/* www-ATLAS of Group Representations. M24 represented as permutations on 1288 points. */ G:=PermutationGroup<1288|\[ 2,1,5,7,3,10,4,12,13,6,11,8,9,19,20,22,23,25,14,15,29,16,17,32,18, 34,35,37,21,40,42,24,45,26,27,49,28,51,52,30,55,31,57,58,33,61,62,64,36,66, 38,39,70,71,41,74,43,44,78,79,46,47,83,48,85,50,87,88,90,53,54,93,94,56,97, 98,100,59,60,104,105,107,63,110,65,113,67,68,117,69,119,120,72,73,124,125,75,76,129,77, 131,132,134,80,81,138,82,140,141,84,144,145,86,147,148,150,89,153,91,92,157,158,160,95,96, 164,165,167,99,170,101,102,174,103,176,168,178,106,181,108,109,185,186,111,112,190,114,115,194,116, 151,196,118,199,200,202,121,122,206,123,208,201,210,126,127,214,128,136,216,130,219,220,222,133,225, 135,228,137,230,231,139,234,235,237,142,143,241,188,243,146,246,247,249,149,252,152,255,256,154,155, 162,156,261,262,264,159,267,161,270,163,250,272,238,166,215,169,278,279,171,172,283,173,285,224,175, 288,289,177,292,179,180,296,297,182,183,301,184,213,303,305,187,308,189,310,263,191,192,314,193,211, 316,195,319,320,197,198,323,324,326,328,203,204,245,205,332,266,207,335,336,209,339,212,342,343,344, 346,347,217,218,351,352,354,221,357,223,360,361,226,227,365,325,229,368,294,370,232,233,374,375,377, 236,380,239,382,240,384,385,242,388,244,349,391,393,248,396,251,399,400,253,254,401,403,257,258,291, 259,407,260,409,410,412,265,415,416,268,269,419,420,271,423,424,273,274,275,429,276,277,432,311,434, 280,281,438,282,440,441,284,443,387,286,287,447,448,450,290,366,453,293,456,295,458,442,460,298,299, 464,300,465,466,302,469,304,471,306,307,475,359,309,444,478,312,481,313,483,484,315,486,487,317,318, 321,491,322,467,494,496,327,498,329,330,502,331,490,504,333,334,507,509,337,338,512,513,340,341,516, 517,519,521,345,463,523,348,433,350,527,528,530,353,533,355,356,372,358,389,538,540,362,363,544,364, 546,547,367,550,551,369,554,371,557,373,461,559,430,376,378,379,404,563,381,566,383,569,570,572,386, 575,576,390,578,579,392,582,394,395,586,397,398,589,590,413,402,593,595,405,545,406,597,408,599,600, 581,411,602,414,604,606,417,609,418,611,612,421,422,616,617,425,426,621,427,574,428,532,431,571,624, 626,435,436,630,437,632,522,439,635,636,637,639,445,642,446,644,645,647,449,495,451,452,653,654,454, 455,658,659,457,619,662,459,665,462,667,668,669,468,672,673,470,675,676,472,473,524,474,681,520,476, 477,598,479,480,686,501,482,689,584,614,485,692,694,488,489,697,698,492,656,493,648,497,577,499,500, 631,503,707,505,709,506,640,711,508,714,510,511,717,585,719,514,515,722,555,724,518,671,726,525,729, 526,731,732,734,529,601,531,738,739,534,535,536,742,537,607,744,539,747,541,542,751,543,596,728,754, 755,756,548,549,759,594,761,552,553,765,766,556,769,770,558,773,560,561,562,776,622,564,565,674,567, 568,779,680,688,678,573,682,783,785,787,580,790,679,583,791,792,587,763,588,795,796,591,592,798,700, 800,801,793,803,805,807,603,808,605,811,608,804,814,610,817,818,613,820,615,822,774,618,825,620,827, 