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D9079 #31827786
Aliases
Splittings
Subgroups
8 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 2 generators on 1304 points:
(1,2,3,4,5,6,7)(8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,172,173,174,175,176,177,178,179,180,181,182,183,184,185,186,187,188,189,190,191,192,193,194,195,196,197,198,199,200,201,202,203,204,205,206,207,208,209,210,211,212,213,214,215,216,217,218,219,220,221,222,223,224,225,226,227,228,229,230,231,232,233,234,235,236,237,238,239,240,241,242,243,244,245,246,247,248,249,250,251,252,253,254,255,256,257,258,259,260,261,262,263,264,265,266,267,268,269,270,271,272,273,274,275,276,277,278,279,280,281,282,283,284,285,286,287,288,289,290,291,292,293,294,295,296,297,298,299,300,301,302,303,304,305,306,307,308,309,310,311,312,313,314,315,316,317,318,319,320,321,322,323,324,325,326,327,328,329,330,331,332,333,334,335,336,337,338,339,340,341,342,343,344,345,346,347,348,349,350,351,352,353,354,355,356,357,358,359,360,361,362,363,364,365,366,367,368,369,370,371,372,373,374,375,376,377,378,379,380,381,382,383,384,385,386,387,388,389,390,391,392,393,394,395,396,397,398,399,400,401,402,403,404,405,406,407,408,409,410,411,412,413,414,415,416,417,418,419,420,421,422,423,424,425,426,427,428,429,430,431,432,433,434,435,436,437,438,439,440,441,442,443,444,445,446,447,448,449,450,451,452,453,454,455,456,457,458,459,460,461,462,463,464,465,466,467,468,469,470,471,472,473,474,475,476,477,478,479,480,481,482,483,484,485,486,487,488,489,490,491,492,493,494,495,496,497,498,499,500,501,502,503,504,505,506,507,508,509,510,511,512,513,514,515,516,517,518,519,520,521,522,523,524,525,526,527,528,529,530,531,532,533,534,535,536,537,538,539,540,541,542,543,544,545,546,547,548,549,550,551,552,553,554,555,556,557,558,559,560,561,562,563,564,565,566,567,568,569,570,571,572,573,574,575,576,577,578,579,580,581,582,583,584,585,586,587,588,589,590,591,592,593,594,595,596,597,598,599,600,601,602,603,604,605,606,607,608,609,610,611,612,613,614,615,616,617,618,619,620,621,622,623,624,625,626,627,628,629,630,631,632,633,634,635,636,637,638,639,640,641,642,643,644,645,646,647,648,649,650,651,652,653,654,655,656,657,658,659,660,661,662,663,664,665,666,667,668,669,670,671,672,673,674,675,676,677,678,679,680,681,682,683,684,685,686,687,688,689,690,691,692,693,694,695,696,697,698,699,700,701,702,703,704,705,706,707,708,709,710,711,712,713,714,715,716,717,718,719,720,721,722,723,724,725,726,727,728,729,730,731,732,733,734,735,736,737,738,739,740,741,742,743,744,745,746,747,748,749,750,751,752,753,754,755,756,757,758,759,760,761,762,763,764,765,766,767,768,769,770,771,772,773,774,775,776,777,778,779,780,781,782,783,784,785,786,787,788,789,790,791,792,793,794,795,796,797,798,799,800,801,802,803,804,805,806,807,808,809,810,811,812,813,814,815,816,817,818,819,820,821,