/* www-ATLAS of Group Representations. Sz(8) represented as permutations on 1456 points. */ G:=PermutationGroup<1456|\[ 2,1,4,3,7,8,5,6,12,14,16,9,19,10,21,11,22,24,13,27,15,17,31,18,33, 35,20,37,39,41,23,44,25,47,26,49,28,51,29,53,30,56,58,32,60,62,34,64,36,67, 38,70,40,55,54,42,75,43,77,45,79,46,81,48,83,85,50,88,90,52,92,94,95,97,57, 100,59,103,61,106,63,109,65,111,66,113,114,68,117,69,119,71,121,72,73,124,74,126,128,76, 130,132,78,135,137,80,139,141,82,144,84,147,86,87,150,152,89,155,91,158,93,161,140,96,165, 98,168,99,170,101,172,102,153,174,104,177,105,179,107,123,108,181,183,110,186,188,112,190,192,115, 194,116,133,197,118,199,201,120,204,206,122,208,209,211,125,213,215,127,217,129,220,131,223,134,225, 227,136,230,138,233,142,236,143,238,239,145,242,146,244,148,246,149,248,151,251,253,154,255,156,257, 157,259,260,159,263,160,265,162,163,268,164,270,166,272,167,274,169,276,278,171,281,283,173,285,175, 288,176,290,292,178,294,296,180,299,301,182,304,184,185,307,309,187,311,189,314,191,247,193,317,319, 195,321,196,324,198,327,200,330,202,203,333,335,205,338,207,341,343,210,346,212,349,214,352,216,355, 218,357,219,359,360,221,363,222,365,224,367,322,226,370,228,373,229,375,231,377,232,379,380,234,383, 235,385,387,237,389,391,240,393,241,395,243,397,399,245,402,354,249,405,250,407,252,287,409,254,411, 382,256,415,417,258,419,421,261,423,262,425,427,264,408,430,266,433,267,435,437,269,439,441,271,443, 445,273,447,316,275,450,277,453,279,280,456,458,282,460,284,463,286,466,468,289,470,472,291,474,293, 476,295,479,297,298,482,326,300,434,302,488,303,490,305,492,306,494,308,478,310,498,312,500,313,502, 503,315,505,506,318,509,320,339,323,513,325,515,516,517,328,520,329,522,331,524,332,526,334,529,336, 532,337,534,535,340,537,538,342,384,344,542,345,544,347,546,348,531,350,550,351,552,353,554,556,356, 559,561,358,563,565,361,567,362,569,364,571,573,366,576,578,368,581,369,583,371,585,372,587,374,589, 376,592,394,378,594,596,381,598,599,601,603,605,386,607,388,610,390,612,392,614,616,617,396,620,398, 622,400,401,624,403,404,627,629,406,631,633,635,410,638,412,413,414,640,642,416,643,418,645,420,648, 422,650,652,424,654,442,426,657,428,429,634,431,432,662,664,665,436,667,438,670,440,673,675,677,444, 680,446,683,448,684,449,686,687,451,690,452,692,454,694,455,696,457,699,459,702,461,704,462,706,707, 464,710,465,712,609,467,715,469,717,471,720,473,723,475,725,726,477,729,480,731,481,733,483,484,735, 485,737,486,738,487,740,489,742,580,491,746,493,748,495,730,496,497,751,753,499,756,501,758,504,661, 760,507,763,508,765,510,766,511,536,512,744,769,514,772,518,721,519,521,774,523,777,779,525,781,527, 783,528,785,530,787,788,533,790,792,794,625,539,796,540,541,799,543,801,803,545,805,807,547,809,548, 811,549,813,815,551,817,819,553,555,823,557,558,826,828,560,830,562,693,564,835,566,837,839,568,841, 842,570,845,572,705,574,575,849,851,577,854,579,857,859,582,861,584,864,795,586,641,749,588,868,590, 591,871,804,593,615,595,876,597,878,600,881,602,604,885,606,888,608,890,636,891,611,893,613,722,894, 618,827,619,897,898,621,901,623,903,626,780,905,628,907,630,632,911,913,637,916,917,639,920,644,923, 