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D16237 #44570334
Aliases
Splittings
Subgroups
8 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 2 generators on 1262 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,172,173,174,175,176,177,178,179,180,181,182,183,184,185,186,187,188,189,190,191,192,193,194,195,196,197,198,199,200,201,202,203,204,205,206,207,208,209,210,211,212,213,214,215,216,217,218,219,220,221,222,223,224,225,226,227,228,229,230,231,232,233,234,235,236,237,238,239,240,241,242,243,244,245,246,247,248,249,250,251,252,253,254,255,256,257,258,259,260,261,262,263,264,265,266,267,268,269,270,271,272,273,274,275,276,277,278,279,280,281,282,283,284,285,286,287,288,289,290,291,292,293,294,295,296,297,298,299,300,301,302,303,304,305,306,307,308,309,310,311,312,313,314,315,316,317,318,319,320,321,322,323,324,325,326,327,328,329,330,331,332,333,334,335,336,337,338,339,340,341,342,343,344,345,346,347,348,349,350,351,352,353,354,355,356,357,358,359,360,361,362,363,364,365,366,367,368,369,370,371,372,373,374,375,376,377,378,379,380,381,382,383,384,385,386,387,388,389,390,391,392,393,394,395,396,397,398,399,400,401,402,403,404,405,406,407,408,409,410,411,412,413,414,415,416,417,418,419,420,421,422,423,424,425,426,427,428,429,430,431,432,433,434,435,436,437,438,439,440,441,442,443,444,445,446,447,448,449,450,451,452,453,454,455,456,457,458,459,460,461,462,463,464,465,466,467,468,469,470,471,472,473,474,475,476,477,478,479,480,481,482,483,484,485,486,487,488,489,490,491,492,493,494,495,496,497,498,499,500,501,502,503,504,505,506,507,508,509,510,511,512,513,514,515,516,517,518,519,520,521,522,523,524,525,526,527,528,529,530,531,532,533,534,535,536,537,538,539,540,541,542,543,544,545,546,547,548,549,550,551,552,553,554,555,556,557,558,559,560,561,562,563,564,565,566,567,568,569,570,571,572,573,574,575,576,577,578,579,580,581,582,583,584,585,586,587,588,589,590,591,592,593,594,595,596,597,598,599,600,601,602,603,604,605,606,607,608,609,610,611,612,613,614,615,616,617,618,619,620,621,622,623,624,625,626,627,628,629,630,631,632,633,634,635,636,637,638,639,640,641,642,643,644,645,646,647,648,649,650,651,652,653,654,655,656,657,658,659,660,661,662,663,664,665,666,667,668,669,670,671,672,673,674,675,676,677,678,679,680,681,682,683,684,685,686,687,688,689,690,691,692,693,694,695,696,697,698,699,700,701,702,703,704,705,706,707,708,709,710,711,712,713,714,715,716,717,718,719,720,721,722,723,724,725,726,727,728,729,730,731,732,733,734,735,736,737,738,739,740,741,742,743,744,745,746,747,748,749,750,751,752,753,754,755,756,757,758,759,760,761,762,763,764,765,766,767,768,769,770,771,772,773,774,775,776,777,778,779,780,781,782,783,784,785,786,787,788,789,790,791,792,793,794,795,796,797,798,799,800,801,802,803,804,805,806,807,808,809,810,811,812,813,814,815,816,817,818,819,820,821,822,823,824,825,826,827,828,829,830,831,832,833,834,835,836,837,838,839,840,841,842,843,844,845,846,847,848,849,850,851,852,853,854,855,856,857,858,859,860,861,862,863,864,865,866,867,868,869,870,871,872,873,874,875,876,877,878,879,880,881,882,883,884,885,886,887,888,889,890,891,892,893,894,895,896,897,898,899,900,901,902,903,904,905,906,907,908,909,910,911,912,913,914,915,916,917,918,919,920,921,922,923,924,925,926,927,928,929,930,931,932,933,934,935,936,937,938,939,940,941,942,943,944,945,946,947,948,949,950,951,952,953,954,955,956,957,958,959,960,961,962,963,964,965,966,967,968,969,970,971,972,973,974,975,976,977,978,979,980,981,982,983,984,985,986,987,988,989,990,991,992,993,994,995,996,997,998,999,1000,1001,1002,1003,1004,1005,1006,1007,1008,1009,1010,1011,1012,1013,1014,1015,1016,1017,1018,1019,1020,1021