,510,511,512,513,514,515,516,517,518,519,520,521,522,523,524,525,526,527,528,529,530,531,532,533,534,535,536,537,538,539,540,541,542,543,544,545,546,547,548,549,550,551,552,553,554,555,556,557,558,559,560,561,562,563,564,565,566,567,568,569,570,571,572,573,574,575,576,577,578,579,580,581,582,583,584,585,586,587,588,589,590,591,592,593,594,595,596,597,598,599,600,601,602,603,604,605,606,607,608,609,610,611,612,613,614,615,616,617,618,619,620,621,622,623,624,625,626,627,628,629,630,631,632,633,634,635,636,637,638,639,640,641,642,643,644,645,646,647,648,649,650,651,652,653,654,655,656,657,658,659,660,661,662,663,664,665,666,667,668,669,670,671,672,673,674,675,676,677,678,679,680,681,682,683,684,685,686,687,688,689,690,691,692,693,694,695,696,697,698,699,700,701,702,703,704,705,706,707,708,709,710,711,712,713,714,715,716,717,718,719,720,721,722,723,724,725,726,727,728,729,730,731,732,733,734,735,736,737,738,739,740,741,742,743,744,745,746,747,748,749,750,751,752,753,754,755,756,757,758,759,760,761,762,763,764,765,766,767,768,769,770,771,772,773,774,775,776,777,778,779,780,781,782,783,784,785,786,787,788,789,790,791,792,793,794,795,796,797,798,799,800,801,802,803,804,805,806,807,808,809,810,811,812,813,814,815,816,817,818,819,820,821,822,823,824,825,826,827,828,829,830,831,832,833,834,835,836,837,838,839,840,841,842,843,844,845,846,847,848,849,850,851,852,853,854,855,856,857,858,859,860,861,862,863,864,865,866,867,868,869,870,871,872,873,874,875,876,877,878,879,880,881,882,883,884,885,886,887,888,889,890,891,892,893,894,895,896,897,898,899,900,901,902,903,904,905,906,907,908,909,910,911,912,913,914,915,916,917,918,919,920,921,922,923,924,925,926,927,928,929,930,931,932,933,934,935,936,937,938,939,940,941,942,943,944,945,946,947,948,949,950,951,952,953,954,955,956,957,958,959,960,961,962,963,964,965,966,967,968,969,970,971,972,973,974,975,976,977,978,979,980,981,982,983,984,985,986,987,988,989,990,991,992,993,994,995,996,997,998,999,1000,1001,1002,1003,1004,1005,1006,1007,1008,1009,1010,1011,1012,1013,1014,1015,1016,1017,1018,1019,1020,1021,1022,1023,1024,1025,1026,1027,1028,1029,1030,1031,1032,1033,1034,1035,1036,1037,1038,1039,1040,1041,1042,1043,1044,1045,1046,1047,1048,1049,1050,1051,1052,1053,1054,1055,1056,1057,1058,1059,1060,1061,1062,1063,1064,1065,1066,1067,1068,1069,1070,1071,1072,1073,1074,1075,1076,1077,1078,1079,1080,1081,1082,1083,1084,1085,1086,1087,1088,1089,1090,1091,1092,1093,1094,1095,1096,1097,1098,1099,1100,1101,1102,1103,1104,1105,1106,1107,1108,1109,1110,1111,1112,1113,1114,1115,1116,1117,1118,1119,1120,1121,1122,1123,1124,1125,1126,1127,1128,1129,1130,1131,1132,1133,1134,1135,1136,1137,1138,1139,1140,1141,1142,1143,1144,1145,1146,1147,1148,1149,1150,1151,1152,1153,1154,1155,1156,1157,1158,1159,1160,1161,1162,1163,1164,1165,1166,1167,1168,1169,1170,1171,1172,1173,1174,1175,1176,1177,1178,1179,1180,1181,1182,1183,1184,1185,1186,1187,1188,1189,1190,1191,1192,1193,1194,1195,1196,1197,1198,1199,1200,1201,1202,1203,1204,1205,1206,1207,1208,1209,1210,1211,1212,1213,1214,1215,1216,1217,1218,1219,1