924,646,926,647,761,649,929,651,932,653,935,655,656,939,658,941,659,943,660,719,663,947,949,666,952, 668,954,669,728,671,958,672,960,674,938,676,963,678,966,679,968,681,970,682,972,973,975,685,977,979, 688,752,689,981,691,983,985,987,989,695,991,697,994,698,996,700,701,998,990,703,1001,1003,1004,708,1006, 709,862,1009,711,1011,1013,713,1015,714,902,716,852,1017,718,1020,1021,927,724,1023,1025,727,1026,1027,1029,1031, 732,1033,734,906,1034,736,1035,1037,884,739,922,1040,741,969,743,745,1043,747,750,1045,1047,754,755,1049,1050, 757,860,759,1054,762,879,764,1058,1060,1062,767,1064,768,1066,1068,770,771,1070,1072,773,921,886,775,776,1074, 778,867,1076,782,1079,1081,784,1083,1085,786,1088,1090,810,789,1094,791,1097,793,1100,1102,1104,797,1106,798,1108, 992,800,953,802,1018,1113,1051,806,1116,808,1118,1120,812,1122,1124,814,1126,816,889,818,1131,820,821,974,822, 1134,824,1022,825,1135,829,1138,831,1140,832,1055,833,1142,834,844,836,951,1144,838,1147,840,997,843,1152,1153, 846,1156,847,848,1048,850,1151,1162,853,1164,855,1166,856,1168,858,1170,863,955,1172,865,866,978,869,1175,870, 872,873,1078,874,1179,875,1181,877,880,882,1184,883,1186,1073,887,1187,1188,892,1190,895,1046,896,1005,899,900, 957,1196,1053,904,986,1194,1199,908,1200,909,1129,910,1203,912,1205,914,1189,915,1207,918,1209,919,1039,925,1086, 928,1212,1028,930,1216,931,1218,933,1220,934,1075,1222,936,1225,937,1227,1228,1230,940,1233,1235,942,1237,1239,944, 1240,945,1241,946,1243,948,1183,950,1246,1248,1211,1249,956,1251,1252,959,1223,961,1255,962,1258,964,1260,965,1262, 967,1185,1191,1061,1259,971,1266,1267,976,980,1268,1269,982,1271,984,1150,988,1273,993,1242,1210,995,1276,1278,1141, 1007,999,1000,1279,1281,1002,1283,1285,1287,1289,1290,1008,1291,1010,1294,1012,1295,1014,1298,1016,1202,1019,1300,1302,1024, 1304,1305,1250,1030,1275,1032,1309,1107,1036,1127,1038,1041,1042,1067,1044,1128,1198,1213,1056,1314,1052,1288,1192,1057,1059, 1317,1171,1063,1319,1065,1321,1069,1322,1071,1146,1111,1077,1193,1316,1324,1080,1326,1082,1329,1084,1331,1087,1117,1333,1089, 1335,1091,1092,1229,1093,1338,1339,1095,1341,1096,1343,1098,1327,1099,1101,1103,1145,1105,1347,1348,1109,1349,1110,1112,1178, 1114,1115,1332,1350,1119,1354,1355,1121,1130,1123,1358,1125,1361,1362,1296,1132,1133,1136,1137,1364,1139,1280,1143,1366,1180, 1148,1367,1149,1154,1272,1155,1282,1157,1370,1158,1371,1159,1197,1160,1161,1163,1373,1375,1165,1167,1265,1378,1169,1380,1173, 1360,1174,1382,1176,1177,1384,1368,1385,1182,1387,1388,1389,1391,1195,1393,1214,1201,1352,1204,1344,1206,1208,1395,1215,1397, 1217,1238,1386,1219,1399,1221,1253,1224,1401,1226,1400,1404,1231,1232,1407,1234,1409,1236,1320,1412,1359,1244,1245,1247,1254, 1415,1318,1363,1256,1257,1369,1417,1261,1346,1301,1263,1264,1353,1270,1413,1274,1277,1307,1356,1284,1286,1422,1292,1376,1293, 1374,1424,1297,1379,1299,1390,1303,1428,1306,1308,1328,1310,1311,1312,1381,1313,1431,1315,1432,1323,1419,1325,1433,1330,1336, 1334,1410,1421,1337,1434,1435,1340,1437,1342,1402,1423,1345,1365,1441,1351,1442,1357,1443,1396,1444,1403,1372,1411,1377,1427, 1426,1425,1383,1448,1446,1392,1394,1398,1405,1406,1447,1408,1440,1452,1438,1414,1416,1418,1420,1455,1430,1436,1429,1450,1449, 