,1022,1023,1024,1025,1026,1027,1028,1029,1030,1031,1032,1033,1034,1035,1036,1037,1038,1039,1040,1041,1042,1043,1044,1045,1046,1047,1048,1049,1050,1051,1052,1053,1054,1055,1056,1057,1058,1059,1060,1061,1062,1063,1064,1065,1066,1067,1068,1069,1070,1071,1072,1073,1074,1075,1076,1077,1078,1079,1080,1081,1082,1083,1084,1085,1086,1087,1088,1089,1090,1091,1092,1093,1094,1095,1096,1097,1098,1099,1100,1101,1102,1103,1104,1105,1106,1107,1108,1109,1110,1111,1112,1113,1114,1115,1116,1117,1118,1119,1120,1121,1122,1123,1124,1125,1126,1127,1128,1129,1130,1131,1132,1133,1134,1135,1136,1137,1138,1139,1140,1141,1142,1143,1144,1145,1146,1147,1148,1149,1150,1151,1152,1153,1154,1155,1156,1157,1158,1159,1160,1161,1162,1163,1164,1165,1166,1167,1168,1169,1170,1171,1172,1173,1174,1175,1176,1177,1178,1179,1180,1181,1182,1183,1184,1185,1186,1187,1188,1189,1190,1191,1192,1193,1194,1195,1196,1197,1198,1199,1200,1201,1202,1203,1204,1205,1206,1207,1208,1209,1210,1211,1212,1213,1214,1215,1216,1217,1218,1219,1220,1221,1222,1223,1224,1225,1226,1227,1228,1229,1230,1231,1232,1233,1234,1235,1236,1237,1238,1239,1240,1241,1242,1243,1244,1245,1246,1247,1248,1249,1250,1251,1252,1253,1254,1255,1256,1257,1258,1259,1260,1261,1262);(2,13)(3,12)(4,11)(5,10)(6,9)(7,8)(15,1262)(16,1261)(17,1260)(18,1259)(19,1258)(20,1257)(21,1256)(22,1255)(23,1254)(24,1253)(25,1252)(26,1251)(27,1250)(28,1249)(29,1248)(30,1247)(31,1246)(32,1245)(33,1244)(34,1243)(35,1242)(36,1241)(37,1240)(38,1239)(39,1238)(40,1237)(41,1236)(42,1235)(43,1234)(44,1233)(45,1232)(46,1231)(47,1230)(48,1229)(49,1228)(50,1227)(51,1226)(52,1225)(53,1224)(54,1223)(55,1222)(56,1221)(57,1220)(58,1219)(59,1218)(60,1217)(61,1216)(62,1215)(63,1214)(64,1213)(65,1212)(66,1211)(67,1210)(68,1209)(69,1208)(70,1207)(71,1206)(72,1205)(73,1204)(74,1203)(75,1202)(76,1201)(77,1200)(78,1199)(79,1198)(80,1197)(81,1196)(82,1195)(83,1194)(84,1193)(85,1192)(86,1191)(87,1190)(88,1189)(89,1188)(90,1187)(91,1186)(92,1185)(93,1184)(94,1183)(95,1182)(96,1181)(97,1180)(98,1179)(99,1178)(100,1177)(101,1176)(102,1175)(103,1174)(104,1173)(105,1172)(106,1171)(107,1170)(108,1169)(109,1168)(110,1167)(111,1166)(112,1165)(113,1164)(114,1163)(115,1162)(116,1161)(117,1160)(118,1159)(119,1158)(120,1157)(121,1156)(122,1155)(123,1154)(124,1153)(125,1152)(126,1151)(127,1150)(128,1149)(129,1148)(130,1147)(131,1146)(132,1145)(133,1144)(134,1143)(135,1142)(136,1141)(137,1140)(138,1139)(139,1138)(140,1137)(141,1136)(142,1135)(143,1134)(144,1133)(145,1132)(146,1131)(147,1130)(148,1129)(149,1128)(150,1127)(151,1126)(152,1125)(153,1124)(154,1123)(155,1122)(156,1121)(157,1120)(158,1119)(159,1118)(160,1117)(161,1116)(162,1115)(163,1114)(164,1113)(165,1112)(166,1111)(167,1110)(168,1109)(169,1108)(170,1107)(171,1106)(172,1105)(173,1104)(174,1103)(175,1102)(176,1101)(177,1100)(178,1099)(179,1098)(180,1097)(181,1096)(182,1095)(183,1094)(184,1093)(185,1092)(186,1091)(187,1090)(188,1089)(189,1088)(190,1087)(191,1086)(192,1085)(193,1084)(194,1083)(195,1082)(196,1081)(197,1080)(198,1079)(199,1078)(200,1077)(201,1076)(202,1075)(203,1074)(204,1073)(205,1072)(206,1071)(207,1070)(208,1069)(209,1068)(210,1067)(211,1066)(212,1065)(213,1064)(214,1063)(215,1062)(216,1061)(217,1060)(218,1059)(219,1058)(220,1057)(221,1056)(222,1055)(223,1054)(224,1053)(225,1052)(226,1051)(227,1050)(228,1049)(229,1048)(230,1047)(231,1046)(232,1045)(233,1044)(234,1043)(235,1042)(236,1041)(237,1040)(238,1039)(239,1038)(240,1037)(241,1036)(242,1035)(243,1034)(244,1033)(245,1032)(246,1031)(247,1030)(248,1029)(249,1028)(250,1027)(251,1026)(252,1025)(253,1024)(254,1023)(255,1022)(256,1021)(257,1020)(258,1019)(259,1018)(260,1017)(261,1016)(262,1015)(263,1014)(264