/* www-ATLAS of Group Representations. U6(2) represented as permutations on 1408 points. */ G:=PermutationGroup<1408|\[ 1,4,6,2,10,3,7,15,9,5,20,12,13,23,8,26,28,30,25,11,35,37,14,41,19, 16,46,17,49,18,52,54,56,51,21,61,22,64,39,66,24,69,71,73,68,27,47,79,29,83, 34,31,88,32,91,33,93,95,97,60,36,62,103,38,107,40,109,45,42,112,43,115,44,74,119, 121,117,124,48,80,126,130,50,134,136,138,133,53,113,144,55,148,57,152,58,155,59,158,160,162, 157,165,63,169,167,172,65,176,67,180,179,70,89,186,72,116,77,118,75,194,76,122,197,78,201, 81,127,128,204,82,131,208,87,84,213,85,216,86,219,221,223,218,143,90,229,227,232,92,149,237, 235,94,214,243,96,247,101,98,252,99,254,100,256,258,102,262,105,264,104,268,269,106,272,192,175, 108,278,276,111,110,283,285,287,282,185,114,293,291,296,298,300,174,303,120,195,308,123,311,312,200, 125,315,317,129,205,206,321,132,324,326,328,323,135,153,334,137,338,142,139,342,140,345,141,347,349, 351,146,353,145,357,358,147,361,234,151,236,150,367,239,253,366,302,154,375,373,378,156,382,384,386, 381,159,240,161,392,163,396,164,399,400,261,166,403,168,343,405,406,170,171,412,413,173,417,333,402, 178,420,177,424,426,428,184,181,387,182,432,183,434,436,290,188,438,187,441,442,189,445,190,448,191, 451,242,193,455,453,306,307,196,449,463,198,199,313,465,202,470,203,318,469,320,207,472,212,209,479, 210,327,211,332,481,482,329,274,215,335,486,489,217,492,493,491,220,265,498,222,502,224,506,225,350, 226,511,228,354,513,517,230,231,522,523,233,527,528,364,530,241,238,368,535,390,371,536,245,538,244, 376,542,246,409,545,251,248,550,249,553,250,284,556,555,370,560,255,393,563,529,257,551,569,259,260, 401,275,263,404,266,267,581,579,379,584,577,270,271,591,589,592,273,418,419,277,597,596,423,279,601, 280,427,281,604,606,602,286,611,288,561,289,617,292,618,537,294,295,625,626,297,629,447,299,309,635, 301,638,305,640,304,644,457,646,574,497,461,608,310,651,314,654,656,658,319,316,471,322,664,474,475, 476,669,663,325,674,330,331,483,678,485,336,487,680,337,682,341,339,340,688,690,692,460,344,695,668, 698,346,503,702,585,348,685,508,559,510,352,712,355,514,714,715,356,518,717,720,711,359,360,727,725, 701,362,363,395,365,734,532,533,733,369,372,440,374,683,743,541,377,543,544,380,599,610,753,750,383, 397,758,385,675,389,388,765,767,509,391,435,772,394,564,634,775,774,568,398,781,779,783,573,459,575, 576,411,788,408,738,407,792,583,410,505,586,797,796,415,800,414,416,593,803,806,422,421,810,546,811, 425,431,814,429,817,430,607,462,799,547,433,612,823,776,818,825,437,439,731,828,749,742,736,791,443, 444,689,834,446,630,631,839,836,565,450,842,844,452,639,454,851,849,854,456,645,458,859,648,649,861, 464,865,866,466,870,467,693,468,835,660,874,662,478,473,881,666,667,500,477,884,886,672,883,480,554, 891,677,484,895,488,863,490,539,900,507,903,905,494,627,495,909,496,657,912,499,915,697,501,917,700, 526,504,921,923,705,920,890,708,709,925,521,512,930,515,516,935,519,718,936,520,939,832,942,938,525, 943,524,944,729,947,619,732,534,531,833,623,737,580,739,740,847,622,540,953,954,764,956,748,621,549, 