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Aliases
Splittings
Subgroups
8 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 2 generators on 1431 points:
(2,3,5,9,17,33,64)(4,7,13,25,48,93,179)(6,11,21,40,78,151,124)(8,15,29,56,108,207,384)(10,19,37,72,139,65,125)(12,23,44,85,164,308,336)(14,27,52,100,193,362,237)(16,31,60,116,222,81,157)(18,35,68,131,34,66,127)(20,39,76,147,277,180,337)(22,42,82,158,297,285,238)(24,46,89,171,321,568,659)(26,50,97,187,350,126,239)(28,54,104,105,201,219,406)(30,58,112,214,397,676,438)(32,62,120,230,426,488,796)(36,70,135,255,94,181,339)(38,74,143,269,152,286,241)(41,80,155,292,263,128,242)(43,84,162,304,429,546,593)(45,87,168,315,557,630,439)(47,91,175,328,580,759,296)(49,95,183,342,67,129,244)(51,99,191,358,622,338,594)(53,102,197,368,394,511,440)(55,106,203,320,566,893,992)(57,110,211,391,493,240,441)(59,114,218,404,688,1020,692)(61,118,226,418,300,534,739)(63,122,233,431,729,950,1243)(69,133,251,79,153,288,248)(71,137,259,471,208,385,660)(73,141,266,140,264,132,249)(75,145,273,492,309,547,595)(77,149,281,504,363,631,443)(83,160,301,535,529,512,444)(86,166,312,553,610,243,445)(88,170,319,564,889,407,693)(90,173,325,574,904,1006,740)(92,177,332,587,925,1151,1119)(96,185,346,355,182,340,531)(98,189,354,615,287,377,447)(101,195,123,235,434,245,448)(103,199,372,644,902,865,932)(107,205,380,649,721,1054,528)(109,209,387,663,130,246,450)(111,213,395,673,262,477,787)(113,216,401,682,951,825,741)(115,220,408,694,621,954,1246)(117,224,415,196,367,442,742)(119,228,422,716,640,972,1025)(121,232,341,596,853,210,389)(134,253,460,165,310,549,598)(136,257,467,194,364,633,454)(138,261,475,783,412,161,303)(142,268,484,278,499,343,599)(144,271,489,298,530,514,455)(146,275,496,805,569,896,993)(148,279,501,351,611,250,456)(150,283,508,821,375,409,696)(154,290,517,464,184,344,601)(156,294,524,486,289,515,457)(159,299,532,521,479,252,458)(163,306,543,861,879,965,744)(167,314,247,452,753,223,413)(169,317,561,885,672,826,745)(172,323,427,724,802,446,453)(174,327,578,206,382,656,988)(176,330,584,919,1120,850,1072)(178,334,590,928,1232,1367,1393)(186,348,606,642,386,661,994)(188,352,613,265,480,256,465)(190,356,618,671,548,866,847)(192,360,626,959,632,966,747)(198,370,641,708,845,650,748)(200,204,378,579,911,449,749)(202,376,423,718,258,469,774)(212,393,670,822,513,651,750)(215,399,679,1010,734,451,751)(217,403,686,1018,1115,1174,1113)(221,410,698,1028,1184,1368,844)(225,417,709,400,681,788,1114)(227,420,713,560,884,1143,1073)(229,424,720,1053,1015,1280,1394)(231,428,726,817,1137,743,1074)(234,433,635,969,1254,1102,666)(236,436,736,485,793,505,816)(254,462,765,322,570,898,997)(260,473,779,398,677,1007,756)(267,483,270,487,293,522,482)(272,491,799,540,728,867,934)(274,494,803,558,880,967,757)(276,498,809,1130,913,1085,539)(280,503,814,623,955,600,935)(282,506,818,638,675,827,758)(284,509,823,1142,894,1198,1265)(291,519,832,777,388,664,998)(295,526,840,801,550,868,936)(302,537,854,851,846,828,760)(305,541,732,874,946,459,761)(307,545,349,608,942,697,702)(311,551,870,617,345,602,858)(313,554,875,948,516,653,762)(316,559,882,435,735,461,763)(318,563,520,834,1148,1108,703)(324,573,597,933,