1453,1439,1451,1454,1445,1456] ,\[ 3,1,5,6,2,9,10,11,13,15,17,18,4,20,16,7,23,25,26,28,29,30,8,32,34, 36,19,38,40,42,43,45,46,12,48,27,50,14,52,54,55,57,59,31,61,53,63,65,66,68, 69,71,72,21,73,74,22,76,44,78,24,80,82,47,84,86,87,89,91,51,93,33,96,98,99, 101,102,104,105,107,108,64,110,35,112,114,115,116,37,118,70,120,39,122,123,41,125,127,129,75, 131,133,134,136,138,79,140,142,143,145,146,148,149,49,151,153,154,156,157,159,160,162,163,164,166, 167,56,169,100,171,58,173,174,175,176,60,178,106,180,62,94,182,184,185,187,189,111,191,126,193, 67,195,196,198,117,200,202,203,205,207,121,141,210,212,124,214,113,216,218,219,221,222,224,77,226, 228,229,231,232,234,235,81,237,239,240,241,83,243,147,245,85,247,249,250,252,88,254,155,256,90, 258,260,261,262,92,264,161,266,267,95,269,165,271,97,273,275,168,277,279,280,282,284,172,286,287, 103,289,291,293,177,295,297,298,300,302,303,305,306,109,308,259,310,312,313,315,316,246,215,318,320, 194,322,323,325,326,328,329,331,332,119,334,336,337,339,340,342,344,345,347,348,350,351,353,354,217, 356,128,358,360,361,362,130,364,223,366,132,368,369,371,372,135,374,230,376,137,378,380,381,382,139, 384,386,388,236,390,290,392,144,394,396,242,398,400,401,403,192,404,150,406,251,408,152,410,253,412, 413,414,416,418,257,420,186,422,158,424,426,428,263,429,431,432,434,383,436,438,268,440,425,442,444, 446,272,248,448,449,451,452,454,455,170,457,379,459,461,462,464,465,467,469,288,471,238,473,389,475, 477,478,480,481,179,483,484,485,486,487,181,489,304,491,183,493,495,479,496,497,311,499,188,501,503, 504,430,190,507,508,510,511,512,367,324,514,197,517,518,519,199,521,330,523,201,525,527,528,530,531, 204,533,338,206,536,538,539,540,208,541,209,543,346,545,211,547,548,549,213,551,352,553,555,557,558, 560,562,357,564,435,566,220,568,570,363,572,574,575,577,579,580,225,582,370,584,227,586,588,373,590, 591,593,393,377,595,281,597,233,600,602,604,502,606,608,609,292,611,613,472,615,526,618,619,447,621, 468,623,244,625,626,620,628,630,405,632,634,636,637,639,433,598,255,641,537,643,624,644,646,647,649, 309,651,653,423,655,270,656,658,659,407,660,661,265,663,599,359,666,668,669,671,672,674,676,678,679, 681,682,397,505,274,685,687,688,689,276,691,453,693,278,695,697,698,700,701,460,703,283,705,707,708, 709,285,711,409,713,714,399,716,718,719,721,722,474,724,726,727,728,294,730,296,732,734,627,515,299, 736,343,411,301,739,741,488,743,744,745,747,492,749,750,307,729,421,752,754,755,757,500,385,759,314, 761,762,317,764,509,740,319,767,535,768,321,770,771,603,773,327,720,520,775,776,778,780,524,617,782, 333,784,529,786,335,789,532,791,793,402,415,795,341,797,798,800,542,802,592,804,806,808,546,810,787, 349,812,814,816,550,818,820,821,822,824,825,355,827,706,829,831,832,833,834,836,665,838,840,567,733, 843,844,846,847,704,848,365,850,852,853,855,856,858,860,581,862,863,865,642,585,494,866,867,869,870, 375,872,544,873,874,875,877,458,879,880,882,883,884,886,887,607,889,387,891,892,723,612,881,391,895, 896,395,826,898,899,900,622,902,417,904,554,516,906,908,909,910,912,914,915,917,918,919,921,922,924, 864,925,419,927,648,928,930,931,933,934,936,937,938,657,940,427,942,913,944,945,946,948,950,951,667, 