/* www-ATLAS of Group Representations. G2(4) represented as permutations on 1365 points. */ G:=PermutationGroup<1365|\[ 2,1,5,7,3,10,4,13,15,6,18,20,8,23,9,26,28,11,31,12,33,35,14,38,39, 16,42,17,45,47,19,50,21,53,22,56,58,24,25,62,64,27,67,68,29,71,30,74,76,32, 79,81,34,84,85,36,88,37,91,93,95,40,98,41,101,103,43,44,106,108,46,111,112,48,115, 49,117,119,51,121,52,82,125,54,55,129,131,57,134,135,59,138,60,141,61,144,146,63,149,150, 65,153,66,156,158,69,161,70,163,165,72,73,169,171,75,174,77,177,78,180,80,183,184,186,83, 189,191,193,86,196,87,132,200,89,90,204,205,92,208,209,94,212,214,96,217,97,220,222,99,100, 226,228,102,231,232,104,235,105,238,240,107,243,109,245,110,248,250,252,113,255,114,258,260,116,233, 264,118,267,268,120,181,272,122,123,276,124,278,279,126,282,127,285,128,288,290,130,293,294,296,133, 299,301,303,136,137,306,308,139,140,312,314,142,317,143,266,320,145,322,323,147,326,148,329,331,333, 151,335,152,338,340,154,155,175,345,157,348,350,159,242,160,355,239,162,359,164,362,363,166,315,167, 367,168,370,372,170,375,376,172,379,173,382,384,386,176,389,215,178,179,394,321,397,182,399,401,402, 185,405,187,188,409,411,190,412,413,192,416,418,194,421,195,424,426,197,198,429,199,431,360,201,434, 202,436,203,438,440,206,443,207,445,447,449,210,452,211,249,455,213,458,460,216,270,218,219,465,467, 221,470,471,223,473,224,476,225,479,227,482,483,229,485,230,488,490,492,494,234,496,498,236,500,237, 454,352,461,504,241,507,509,495,244,298,512,246,247,515,517,472,251,520,522,253,524,254,527,528,256, 257,532,534,259,537,538,261,540,262,543,263,546,547,265,550,552,554,556,269,559,561,271,417,273,566, 274,275,569,571,277,573,575,577,280,580,281,283,284,584,586,286,398,287,590,592,289,594,595,291,597, 292,593,601,295,604,297,607,609,300,612,302,615,304,501,305,619,621,307,579,309,624,310,627,311,629, 628,313,632,351,316,635,637,318,639,319,353,641,643,645,324,648,325,548,650,327,328,366,330,655,656, 332,658,623,334,568,662,336,337,665,339,572,668,341,587,342,671,343,673,344,358,346,678,347,563,349, 439,683,684,354,687,689,356,562,357,510,685,361,652,695,364,698,365,701,702,368,704,369,706,371,708, 709,373,374,712,714,716,377,717,378,720,722,380,381,726,383,589,729,385,730,732,387,388,468,737,390, 634,391,638,392,743,393,745,747,395,749,396,508,499,752,754,400,757,480,403,681,404,486,406,763,407, 733,408,715,444,410,769,591,771,414,773,415,489,777,541,419,582,420,427,422,423,610,425,787,788,790, 428,793,795,430,798,800,432,801,433,596,805,435,807,809,437,812,814,815,441,818,442,820,478,446,823, 824,448,451,450,774,631,453,831,551,456,796,457,553,459,838,462,841,463,844,464,847,849,466,851,469, 854,513,856,858,474,475,861,477,863,865,866,481,867,808,484,871,872,487,874,864,491,876,493,682,878, 880,852,497,883,884,570,674,502,503,511,686,505,891,506,894,896,898,900,902,514,905,907,516,908,742, 518,519,912,521,834,523,916,525,526,920,922,529,925,530,578,531,533,929,781,535,932,536,802,936,937, 