822,823,824,825,826,827,828,829,830,831,832,833,834,835,836,837,838,839,840,841,842,843,844,845,846,847,848,849,850,851,852,853,854,855,856,857,858,859,860,861,862,863,864,865,866,867,868,869,870,871,872,873,874,875,876,877,878,879,880,881,882,883,884,885,886,887,888,889,890,891,892,893,894,895,896,897,898,899,900,901,902,903,904,905,906,907,908,909,910,911,912,913,914,915,916,917,918,919,920,921,922,923,924,925,926,927,928,929,930,931,932,933,934,935,936,937,938,939,940,941,942,943,944,945,946,947,948,949,950,951,952,953,954,955,956,957,958,959,960,961,962,963,964,965,966,967,968,969,970,971,972,973,974,975,976,977,978,979,980,981,982,983,984,985,986,987,988,989,990,991,992,993,994,995,996,997,998,999,1000,1001,1002,1003,1004,1005,1006,1007,1008,1009,1010,1011,1012,1013,1014,1015,1016,1017,1018,1019,1020,1021,1022,1023,1024,1025,1026,1027,1028,1029,1030,1031,1032,1033,1034,1035,1036,1037,1038,1039,1040,1041,1042,1043,1044,1045,1046,1047,1048,1049,1050,1051,1052,1053,1054,1055,1056,1057,1058,1059,1060,1061,1062,1063,1064,1065,1066,1067,1068,1069,1070,1071,1072,1073,1074,1075,1076,1077,1078,1079,1080,1081,1082,1083,1084,1085,1086,1087,1088,1089,1090,1091,1092,1093,1094,1095,1096,1097,1098,1099,1100,1101,1102,1103,1104,1105,1106,1107,1108,1109,1110,1111,1112,1113,1114,1115,1116,1117,1118,1119,1120,1121,1122,1123,1124,1125,1126,1127,1128,1129,1130,1131,1132,1133,1134,1135,1136,1137,1138,1139,1140,1141,1142,1143,1144,1145,1146,1147,1148,1149,1150,1151,1152,1153,1154,1155,1156,1157,1158,1159,1160,1161,1162,1163,1164,1165,1166,1167,1168,1169,1170,1171,1172,1173,1174,1175,1176,1177,1178,1179,1180,1181,1182,1183,1184,1185,1186,1187,1188,1189,1190,1191,1192,1193,1194,1195,1196,1197,1198,1199,1200,1201,1202,1203,1204,1205,1206,1207,1208,1209,1210,1211,1212,1213,1214,1215,1216,1217,1218,1219,1220,1221,1222,1223,1224,1225,1226,1227,1228,1229,1230,1231,1232,1233,1234,1235,1236,1237,1238,1239,1240,1241,1242,1243,1244,1245,1246,1247,1248,1249,1250,1251,1252,1253,1254,1255,1256,1257,1258,1259,1260,1261,1262,1263,1264,1265,1266,1267,1268,1269,1270,1271,1272,1273,1274,1275,1276,1277,1278,1279,1280,1281,1282,1283,1284,1285,1286,1287,1288,1289,1290,1291,1292,1293,1294,1295,1296,1297,1298,1299,1300,1301,1302,1303,1304);(2,7)(3,6)(4,5)(9,1304)(10,1303)(11,1302)(12,1301)(13,1300)(14,1299)(15,1298)(16,1297)(17,1296)(18,1295)(19,1294)(20,1293)(21,1292)(22,1291)(23,1290)(24,1289)(25,1288)(26,1287)(27,1286)(28,1285)(29,1284)(30,1283)(31,1282)(32,1281)(33,1280)(34,1279)(35,1278)(36,1277)(37,1276)(38,1275)(39,1274)(40,1273)(41,1272)(42,1271)(43,1270)(44,1269)(45,1268)(46,1267)(47,1266)(48,1265)(49,1264)(50,1263)(51,1262)(52,1261)(53,1260)(54,1259)(55,1258)(56,1257)(57,1256)(58,1255)(59,1254)(60,1253)(61,1252)(62,1251)(63,1250)(64,1249)(65,1248)(66,1247)(67,1246)(68,1245)(69,1244)(70,1243)(71,1242)(72,1241)(73,1240)(74,1239)(75,1238