751,752,548,963,964,962,757,552,906,967,971,902,974,746,557,977,558,980,769,827,982,562,773,567,566, 614,777,986,571,988,570,992,572,784,785,994,787,578,998,1000,624,582,1005,1006,934,588,587,798,609,590, 1010,1008,594,804,1013,595,1015,1017,1019,598,600,812,1021,603,1026,1025,605,615,819,820,821,969,613,1032,616, 1034,770,620,1038,1039,831,722,735,628,659,633,1043,838,632,1045,1047,636,1037,637,845,1051,741,1054,642,1056, 641,979,853,643,855,1060,1064,1066,647,860,650,1069,681,1070,652,653,1009,1074,869,655,1073,1079,1033,661,1083, 1084,877,878,892,880,665,1087,673,670,1091,671,1093,957,1028,707,676,879,893,1098,679,896,897,898,1102,684, 901,762,686,959,687,759,1107,1103,691,1077,1111,694,1112,1114,696,1030,699,1095,1119,706,703,1123,704,1124,710, 1127,1002,1130,1126,713,1134,932,1136,795,716,719,1142,724,721,940,941,723,726,728,945,946,730,948,1149,1141, 1138,952,744,745,955,747,888,1153,904,1156,1117,756,754,755,1161,966,760,1163,822,1129,761,1135,973,763,1170, 976,766,1168,852,768,1175,771,983,1177,985,778,1046,780,1182,1181,1185,782,993,786,1188,1189,1190,789,1063,790, 1001,927,1195,1192,793,794,1007,802,867,801,1203,1204,805,1014,807,1208,808,1018,809,1159,813,1211,1213,1207,816, 815,1062,889,1218,916,1221,824,873,826,1035,1164,843,829,830,1225,1041,1226,837,1128,840,987,841,1186,1110,1050, 846,1052,1053,848,1055,850,1120,1233,1234,856,1061,1027,999,857,1065,858,1240,1068,862,864,1242,1072,871,868,1113, 1076,910,1078,872,1115,1109,1082,875,876,1085,1202,882,1216,1139,1254,885,1252,887,1261,918,1262,1097,894,1099,1241, 1101,899,908,1104,1105,1106,907,1267,1081,1049,911,913,1075,914,1080,1270,961,1220,919,1057,1121,1274,922,924,1224, 929,926,1044,970,928,1260,1282,1284,931,972,933,1137,951,1089,1140,950,937,1292,1144,1291,1146,1172,1223,949,1298, 1151,1299,958,1303,1155,960,1306,1304,1020,1308,965,1206,968,1036,1200,1310,1167,978,1311,975,1315,1147,1307,1196,981, 1176,984,1312,1179,1324,990,989,1183,1248,991,1048,1250,995,996,997,1235,1004,1287,1194,1003,1174,1210,1198,1322,1165, 1201,1086,1011,1012,1205,1162,1024,1016,1263,1197,1022,1338,1023,1214,1275,1088,1333,1029,1219,1118,1031,1222,1148,1125,1040, 1042,1227,1285,1246,1336,1266,1350,1058,1059,1191,1352,1237,1238,1239,1067,1100,1071,1316,1244,1245,1229,1271,1184,1272,1187, 1347,1092,1295,1090,1255,1281,1288,1258,1356,1131,1094,1096,1209,1264,1265,1231,1108,1364,1269,1116,1247,1249,1273,1122,1215, 1368,1277,1294,1345,1370,1256,1132,1283,1133,1228,1286,1193,1257,1367,1290,1145,1143,1376,1278,1253,1296,1329,1150,1152,1325, 1351,1302,1154,1158,1305,1157,1173,1160,1382,1166,1169,1178,1383,1314,1171,1243,1317,1319,1318,1388,1321,1199,1323,1180,1300, 1326,1371,1328,1297,1330,1354,1332,1217,1334,1335,1230,1337,1212,1339,1384,1378,1395,1343,1344,1279,1346,1251,1348,1349,1232, 1301,1236,1380,1331,1401,1259,1357,1358,1359,1360,1361,1402,1404,1268,1365,1366,1289,1276,1369,1280,1327,1372,1398,1374,1407, 1293,1377,1341,1379,1353,1381,1309,1313,1340,1385,1386,1387,1320,1389,1390,1391,1392,1393,1394,1342,1396,1397,1373,1399,1400, 