539,940,860,542,544,944,545,576,813,946,803,549,950,952,825,955,700,555,957,557,960,558,963,560,821, 889,564,966,565,903,784,567,970,759,973,974,976,574,958,979,981,983,985,581,988,583,933,585,630,991, 993,588,996,998,999,719,930,1000,756,1002,1003,598,599,1006,600,1009,1010,602,1011,603,636,1015,605,931,606, 608,723,736,1020,611,1023,613,664,614,934,1027,616,734,617,618,1030,1031,620,1034,622,750,1036,625,626,740, 887,1040,1042,1043,1028,633,1047,1048,705,1049,990,1051,640,870,840,642,1056,1057,644,1007,1059,646,1062,647,982, 649,677,1065,651,961,653,1070,654,1071,728,657,1073,659,670,660,661,663,1080,1082,839,666,667,1085,669,1087, 672,913,675,1089,676,1060,1090,679,680,1092,1094,826,1096,751,1022,688,1100,1101,690,953,691,1104,692,1107,693, 901,694,755,1069,696,1110,697,699,1114,1075,1116,703,877,1119,1120,707,1123,1102,1125,710,1127,711,923,1130,713, 1050,1132,1133,718,782,799,721,772,810,1139,724,725,1140,1142,727,1143,1145,1103,731,1149,735,1150,1152,1153,738, 1155,739,895,1157,741,1159,744,764,1161,746,855,1084,748,1021,1078,753,1166,1167,1135,758,971,1171,760,761,1038, 762,1174,1138,765,1176,766,850,767,1178,768,1180,1035,770,1183,836,775,1185,776,1188,1189,778,1061,779,780,783, 1193,785,786,1077,1195,789,845,1045,791,792,794,1200,1201,1014,797,1204,1205,1206,1207,804,964,890,806,1210,1211, 1163,811,830,1074,816,817,1215,1108,819,987,822,1218,975,1187,827,1222,828,829,1224,1008,1226,832,833,835,926, 837,1231,1232,1234,1235,842,843,1237,846,881,997,848,1063,1239,853,1241,1243,1244,904,857,859,1098,862,1029,910, 1179,1004,965,1148,868,1147,869,1238,962,873,1118,875,1097,879,882,1151,885,1197,886,1257,888,1088,1072,1236,892, 893,918,943,897,1217,1261,899,1033,1177,906,1227,1122,1265,909,1267,911,1269,1086,914,915,1273,1112,917,1124,919, 1277,921,1271,1154,924,1279,927,928,1280,969,1202,1251,978,935,938,1285,939,941,1199,942,1281,1081,1079,945,947, 1091,948,949,1129,951,1260,954,1170,956,1292,959,1194,1026,1246,1296,967,968,1191,1298,1158,972,1300,1301,977,1247, 980,1109,984,1076,986,1303,1305,989,1307,992,1308,1039,994,995,1284,1168,1310,1001,1162,1005,1313,1093,1314,1144,1012, 1013,1136,1312,1016,1017,1018,1019,1274,1272,1024,1025,1311,1319,1219,1032,1321,1105,1037,1214,1240,1254,1041,1255,1044,1324, 1046,1111,1325,1229,1327,1052,1053,1328,1054,1055,1099,1058,1083,1064,1220,1066,1293,1067,1068,1333,1164,1175,1336,1338,1299, 1137,1259,1304,1221,1223,1340,1095,1342,1252,1156,1106,1344,1332,1276,1113,1294,1115,1345,1117,1347,1128,1209,1121,1208,1317, 1264,1126,1295,1131,1134,1146,1282,1352,1190,1141,1286,1353,1354,1350,1318,1291,1160,1242,1266,1278,1165,1341,1169,1250,1172, 1173,1335,1181,1253,1182,1306,1184,1186,1356,1192,1212,1203,1196,1198,1358,1359,1275,1290,1213,1355,1216,1361,1339,1225,1228, 1348,1230,1233,1329,1362,1363,1263,1245,1364,1302,1248,1351,1249,1323,1256,1297,1258,1346,1262,1268,1343,1270,1326,1365,1289, 