478,414,704)(326,576,730,1063,1244,1144,755)(329,582,916,1097,637,746,768)(331,586,923,1101,588,926,1231)(333,589,662,995,1267,390,667)(335,592,794,518,830,771,366)(347,605,627,365,634,968,769)(353,614,881,500,811,604,619)(357,620,952,1017,897,1200,1266)(359,624,957,612,947,466,770)(361,628,962,1039,648,699,1030)(369,639,685,835,789,468,772)(371,643,790,1062,784,1109,706)(373,646,979,1221,1186,1253,1076)(374,381,654,984,1080,416,707)(379,652,924,1229,831,989,1099)(383,657,990,1263,808,1129,1346)(392,668,806,481,725,472,778)(396,674,1004,609,944,1239,1077)(402,684,1016,1250,1159,983,1078)(405,690,1022,1284,1215,752,1079)(411,700,1032,1289,1092,1320,910)(419,712,542,860,1067,754,1081)(421,715,1047,907,1211,1365,1334)(425,722,1056,1302,1297,1193,1158)(430,603,937,1170,571,900,1203)(432,731,1064,1249,1395,1075,1311)(437,738,1070,815,1136,960,1248)(463,767,1093,581,914,1087,556)(470,775,1035,567,895,873,1179)(474,781,1105,689,1021,1283,1051)(476,785,1110,711,538,856,1083)(490,798,536,852,848,836,791)(495,804,1126,890,1194,719,1052)(497,807,1128,905,1207,1272,1084)(502,813,616,949,523,695,792)(507,820,1139,976,1206,1175,1235)(510,824,943,1238,1055,1043,857)(525,838,797,533,849,837,795)(527,842,1155,1127,899,1201,1269)(544,863,1171,1190,1005,1145,1086)(552,872,1049,974,665,999,786)(555,876,1182,1003,869,1176,1167)(562,886,1191,1040,1160,985,1088)(565,891,1195,912,1216,764,1089)(572,727,1061,1141,829,986,1090)(575,906,1209,1276,1068,766,1091)(577,909,970,1255,1335,1330,1036)(583,918,996,1268,1013,705,1037)(585,921,1225,1342,1189,1352,1095)(591,930,1009,1274,1400,1326,1001)(607,941,980,678,1008,1273,1096)(625,958,1208,956,1247,939,953)(629,963,1251,1298,1199,1375,1398)(636,658,991,1124,871,1177,961)(645,977,1212,1180,1241,773,1098)(647,981,1135,1349,1237,1031,1038)(655,987,1262,1321,917,1220,1324)(669,1002,1131,812,1134,940,975)(680,1011,1277,1117,833,1146,1103)(683,1014,1245,1150,1060,780,1104)(687,1019,1282,1350,1370,1391,1312)(691,1024,1240,1392,1313,710,1041)(701,1033,1291,1406,1357,1407,1422)(714,1046,892,1197,1360,1260,1314)(717,1050,978,1257,1381,1082,1315)(723,1058,1304,1409,1048,1299,1214)(733,971,1034,1292,1344,1204,1377)(737,1069,800,1123,862,1169,1187)(776,1100,1294,982,1057,1303,878)(782,1106,1296,1026,964,1252,1366)(810,1132,1348,1223,1338,1166,1316)(819,1138,973,1042,1161,1027,1116)(839,1029,1122,859,1066,1181,1242)(841,1153,1125,883,1188,931,1118)(843,1157,1358,1347,1217,1317,888)(855,1165,1164,1163,1162,1152,1121)(864,1173,1336,1149,1353,1331,1044)(877,1183,1301,1281,1202,1376,1112)(887,1192,1355,1307,1111,1332,1045)(901,1205,1325,927,1000,1270,1133)(903,938,1236,945,915,1218,1318)(908,1065,1308,1396,1361,1261,1319)(920,1224,1339,1168,1309,1094,1322)(922,1227,1275,1401,1380,1417,1293)(929,1233,1390,1323,1415,1228,1329)(1012,1278,1354,1341,1178,1300,1259)(1023,1285,1405,1388,1147,1264,1327)(1059,1305,1410,1429,1387,1404,1428)(1071,1310,1140,1351,1258,1384,1371)(1107,1328,1408,1287,1369,1333,1185)(1154,1290,1343,1196,1373,1230,1389)(1156,1356,1345,1210,1379,1402,1337)(1172,1363,1372,1295,1362,1288,1340)(1213,1256,1306,1411,1423,1382,1412)(1219,1383,1413,1222,1271,1399,1286)(1226,1386,1420,1374,1427,1