1355,1362,1403,1363,1405,1406,1375,1408] ,\[ 2,5,1,8,11,12,3,16,4,18,14,21,6,7,24,27,9,31,10,33,36,13,39,42,15, 44,29,47,17,50,53,19,57,20,59,38,62,22,65,23,67,70,25,74,26,76,78,28,81,84, 30,86,55,89,32,92,94,34,98,35,100,102,37,105,68,56,40,41,110,72,113,43,116,118,45, 122,46,125,126,48,129,49,132,135,51,139,52,141,143,54,146,149,150,96,153,58,156,159,60,163, 61,166,167,63,171,64,174,66,178,181,69,183,185,71,188,190,73,120,192,75,195,196,77,199,128, 202,79,80,205,121,82,209,83,211,137,214,85,217,220,87,224,88,226,227,90,231,91,234,236,238, 93,240,242,95,245,248,97,250,161,200,99,255,257,101,260,170,263,103,266,104,270,162,106,274,107, 276,108,279,109,281,284,111,288,112,290,291,114,295,115,299,117,302,119,305,307,198,309,123,262,124, 313,316,127,318,207,130,131,322,325,133,329,134,331,333,136,336,337,138,340,222,343,140,346,348,142, 230,352,144,355,145,359,223,147,363,148,177,365,368,151,370,152,372,373,154,377,155,380,383,157,323, 158,388,160,390,393,394,259,397,164,401,165,378,404,405,168,292,169,408,410,273,172,415,173,418,175, 264,176,422,425,179,429,180,203,286,431,182,433,435,184,294,407,186,439,187,443,287,189,446,301,449, 191,452,453,193,457,194,459,460,462,197,297,400,466,201,468,283,471,473,204,206,475,387,208,477,327, 265,210,480,328,212,483,213,485,486,215,339,216,490,218,494,219,496,424,221,500,503,504,350,507,225, 509,512,513,228,516,229,519,520,362,232,525,233,529,235,531,237,533,369,239,357,241,376,537,243,540, 244,543,253,246,546,247,548,385,551,249,554,251,557,252,559,254,364,562,564,256,566,568,258,571,573, 574,261,576,326,578,579,267,582,268,585,269,587,589,271,285,272,594,419,275,596,277,598,278,600,427, 602,280,603,605,282,608,609,612,613,437,615,289,618,620,293,622,623,311,296,628,630,298,632,634,300, 636,456,639,303,642,304,645,306,320,493,308,649,445,310,312,655,314,659,315,428,662,317,665,319,667, 321,670,324,672,330,675,677,441,332,488,679,334,335,482,683,338,685,687,689,341,693,342,668,344,697, 345,700,701,703,347,705,707,349,709,351,710,515,713,353,354,716,717,356,371,721,358,723,725,360,728, 361,727,731,392,591,735,366,737,367,739,487,742,743,374,746,375,748,544,379,420,751,381,698,382,755, 757,384,760,762,386,764,766,389,769,556,391,414,773,426,395,776,396,778,779,398,724,399,785,575,402, 786,403,421,789,406,733,793,409,795,502,411,718,412,799,413,802,803,416,805,417,808,599,809,423,696, 812,565,806,815,607,818,430,593,819,432,821,822,626,434,810,436,826,450,438,829,440,484,831,442,497, 834,444,835,514,837,447,840,448,619,842,690,451,846,848,849,454,853,455,856,647,708,458,461,652,463, 863,464,465,868,657,871,467,873,875,469,470,878,472,801,666,474,694,476,882,885,478,888,479,616,890, 481,893,674,896,897,489,726,899,491,902,492,860,906,691,908,495,910,911,498,913,499,916,692,501,586, 524,919,922,505,510,506,858,508,706,926,511,928,931,932,933,719,798,517,518,937,940,521,784,522,864, 523,744,945,526,527,788,528,530,949,736,532,950,534,606,535,536,745,765,538,539,955,541,958,542,545, 752,547,961,549,965,550,966,967,552,970,553,973,555,976,730,768,978,558,771,560,561,734,984,563,843, 