953,437,955,956,957,439,959,673,961,441,962,964,965,443,967,680,969,445,971,973,974,976,684,978,813, 980,450,751,982,690,984,986,988,990,694,992,993,456,995,699,997,596,991,999,1000,1002,573,559,1005,463, 1007,1008,1010,710,1012,1014,890,466,1016,715,901,1017,1018,1019,470,1022,926,610,1024,857,742,476,1028,1030,1032, 731,842,983,482,748,735,1036,1038,1039,738,903,1041,765,1042,725,490,868,1044,640,1046,1048,1029,498,506,1051, 1052,1053,605,1055,1056,1057,763,1059,1061,1063,766,1065,534,1067,1037,1069,513,1071,923,905,894,774,1073,522,1075, 746,977,1077,1078,1080,1082,783,1084,1086,1087,1089,1091,1092,1093,1095,1096,1098,1099,1101,1103,1105,796,1107,737,696, 1109,1110,1111,717,1112,1114,972,1115,807,1117,1119,1121,811,1123,686,1125,1127,1128,1129,1130,1132,1133,552,1050,779, 823,975,556,1021,1136,1137,830,1139,561,1141,987,692,563,1143,835,569,565,1145,1146,1148,1149,1150,1151,1153,1154, 1155,571,1157,1158,1159,1160,1161,576,1163,854,1165,578,1167,1068,1169,1171,583,954,645,1072,1173,587,1174,589,1176, 1177,1178,616,1045,594,1180,876,1182,1183,893,601,1185,949,885,758,631,871,1189,1191,1192,614,1193,828,1194,683, 1195,1197,1040,794,1076,1198,907,1122,629,1201,888,1202,911,1204,633,1206,635,712,1066,1208,638,1210,772,1211,1190, 760,1213,1214,1215,650,1217,932,1219,652,1221,1222,1223,1224,654,1226,675,1229,1231,1232,1234,1236,941,1238,1079,1205, 1054,1020,662,1242,947,1244,664,1245,1247,1074,1172,1250,1026,670,1253,958,1248,1254,1256,1257,963,1259,677,1261,1207, 966,1184,1263,1264,1265,970,1203,805,1134,1124,753,981,1270,1272,841,996,1240,1274,1275,1241,1209,994,1277,985,1140, 1006,1104,702,1280,1168,1282,1284,1286,1288,998,1249,1287,1292,1293,1106,1255,1296,1297,1299,1015,1187,801,1301,1094,1303, 1298,1306,1307,1268,1108,1308,1310,1311,815,769,1281,859,968,1312,777,1035,897,1313,1049,756,1315,861,920,1279,1316, 1070,1318,819,1233,1320,916,1126,1060,1147,1102,952,1278,781,1323,943,1325,1327,1328,1330,1090,1305,785,1332,1334,1235, 1331,1336,1337,788,1228,1339,1023,1340,790,1342,1097,1344,792,1326,1345,837,1346,989,1011,1031,1289,799,1350,851,803, 1351,1352,1116,1349,1353,809,1356,1013,1357,1199,1359,1360,1188,817,1131,1363,1062,1144,1004,1348,1365,878,1142,1243,1179, 1317,839,1368,1358,845,1271,1369,1156,1285,1003,1269,1372,849,1196,1033,1162,1374,1376,1377,1166,1258,1001,1379,1170,1034, 979,1381,1383,1175,1361,1113,1367,1218,1386,1290,1300,1390,1392,1251,1246,1276,1200,1267,1266,1394,1324,1321,929,1396,1239, 1216,1398,1181,1385,1400,1220,935,1252,1402,1225,1403,1405,1406,939,1064,1408,1335,1410,1411,1273,1152,1366,1413,1414,960, 1393,1416,1295,1347,1227,1378,1058,1260,1135,1418,1085,1419,1420,1371,1186,1404,1027,1387,1283,1421,1329,1291,1423,1009,1375, 1424,1425,1120,1025,1426,1427,1338,1304,1409,1364,1429,1212,1430,1262,1043,1309,1047,1314,1100,1417,1322,1397,1081,1370,1083, 1382,1088,1355,1354,1230,1401,1436,1384,1341,1438,1439,1440,1138,1118,1437,1333,1362,1389,1395,1319,1445,1431,1407,1164,1446, 1428,1447,1442,1391,1443,1449,1343,1450,1412,1451,1373,1444,1432,1237,1453,1415,1380,1454,1441,1399,1294,1302,1433,1452,1456, 1435,1422,1434,1388,1455,1448] >; print "Group G is Sz(8) < Sym(1456)";