,1013)(265,1012)(266,1011)(267,1010)(268,1009)(269,1008)(270,1007)(271,1006)(272,1005)(273,1004)(274,1003)(275,1002)(276,1001)(277,1000)(278,999)(279,998)(280,997)(281,996)(282,995)(283,994)(284,993)(285,992)(286,991)(287,990)(288,989)(289,988)(290,987)(291,986)(292,985)(293,984)(294,983)(295,982)(296,981)(297,980)(298,979)(299,978)(300,977)(301,976)(302,975)(303,974)(304,973)(305,972)(306,971)(307,970)(308,969)(309,968)(310,967)(311,966)(312,965)(313,964)(314,963)(315,962)(316,961)(317,960)(318,959)(319,958)(320,957)(321,956)(322,955)(323,954)(324,953)(325,952)(326,951)(327,950)(328,949)(329,948)(330,947)(331,946)(332,945)(333,944)(334,943)(335,942)(336,941)(337,940)(338,939)(339,938)(340,937)(341,936)(342,935)(343,934)(344,933)(345,932)(346,931)(347,930)(348,929)(349,928)(350,927)(351,926)(352,925)(353,924)(354,923)(355,922)(356,921)(357,920)(358,919)(359,918)(360,917)(361,916)(362,915)(363,914)(364,913)(365,912)(366,911)(367,910)(368,909)(369,908)(370,907)(371,906)(372,905)(373,904)(374,903)(375,902)(376,901)(377,900)(378,899)(379,898)(380,897)(381,896)(382,895)(383,894)(384,893)(385,892)(386,891)(387,890)(388,889)(389,888)(390,887)(391,886)(392,885)(393,884)(394,883)(395,882)(396,881)(397,880)(398,879)(399,878)(400,877)(401,876)(402,875)(403,874)(404,873)(405,872)(406,871)(407,870)(408,869)(409,868)(410,867)(411,866)(412,865)(413,864)(414,863)(415,862)(416,861)(417,860)(418,859)(419,858)(420,857)(421,856)(422,855)(423,854)(424,853)(425,852)(426,851)(427,850)(428,849)(429,848)(430,847)(431,846)(432,845)(433,844)(434,843)(435,842)(436,841)(437,840)(438,839)(439,838)(440,837)(441,836)(442,835)(443,834)(444,833)(445,832)(446,831)(447,830)(448,829)(449,828)(450,827)(451,826)(452,825)(453,824)(454,823)(455,822)(456,821)(457,820)(458,819)(459,818)(460,817)(461,816)(462,815)(463,814)(464,813)(465,812)(466,811)(467,810)(468,809)(469,808)(470,807)(471,806)(472,805)(473,804)(474,803)(475,802)(476,801)(477,800)(478,799)(479,798)(480,797)(481,796)(482,795)(483,794)(484,793)(485,792)(486,791)(487,790)(488,789)(489,788)(490,787)(491,786)(492,785)(493,784)(494,783)(495,782)(496,781)(497,780)(498,779)(499,778)(500,777)(501,776)(502,775)(503,774)(504,773)(505,772)(506,771)(507,770)(508,769)(509,768)(510,767)(511,766)(512,765)(513,764)(514,763)(515,762)(516,761)(517,760)(518,759)(519,758)(520,757)(521,756)(522,755)(523,754)(524,753)(525,752)(526,751)(527,750)(528,749)(529,748)(530,747)(531,746)(532,745)(533,744)(534,743)(535,742)(536,741)(537,740)(538,739)(539,738)(540,737)(541,736)(542,735)(543,734)(544,733)(545,732)(546,731)(547,730)(548,729)(549,728)(550,727)(551,726)(552,725)(553,724)(554,723)(555,722)(556,721)(557,720)(558,719)(559,718)(560,717)(561,716)(562,715)(563,714)(564,713)(565,712)(566,711)(567,710)(568,709)(569,708)(570,707)(571,706)(572,705)(573,704)(574,703)(575,702)(576,701)(577,700)(578,699)(579,698)(580,697)(581,696)(582,695)(583,694)(584,693)(585,692)(586,691)(587,690)(588,689)(589,688)(590,687)(591,686)(592,685)(593,684)(594,683)(595,682)(596,681)(597,680)(598,679)(599,678)(600,677)(601,676)(602,675)(603,674)(604,673)(605,672)(606,671)(607,670)(608,669)(609,668)(610,667)(611,666)(612,665)(613,664)(614,663)(615,662)(616,661)(617,660)(618,659)(619,658)(620,657)(621,656)(622,655)(623,654)(624,653)(625,652)(626,651)(627,650)(628,649)(629,648)(630,647)(631,646)(632,645)(633,644)(634,643)(635,642)(636,641)(637,640)(638,639)
Polycyclic presentation:
2,13,1249|b^a=b^12,c^a=c^1248
Conjugacy classes & character table
8120 conjugacy classes. The character table is too large to display.
Relationships
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32474, 5);
Finite Group Databasebeta