611,567,782,987,569,990,570,775,572,867,995,577,997,999,580,581,1003,794,583,930,584,877,588,880,1008, 590,1002,1011,592,1014,797,595,1018,597,894,1020,1022,601,1024,1027,604,983,1017,1030,610,777,627,909,614,1034, 1035,617,756,830,621,1040,624,625,1033,1042,629,838,631,1044,1046,633,1049,635,839,637,1052,638,852,1055,640, 1058,641,1059,1060,643,1063,644,646,1067,648,681,650,682,651,1071,1073,653,1075,654,1077,1078,656,1081,658,876, 660,661,879,663,664,1085,714,669,1089,887,891,671,1094,673,1096,825,676,1054,678,1099,741,1100,680,901,1103, 684,1105,895,686,1068,1108,688,944,1110,754,833,1112,1113,695,1116,918,1117,699,1120,702,1006,924,934,704,1125, 1128,711,1131,712,1133,836,1135,1137,715,1138,1140,1143,720,1144,941,722,1146,953,845,946,729,942,732,1150,951, 738,740,1102,943,957,1151,747,1154,749,750,1157,753,1158,1160,1032,969,1162,758,759,1165,964,761,975,1168,763, 994,1171,1173,767,851,770,823,772,915,774,1178,1180,1181,780,1184,781,1115,783,981,996,787,1148,1191,1001,1193, 790,791,1196,792,1123,1198,796,1200,800,866,870,804,1205,1016,1207,807,952,960,1190,1204,811,1212,813,1215,814, 1217,1219,816,817,1031,820,1037,824,1222,912,827,828,1223,903,1041,832,862,1201,1206,938,1048,1228,841,993,844, 1072,1230,847,861,1232,1233,850,1005,1062,1235,854,855,1237,1051,857,1240,988,859,979,1242,1243,865,1244,1164,1084, 869,1012,1246,1111,872,1248,874,1250,1245,1252,881,1130,883,1136,884,1256,886,1259,1095,889,1097,892,954,1209,1262, 898,1265,1070,900,1106,904,905,1268,907,1269,1149,1036,1187,1270,914,985,1272,917,923,1275,920,921,1278,1057,962, 925,1045,1129,927,1280,1281,929,1199,1285,1088,1286,1274,1287,935,1289,936,1015,1279,1293,939,1295,947,948,1297,1029, 1241,956,1301,1155,959,1304,1126,1307,963,1309,1109,1203,1267,968,1167,971,972,1251,974,1313,1316,977,1318,980,1163, 982,1159,1322,986,1183,1107,1325,989,1306,1080,991,992,1069,1328,1039,1303,998,1329,1000,1291,1315,1004,1332,1007,1227, 1009,1010,1074,1334,1050,1013,1056,1292,1019,1021,1166,1214,1192,1023,1340,1025,1341,1026,1220,1028,1343,1258,1344,1038,1323, 1189,1043,1348,1047,1231,1053,1124,1195,1333,1351,1061,1239,1064,1065,1300,1066,1354,1238,1234,1076,1185,1079,1249,1082,1312, 1083,1356,1086,1087,1090,1360,1091,1092,1361,1093,1221,1264,1098,1101,1263,1104,1363,1161,1320,1365,1114,1366,1118,1119,1276, 1121,1122,1174,1127,1134,1283,1371,1132,1311,1358,1359,1298,1139,1374,1141,1142,1257,1377,1145,1378,1147,1379,1373,1261,1152, 1271,1153,1381,1347,1156,1327,1382,1319,1337,1216,1383,1169,1384,1170,1331,1386,1172,1188,1175,1176,1177,1346,1179,1389,1352, 1182,1186,1305,1391,1194,1197,1369,1202,1336,1208,1210,1211,1393,1213,1310,1394,1218,1397,1395,1224,1225,1226,1399,1229,1294, 1353,1400,1236,1266,1247,1357,1253,1254,1255,1335,1388,1260,1364,1308,1302,1367,1273,1405,1277,1284,1324,1282,1288,1375,1290, 1349,1350,1296,1355,1299,1339,1321,1368,1338,1314,1387,1317,1403,1408,1326,1392,1330,1385,1396,1398,1342,1401,1345,1376,1407, 1380,1370,1362,1404,1402,1372,1390,1406] >; print "Group G is U6(2) < Sym(1408)";