220,1221,1222,1223,1224,1225,1226,1227,1228,1229,1230,1231,1232,1233,1234,1235,1236,1237,1238,1239,1240,1241,1242,1243,1244);(1,3,2,4)(6,7)(9,1244)(10,1243)(11,1242)(12,1241)(13,1240)(14,1239)(15,1238)(16,1237)(17,1236)(18,1235)(19,1234)(20,1233)(21,1232)(22,1231)(23,1230)(24,1229)(25,1228)(26,1227)(27,1226)(28,1225)(29,1224)(30,1223)(31,1222)(32,1221)(33,1220)(34,1219)(35,1218)(36,1217)(37,1216)(38,1215)(39,1214)(40,1213)(41,1212)(42,1211)(43,1210)(44,1209)(45,1208)(46,1207)(47,1206)(48,1205)(49,1204)(50,1203)(51,1202)(52,1201)(53,1200)(54,1199)(55,1198)(56,1197)(57,1196)(58,1195)(59,1194)(60,1193)(61,1192)(62,1191)(63,1190)(64,1189)(65,1188)(66,1187)(67,1186)(68,1185)(69,1184)(70,1183)(71,1182)(72,1181)(73,1180)(74,1179)(75,1178)(76,1177)(77,1176)(78,1175)(79,1174)(80,1173)(81,1172)(82,1171)(83,1170)(84,1169)(85,1168)(86,1167)(87,1166)(88,1165)(89,1164)(90,1163)(91,1162)(92,1161)(93,1160)(94,1159)(95,1158)(96,1157)(97,1156)(98,1155)(99,1154)(100,1153)(101,1152)(102,1151)(103,1150)(104,1149)(105,1148)(106,1147)(107,1146)(108,1145)(109,1144)(110,1143)(111,1142)(112,1141)(113,1140)(114,1139)(115,1138)(116,1137)(117,1136)(118,1135)(119,1134)(120,1133)(121,1132)(122,1131)(123,1130)(124,1129)(125,1128)(126,1127)(127,1126)(128,1125)(129,1124)(130,1123)(131,1122)(132,1121)(133,1120)(134,1119)(135,1118)(136,1117)(137,1116)(138,1115)(139,1114)(140,1113)(141,1112)(142,1111)(143,1110)(144,1109)(145,1108)(146,1107)(147,1106)(148,1105)(149,1104)(150,1103)(151,1102)(152,1101)(153,1100)(154,1099)(155,1098)(156,1097)(157,1096)(158,1095)(159,1094)(160,1093)(161,1092)(162,1091)(163,1090)(164,1089)(165,1088)(166,1087)(167,1086)(168,1085)(169,1084)(170,1083)(171,1082)(172,1081)(173,1080)(174,1079)(175,1078)(176,1077)(177,1076)(178,1075)(179,1074)(180,1073)(181,1072)(182,1071)(183,1070)(184,1069)(185,1068)(186,1067)(187,1066)(188,1065)(189,1064)(190,1063)(191,1062)(192,1061)(193,1060)(194,1059)(195,1058)(196,1057)(197,1056)(198,1055)(199,1054)(200,1053)(201,1052)(202,1051)(203,1050)(204,1049)(205,1048)(206,1047)(207,1046)(208,1045)(209,1044)(210,1043)(211,1042)(212,1041)(213,1040)(214,1039)(215,1038)(216,1037)(217,1036)(218,1035)(219,1034)(220,1033)(221,1032)(222,1031)(223,1030)(224,1029)(225,1028)(226,1027)(227,1026)(228,1025)(229,1024)(230,1023)(231,1022)(232,1021)(233,1020)(234,1019)(235,1018)(236,1017)(237,1016)(238,1015)(239,1014)(240,1013)(241,1012)(242,1011)(243,1010)(244,1009)(245,1008)(246,1007)(247,1006)(248,1005)(249,1004)(250,1003)(251,1002)(252,1001)(253,1000)(254,999)(255,998)(256,997)(257,996)(258,995)(259,994)(260,993)(261,992)(262,991)(263,990)(264,989)(265,988)(266,987)(267,986)(268,985)(269,984)(270,983)(271,982)(272,981)(273,980)(274,979)(275,978)(276,977)(277,976)(278,975)(279,974)(280,973)(281,972)(282,971)(283,970)(284,969)(285,968)(286,967)(287,966)(288,965)(289,964)(290,963)(291,962)(292,961)(293,960)(294,959)(295,958)(296,957)(297,956)(298,955)(299,954)(300,953)(301,952)(302,951)(303,950)(304,949)(305,948)(306,947)(307,946)(308,945)(309,944)(310,943)(311,942)(312,941)(313,940)(314,939)(315,938)(316,937