1337,1283,1287,1288,1320,1309,1360,1315,1316,1357,1322,1330,1331,1334,1349] ,\[ 3,4,6,8,9,11,12,14,16,17,19,21,22,24,25,27,29,30,1,32,34,36,37,2,40, 41,43,44,46,48,49,51,52,54,55,57,59,60,61,63,65,66,5,69,70,72,73,75,77,78, 80,82,83,7,86,87,89,90,92,94,96,97,99,100,102,58,104,105,107,109,110,10,113,114,79, 116,118,120,18,122,123,124,126,127,128,130,132,133,13,136,137,139,140,142,143,145,147,148,15,151, 152,154,155,157,159,160,162,158,164,166,167,168,170,172,173,175,176,178,179,181,182,20,185,187,188, 190,192,194,195,197,198,199,201,202,203,42,206,207,23,210,211,213,215,216,218,219,221,223,224,225, 227,229,230,26,233,234,236,237,239,241,242,28,244,246,247,249,251,253,254,256,257,259,261,262,263, 265,266,31,269,270,271,273,274,275,144,277,33,280,281,283,284,286,287,289,291,292,35,295,297,298, 300,302,304,204,305,307,309,310,311,313,315,316,38,318,319,81,321,39,324,325,327,328,330,332,169, 334,336,337,339,341,342,343,344,346,347,349,351,352,353,354,356,357,358,360,361,45,364,255,365,366, 368,369,371,373,374,47,377,378,380,381,383,385,387,388,390,391,392,393,395,396,50,398,400,134,403, 404,406,407,408,410,131,375,53,414,415,417,419,420,422,423,425,427,428,296,189,430,56,432,433,424, 435,183,437,439,441,442,444,421,446,448,450,451,453,394,454,456,457,459,461,462,463,464,238,466,468, 469,62,472,449,474,475,477,478,480,481,64,208,484,486,487,489,491,493,476,495,497,418,499,67,501, 502,503,68,505,506,508,510,511,149,411,482,513,514,516,71,518,519,521,523,125,525,526,150,529,530, 531,533,535,536,74,524,539,541,542,544,545,76,548,549,551,553,555,557,558,560,562,563,564,565,567, 568,512,570,331,572,574,576,578,579,370,581,582,583,585,587,588,84,589,591,593,465,85,596,88,598, 599,600,602,603,605,606,608,610,611,613,614,616,306,617,618,620,622,362,91,623,625,626,228,628,630, 338,631,93,633,634,636,214,638,317,640,95,642,644,646,647,559,504,649,651,652,653,654,184,98,657, 103,359,659,660,661,663,664,436,666,667,101,386,345,669,670,672,479,674,675,676,677,679,680,681,409, 682,108,685,686,688,690,691,106,692,655,693,694,604,696,697,699,700,683,573,703,111,705,592,707,112, 710,711,621,713,715,471,350,718,719,721,723,724,725,727,728,115,656,584,731,733,734,735,736,738,739, 117,740,741,742,744,186,746,748,146,119,619,750,751,753,755,756,121,758,759,473,760,761,762,556,764, 765,766,767,768,538,163,770,712,772,774,775,776,778,779,780,781,782,783,784,785,786,737,129,789,791, 792,794,796,797,799,492,470,802,803,804,639,806,808,810,811,813,135,816,817,819,509,821,822,402,138, 825,826,515,827,828,829,830,141,832,833,834,835,836,837,839,840,842,843,845,846,848,850,809,852,853, 716,855,857,859,161,860,276,862,864,431,668,320,868,869,870,312,873,226,153,875,389,793,416,877,879, 881,882,494,156,885,886,887,888,884,323,889,890,892,893,895,897,899,901,903,904,906,329,698,165,909, 910,911,913,914,878,915,917,918,919,921,923,924,248,926,927,928,847,171,930,931,933,934,935,876,938, 939,941,942,314,943,174,945,340,455,947,948,949,951,953,954,177,397,956,958,959,961,962,729,964,180, 