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