)(317,936)(318,935)(319,934)(320,933)(321,932)(322,931)(323,930)(324,929)(325,928)(326,927)(327,926)(328,925)(329,924)(330,923)(331,922)(332,921)(333,920)(334,919)(335,918)(336,917)(337,916)(338,915)(339,914)(340,913)(341,912)(342,911)(343,910)(344,909)(345,908)(346,907)(347,906)(348,905)(349,904)(350,903)(351,902)(352,901)(353,900)(354,899)(355,898)(356,897)(357,896)(358,895)(359,894)(360,893)(361,892)(362,891)(363,890)(364,889)(365,888)(366,887)(367,886)(368,885)(369,884)(370,883)(371,882)(372,881)(373,880)(374,879)(375,878)(376,877)(377,876)(378,875)(379,874)(380,873)(381,872)(382,871)(383,870)(384,869)(385,868)(386,867)(387,866)(388,865)(389,864)(390,863)(391,862)(392,861)(393,860)(394,859)(395,858)(396,857)(397,856)(398,855)(399,854)(400,853)(401,852)(402,851)(403,850)(404,849)(405,848)(406,847)(407,846)(408,845)(409,844)(410,843)(411,842)(412,841)(413,840)(414,839)(415,838)(416,837)(417,836)(418,835)(419,834)(420,833)(421,832)(422,831)(423,830)(424,829)(425,828)(426,827)(427,826)(428,825)(429,824)(430,823)(431,822)(432,821)(433,820)(434,819)(435,818)(436,817)(437,816)(438,815)(439,814)(440,813)(441,812)(442,811)(443,810)(444,809)(445,808)(446,807)(447,806)(448,805)(449,804)(450,803)(451,802)(452,801)(453,800)(454,799)(455,798)(456,797)(457,796)(458,795)(459,794)(460,793)(461,792)(462,791)(463,790)(464,789)(465,788)(466,787)(467,786)(468,785)(469,784)(470,783)(471,782)(472,781)(473,780)(474,779)(475,778)(476,777)(477,776)(478,775)(479,774)(480,773)(481,772)(482,771)(483,770)(484,769)(485,768)(486,767)(487,766)(488,765)(489,764)(490,763)(491,762)(492,761)(493,760)(494,759)(495,758)(496,757)(497,756)(498,755)(499,754)(500,753)(501,752)(502,751)(503,750)(504,749)(505,748)(506,747)(507,746)(508,745)(509,744)(510,743)(511,742)(512,741)(513,740)(514,739)(515,738)(516,737)(517,736)(518,735)(519,734)(520,733)(521,732)(522,731)(523,730)(524,729)(525,728)(526,727)(527,726)(528,725)(529,724)(530,723)(531,722)(532,721)(533,720)(534,719)(535,718)(536,717)(537,716)(538,715)(539,714)(540,713)(541,712)(542,711)(543,710)(544,709)(545,708)(546,707)(547,706)(548,705)(549,704)(550,703)(551,702)(552,701)(553,700)(554,699)(555,698)(556,697)(557,696)(558,695)(559,694)(560,693)(561,692)(562,691)(563,690)(564,689)(565,688)(566,687)(567,686)(568,685)(569,684)(570,683)(571,682)(572,681)(573,680)(574,679)(575,678)(576,677)(577,676)(578,675)(579,674)(580,673)(581,672)(582,671)(583,670)(584,669)(585,668)(586,667)(587,666)(588,665)(589,664)(590,663)(591,662)(592,661)(593,660)(594,659)(595,658)(596,657)(597,656)(598,655)(599,654)(600,653)(601,652)(602,651)(603,650)(604,649)(605,648)(606,647)(607,646)(608,645)(609,644)(610,643)(611,642)(612,641)(613,640)(614,639)(615,638)(616,637)(617,636)(618,635)(619,634)(620,633)(621,632)(622,631)(623,630)(624,629)(625,628)(626,627)
Polycyclic presentation:
2,3,1237,2|a^2=d,b^a=b^2,c^a=c^1236
Conjugacy classes & character table
3714 conjugacy classes. The character table is too large to display.
Relationships
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(14844, 6);
Finite Group Databasebeta