)(76,1237)(77,1236)(78,1235)(79,1234)(80,1233)(81,1232)(82,1231)(83,1230)(84,1229)(85,1228)(86,1227)(87,1226)(88,1225)(89,1224)(90,1223)(91,1222)(92,1221)(93,1220)(94,1219)(95,1218)(96,1217)(97,1216)(98,1215)(99,1214)(100,1213)(101,1212)(102,1211)(103,1210)(104,1209)(105,1208)(106,1207)(107,1206)(108,1205)(109,1204)(110,1203)(111,1202)(112,1201)(113,1200)(114,1199)(115,1198)(116,1197)(117,1196)(118,1195)(119,1194)(120,1193)(121,1192)(122,1191)(123,1190)(124,1189)(125,1188)(126,1187)(127,1186)(128,1185)(129,1184)(130,1183)(131,1182)(132,1181)(133,1180)(134,1179)(135,1178)(136,1177)(137,1176)(138,1175)(139,1174)(140,1173)(141,1172)(142,1171)(143,1170)(144,1169)(145,1168)(146,1167)(147,1166)(148,1165)(149,1164)(150,1163)(151,1162)(152,1161)(153,1160)(154,1159)(155,1158)(156,1157)(157,1156)(158,1155)(159,1154)(160,1153)(161,1152)(162,1151)(163,1150)(164,1149)(165,1148)(166,1147)(167,1146)(168,1145)(169,1144)(170,1143)(171,1142)(172,1141)(173,1140)(174,1139)(175,1138)(176,1137)(177,1136)(178,1135)(179,1134)(180,1133)(181,1132)(182,1131)(183,1130)(184,1129)(185,1128)(186,1127)(187,1126)(188,1125)(189,1124)(190,1123)(191,1122)(192,1121)(193,1120)(194,1119)(195,1118)(196,1117)(197,1116)(198,1115)(199,1114)(200,1113)(201,1112)(202,1111)(203,1110)(204,1109)(205,1108)(206,1107)(207,1106)(208,1105)(209,1104)(210,1103)(211,1102)(212,1101)(213,1100)(214,1099)(215,1098)(216,1097)(217,1096)(218,1095)(219,1094)(220,1093)(221,1092)(222,1091)(223,1090)(224,1089)(225,1088)(226,1087)(227,1086)(228,1085)(229,1084)(230,1083)(231,1082)(232,1081)(233,1080)(234,1079)(235,1078)(236,1077)(237,1076)(238,1075)(239,1074)(240,1073)(241,1072)(242,1071)(243,1070)(244,1069)(245,1068)(246,1067)(247,1066)(248,1065)(249,1064)(250,1063)(251,1062)(252,1061)(253,1060)(254,1059)(255,1058)(256,1057)(257,1056)(258,1055)(259,1054)(260,1053)(261,1052)(262,1051)(263,1050)(264,1049)(265,1048)(266,1047)(267,1046)(268,1045)(269,1044)(270,1043)(271,1042)(272,1041)(273,1040)(274,1039)(275,1038)(276,1037)(277,1036)(278,1035)(279,1034)(280,1033)(281,1032)(282,1031)(283,1030)(284,1029)(285,1028)(286,1027)(287,1026)(288,1025)(289,1024)(290,1023)(291,1022)(292,1021)(293,1020)(294,1019)(295,1018)(296,1017)(297,1016)(298,1015)(299,1014)(300,1013)(301,1012)(302,1011)(303,1010)(304,1009)(305,1008)(306,1007)(307,1006)(308,1005)(309,1004)(310,1003)(311,1002)(312,1001)(313,1000)(314,999)(315,998)(316,997)(317,996)(318,995)(319,994)(320,993)(321,992)(322,991)(323,990)(324,989)(325,988)(326,987)(327,986)(328,985)(329,984)(330,983)(331,982)(332,981)(333,980)(334,979)(335,978)(336,977)(337,976)(338,975)(339,974)(340,973)(341,972)(342,971)(343,970)(344,969)(345,968)(346,967)(347,966)(348,965)(349,964)(350,963)(351,962)(352,961)(353,960)(354,959)(355,958)(356,957)(357,956)(358,955)(359,954)(360,953)(361,952)(362,951)(363,950)(364,949)(365,948)(366,947)(367,946)(368,945)