397,1414)(1234,1279,1403,1426,1421,1378,1416)(1359,1425,1424,1385,1419,1364,1418)(1430,1431);(1,2,4,8,16,32,63,123,236,437,397,40,79,154,291,520,339,595,696,362,630,54,105,202,253,461,764,340,224,416,708,1040,545,694,1026,856,1166,1041,972,926,1220,1349,722,1057,1302,1328,1375,935,1235,1105,1327,1399,242,444,744,286,512,826,1144,1352,1205,1378,1379,798,1121,1338,852,1163,76,148,280,155,293,523,193,363,632,944,1240,372,645,978,561,179,336,406,692,1025,23,45,88,129,245,449,615,948,1229,1388,1278,303,539,857,534,850,707,1039,1294,914,1217,410,699,1031,1100,1197,1374,1236,779,1103,1268,125,238,439,740,1072,667,1001,1188,1348,1424,1207,487,795,1118,1337,1418,37,73,142,78,152,287,513,654,986,1261,1022,197,369,640,315,558,881,216,402,685,7,14,28,55,107,206,383,658,921,1226,1008,157,296,528,844,1158,413,703,1035,966,1253,205,381,655,767,1094,1323,933,471,777,1102,1326,793,1116,1310,849,1162,1362,880,1130,1347,1423,1305,1351,930,1234,1363,17,34,67,130,247,453,755,378,651,983,688,100,194,365,635,970,613,110,212,394,672,283,404,689,526,841,1154,634,582,917,1221,1358,981,1053,1301,1192,594,932,774,1099,1324,91,176,331,452,754,1082,1243,1393,1346,1422,1428,483,791,1069,530,846,1160,1361,1427,1383,1410,1033,1138,589,927,1169,1132,191,359,625,312,441,741,201,375,648,506,819,686,624,431,730,350,610,911,1215,1381,145,274,495,290,518,831,959,1093,1321,1413,1155,643,975,1182,884,1189,1061,467,771,1097,31,61,119,229,425,723,1059,1306,1128,1345,1401,264,479,735,1068,1309,1037,1293,1373,1392,1304,657,816,330,585,922,807,97,188,353,164,309,548,102,198,371,279,502,401,683,1015,574,905,1208,576,908,1212,70,136,258,470,776,1101,1325,765,1090,1318,840,367,637,875,1181,1367,724,255,464,769,1096,824,1024,1286,1157,1359,1426,1255,805,1127,1344,1421,1136,433,733,1066,1114,1334,1194,1238,1056,334,591,173,326,577,494,48,94,182,341,597,668,50,98,190,357,621,214,398,678,1009,1275,957,323,572,902,1148,628,716,1049,876,1074,1203,460,762,1087,524,837,1151,553,874,1180,947,1241,1126,1343,1420,498,810,1133,834,1149,1354,1395,1415,1405,1291,1407,813,232,430,728,785,1111,1098,941,720,122,234,87,169,318,271,490,395,352,230,427,725,1060,566,894,1199,863,1172,1047,977,928,1225,622,753,1080,1313,832,356,619,870,551,871,898,251,457,759,292,521,835,1150,1355,1211,1380,1308,803,1125,1342,261,476,786,1112,1333,1277,1402,1320,1284,1032,1290,499,118,227,421,473,780,770,605,422,717,664,42,83,161,141,267,211,392,669,321,569,897,317,562,887,541,859,713,1045,1297,919,1223,450,750,1077,517,185,347,549,867,1175,568,131,248,454,756,1083,681,1013,1191,1372,1400,1063,492,801,1124,1341,1252,998,1269,1368,1010,1276,1089,1142,698,1029,1288,58,113,217,257,468,773,344,226,419,385,19,38,75,146,276,108,208,386,662,996,1014,166,313,555,877,1184,418,711,1043,436,737,244,447,747,288,514,827,308,546,865,1174,1365,799,1122,1339,854,1164,1267,885,1190,1273,1247,1315,1283,990,1264,954,663,997,1179,1366,1376,761,1086,408,695,1027,27,53,103,133,252,459,181,116,223,414,705,306,544,864,537,855,709,639,587,916,1134,424,721,1055,1106,1198,599,934,1052,1263,1270,127,241,443,151,285,511,825,1143,900,1204,1209,489,797,1120,535,851,994,1266,1398,1007,1272,1079,1020,656,989,608,943,1176,1332