554,965,967,968,969,641,496,971,972,440,975,977,372,978,980,982,984,986,987,920,989,990,648,191,992, 994,995,997,235,937,193,252,1001,999,800,1004,788,1005,1007,1008,196,597,231,1012,1013,1014,443,1016,294,1017, 1018,200,1019,1021,1022,1024,303,1025,812,1026,932,1028,807,1029,684,571,1032,1033,205,1035,438,1037,1038,891,1039, 957,1041,209,1044,1045,1046,546,726,212,1050,872,861,1052,1053,1054,1055,662,609,1058,217,1060,1061,1063,814,308, 1064,220,1066,1067,1068,1069,376,907,222,1072,434,1074,1075,1076,1077,1078,1079,1081,245,944,1083,1084,1009,1086,1088, 795,232,1006,905,820,488,1002,1042,1091,1093,1095,532,250,1097,1098,1099,240,627,1102,1103,637,1105,1106,528,1030, 243,1108,624,1109,678,1111,1112,1113,1096,1115,1117,1118,1104,1043,1121,1122,260,1124,1071,1126,763,1128,1129,1131,1125, 854,282,326,1134,1135,1136,1137,258,1138,979,993,1040,1141,963,645,1144,1146,1147,1148,976,824,1151,264,601,1154, 671,936,1156,1158,805,1160,689,267,929,1162,268,1163,635,1164,594,1165,272,1090,1168,1169,1170,1172,517,520,1173, 966,367,1175,379,278,586,1177,498,279,1179,500,1181,1182,1059,1184,534,1186,1187,285,1133,1190,673,1191,752,1192, 288,757,1194,290,1183,1196,1197,1198,1101,1199,1011,293,537,1202,1203,777,1152,1027,643,1208,299,1209,527,856,301, 483,1212,773,1213,1214,898,1216,1217,702,1132,701,1219,1220,1116,1221,1223,1065,1218,1225,1120,1227,1228,1229,704,1226, 1230,771,1233,566,844,1236,823,1238,838,1174,866,1114,322,1240,985,1242,1087,607,612,1245,1246,384,1241,1247,1248, 333,1249,717,790,946,335,1250,1234,458,1251,1252,714,1253,1254,1255,1110,1256,983,960,348,973,467,1258,1080,749, 485,1259,355,974,1260,1171,1262,922,1263,815,363,1264,1266,743,1268,447,1145,1270,1271,1272,1239,908,1274,1275,1276, 412,787,1278,1023,858,413,1193,798,1281,991,1282,1283,1284,1200,1280,580,1020,769,382,1034,1286,970,1287,550,1288, 1289,595,1269,1051,831,1149,687,1290,1291,1062,1277,1293,1294,1295,732,747,1297,399,730,401,1299,1285,405,940,1180, 988,1302,1010,883,575,1304,1306,1127,543,1107,981,1307,709,1123,1048,1309,1159,880,1311,1312,522,426,867,1315,1303, 629,429,1139,1316,801,1206,1092,1279,1317,1142,1318,1205,1320,1314,996,561,1322,1049,445,1257,590,851,1201,1323,452, 896,1305,1326,1215,1231,950,1298,460,1321,1178,1047,1094,841,1329,1330,1204,1331,1332,1310,1334,1188,1335,1337,1195,1089, 1119,1273,490,1327,1339,1341,1057,1157,1343,507,1292,1345,1265,1130,695,916,1267,1036,1346,1348,1349,632,1350,1224,1333, 1336,1351,902,1210,1167,745,1301,615,1324,569,540,665,1211,547,552,1328,1319,1237,1166,1100,863,1355,1153,1031,998, 720,577,1015,1143,1155,1347,952,912,1357,1243,1342,865,1358,1340,1235,1360,955,1353,1313,849,1354,1338,1189,722,1185, 1056,1082,1000,706,1222,650,1352,708,1359,658,1344,1296,818,754,900,1363,1365,1361,925,1325,1232,1176,1308,1085,874, 1364,1244,1150,871,1140,1161,1300,1261,1362,1073,894,1070,1207,1356,1003] >; print "Group G is G2(4) < Sym(1365)";