(369,944)(370,943)(371,942)(372,941)(373,940)(374,939)(375,938)(376,937)(377,936)(378,935)(379,934)(380,933)(381,932)(382,931)(383,930)(384,929)(385,928)(386,927)(387,926)(388,925)(389,924)(390,923)(391,922)(392,921)(393,920)(394,919)(395,918)(396,917)(397,916)(398,915)(399,914)(400,913)(401,912)(402,911)(403,910)(404,909)(405,908)(406,907)(407,906)(408,905)(409,904)(410,903)(411,902)(412,901)(413,900)(414,899)(415,898)(416,897)(417,896)(418,895)(419,894)(420,893)(421,892)(422,891)(423,890)(424,889)(425,888)(426,887)(427,886)(428,885)(429,884)(430,883)(431,882)(432,881)(433,880)(434,879)(435,878)(436,877)(437,876)(438,875)(439,874)(440,873)(441,872)(442,871)(443,870)(444,869)(445,868)(446,867)(447,866)(448,865)(449,864)(450,863)(451,862)(452,861)(453,860)(454,859)(455,858)(456,857)(457,856)(458,855)(459,854)(460,853)(461,852)(462,851)(463,850)(464,849)(465,848)(466,847)(467,846)(468,845)(469,844)(470,843)(471,842)(472,841)(473,840)(474,839)(475,838)(476,837)(477,836)(478,835)(479,834)(480,833)(481,832)(482,831)(483,830)(484,829)(485,828)(486,827)(487,826)(488,825)(489,824)(490,823)(491,822)(492,821)(493,820)(494,819)(495,818)(496,817)(497,816)(498,815)(499,814)(500,813)(501,812)(502,811)(503,810)(504,809)(505,808)(506,807)(507,806)(508,805)(509,804)(510,803)(511,802)(512,801)(513,800)(514,799)(515,798)(516,797)(517,796)(518,795)(519,794)(520,793)(521,792)(522,791)(523,790)(524,789)(525,788)(526,787)(527,786)(528,785)(529,784)(530,783)(531,782)(532,781)(533,780)(534,779)(535,778)(536,777)(537,776)(538,775)(539,774)(540,773)(541,772)(542,771)(543,770)(544,769)(545,768)(546,767)(547,766)(548,765)(549,764)(550,763)(551,762)(552,761)(553,760)(554,759)(555,758)(556,757)(557,756)(558,755)(559,754)(560,753)(561,752)(562,751)(563,750)(564,749)(565,748)(566,747)(567,746)(568,745)(569,744)(570,743)(571,742)(572,741)(573,740)(574,739)(575,738)(576,737)(577,736)(578,735)(579,734)(580,733)(581,732)(582,731)(583,730)(584,729)(585,728)(586,727)(587,726)(588,725)(589,724)(590,723)(591,722)(592,721)(593,720)(594,719)(595,718)(596,717)(597,716)(598,715)(599,714)(600,713)(601,712)(602,711)(603,710)(604,709)(605,708)(606,707)(607,706)(608,705)(609,704)(610,703)(611,702)(612,701)(613,700)(614,699)(615,698)(616,697)(617,696)(618,695)(619,694)(620,693)(621,692)(622,691)(623,690)(624,689)(625,688)(626,687)(627,686)(628,685)(629,684)(630,683)(631,682)(632,681)(633,680)(634,679)(635,678)(636,677)(637,676)(638,675)(639,674)(640,673)(641,672)(642,671)(643,670)(644,669)(645,668)(646,667)(647,666)(648,665)(649,664)(650,663)(651,662)(652,661)(653,660)(654,659)(655,658)(656,657)
Polycyclic presentation:
2,7,1297|b^a=b^6,c^a=c^1296
Conjugacy classes & character table
4541 conjugacy classes. The character table is too large to display.
Relationships
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18158, 3);
Finite Group Databasebeta