,1251,1200,456,758,218,405,691,11,22,43,66,128,243,446,746,923,1228,1011,160,302,538,299,533,415,706,1038,580,913,220,409,697,775,891,1196,937,715,1048,995,64,124,237,438,739,389,666,882,1187,1371,904,269,486,794,1117,1336,660,993,1265,676,1006,749,821,380,653,985,823,866,1109,962,1250,1396,1004,112,215,400,3,6,12,24,47,92,178,335,584,920,677,80,156,295,527,843,222,412,702,631,965,106,204,379,462,766,1092,596,417,710,1042,1295,484,792,1070,532,848,1161,557,879,1186,1370,1058,1139,590,929,1171,384,659,992,1246,1394,445,745,203,377,650,508,822,1141,626,960,1249,673,56,109,210,390,149,282,507,294,525,839,364,328,581,915,1219,646,980,1259,886,337,593,693,988,1231,46,90,174,246,451,752,949,1242,1389,1406,1403,266,482,736,297,529,845,1159,1360,1218,1382,700,818,332,588,861,809,1131,1104,952,1245,239,440,104,200,374,281,505,817,358,623,956,796,1119,578,910,1214,74,144,272,153,289,516,829,987,1262,1397,1285,370,642,974,559,883,726,403,687,925,15,30,59,115,221,411,701,1034,1227,1387,1274,139,263,434,734,1067,704,1036,1195,1239,1391,382,504,175,329,583,496,806,778,618,951,1244,670,52,101,196,147,278,500,812,1135,1350,1411,1282,325,575,907,35,69,134,254,463,768,1095,652,984,1260,1021,195,366,636,971,1256,426,213,396,675,1005,509,690,1023,842,1156,1357,969,918,1222,1384,1425,814,233,432,732,787,1113,889,942,1237,177,333,89,172,324,273,493,802,354,616,950,391,25,49,96,186,349,609,945,979,1258,1292,1018,171,322,571,901,360,627,961,554,742,1073,376,649,982,820,1140,1019,958,731,1065,611,946,1216,1289,1390,275,497,808,519,833,1147,1248,1322,1414,1429,1356,501,120,231,429,475,784,772,606,940,62,121,44,86,167,143,270,488,187,351,612,480,789,319,565,892,543,862,1170,644,976,991,1137,586,924,1230,1129,189,355,617,310,550,869,199,373,647,503,815,684,1017,1281,906,1210,1064,909,1213,1232,137,260,474,782,1107,1329,1416,1091,1319,1412,1153,277,60,117,225,259,472,465,346,604,939,387,21,41,81,72,140,265,481,790,1115,1335,1016,168,316,560,304,540,858,1167,1303,592,931,327,579,912,804,95,184,345,603,938,1002,99,192,361,629,964,399,680,1012,1279,1404,729,573,903,1206,1353,963,1050,1300,1183,1311,1377,763,1088,1317,838,1152,29,57,111,135,256,466,183,343,600,207,9,18,36,71,138,262,478,641,973,1254,682,85,165,311,552,873,601,936,1054,235,435,170,320,567,491,800,674,614,428,727,1062,1307,895,1028,1287,1173,1364,1299,1257,1233,1386,955,1081,1314,1409,1146,620,953,1177,872,1178,1201,458,760,1085,522,836,13,26,51,68,132,250,93,180,338,477,788,162,305,542,301,536,853,368,638,968,811,228,423,719,781,893,342,598,718,1051,999,84,163,307,268,485,393,671,1003,570,899,1202,563,888,1193,860,1168,1046,1298,1408,1224,1385,751,1078,1312,830,348,607,868,1110,1331,896,249,455,757,1084,1316,5,10,20,33,65,126,240,442,743,1075,679,82,159,300,158,298,531,847,1030,633,967,114,219,407,469,564,890,602,420,714,661,39,77,150,284,510,209,388,665,1000,1271,1280,314,556,878,1185,1369,712,1044,1296,738,1071,448,748,1076,515,828,1145,547,783,1108,1330,1417,1123,1340,1419,1165)
Conjugacy classes & character table
422 conjugacy classes. The character table is too large to display.
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20006, 2);
Finite Group Databasebeta