623,828,649,625,831,627,628,835,629,837,838,839,633,634,843,844,638,846,641,847,746,643,849,850,852, 646,854,856,650,651,652,860,862,655,865,657,867,693,869,660,661,873,768,663,664,876,877,666,721,880, 670,881,883,677,885,886,887,683,784,684,890,685,891,892,687,690,691,703,794,695,696,872,699,902,701, 702,802,704,712,705,904,706,708,830,907,710,910,864,713,861,913,715,716,819,718,915,720,845,918,723, 920,725,727,922,809,730,925,926,928,733,842,735,736,737,933,934,836,740,741,823,743,745,941,748,749, 944,750,946,752,948,753,857,951,899,757,815,758,956,813,760,958,762,960,764,962,963,797,767,967,968, 771,772,972,911,775,777,882,778,975,780,781,782,979,980,786,788,789,984,985,987,931,989,898,859,959, 992,799,903,806,995,996,810,998,921,812,879,1000,816,1003,821,1004,917,824,1006,826,909,829,1009,1010,832, 833,1014,834,1016,1017,896,1020,840,841,1024,1025,1026,1028,1029,1030,848,1032,1034,851,1037,853,1040,855,949,1044, 858,1046,1047,1048,1050,863,1053,866,900,868,1055,870,871,1059,1060,1061,874,875,1065,1066,1068,878,1071,1073,884, 1015,1077,1021,888,889,1051,1001,999,893,894,986,895,1072,897,1083,1084,901,993,1086,905,906,1022,908,983,912, 982,1090,914,916,1093,919,1094,1096,923,924,1099,1100,1102,927,976,929,930,1018,1108,932,978,997,1111,935,936, 937,1116,938,939,940,1095,942,1118,943,1120,1069,945,1038,1076,947,1041,1115,1126,950,1128,952,953,954,1131,955, 981,1132,957,1134,961,1137,1138,1125,964,965,966,1143,1144,1146,969,970,1150,971,1036,1152,973,988,974,1075,1074, 1039,977,1107,1089,1155,1157,1159,990,991,1162,994,1087,1164,1079,1002,1167,1168,1005,1007,1031,1008,1171,1172,1011,1012, 1175,1013,1169,1177,1179,1180,1078,1019,1183,1170,1023,1123,1186,1114,1042,1027,1188,1033,1189,1035,1191,1192,1112,1193,1058, 1043,1195,1045,1130,1129,1049,1052,1200,1054,1202,1203,1056,1057,1204,1206,1208,1210,1062,1063,1211,1064,1212,1213,1215,1067, 1218,1070,1221,1205,1080,1196,1081,1222,1082,1185,1161,1085,1217,1088,1226,1227,1091,1092,1103,1110,1097,1098,1231,1232,1101, 1234,1104,1235,1105,1106,1214,1182,1109,1236,1160,1113,1187,1117,1119,1238,1121,1122,1124,1194,1127,1156,1241,1242,1243,1133, 1245,1135,1136,1139,1154,1140,1248,1141,1249,1142,1145,1147,1148,1181,1149,1252,1163,1151,1253,1220,1153,1158,1223,1251,1225, 1165,1166,1256,1258,1250,1173,1174,1262,1176,1178,1184,1246,1190,1264,1240,1197,1198,1199,1254,1201,1237,1268,1207,1209,1230, 1224,1216,1219,1244,1263,1228,1272,1229,1275,1260,1265,1233,1255,1239,1261,1277,1267,1247,1271,1270,1269,1257,1273,1280,1259, 1276,1266,1283,1279,1274,1284,1285,1278,1281,1282,1287,1286,1288] ,\[ 3,4,6,8,9,1,11,2,14,15,16,17,18,5,21,7,24,26,27,28,10,30,31,12,33, 13,36,38,39,41,43,44,46,47,48,19,50,20,53,54,22,56,23,59,60,25,63,65,49,67, 68,69,29,72,73,75,76,77,32,80,81,82,34,84,35,86,37,89,91,92,85,40,95,96,42, 99,101,102,103,45,106,108,109,111,112,114,115,116,51,118,52,121,122,123,55,126,127,128,57,130, 58,133,135,136,137,61,139,62,142,143,64,71,146,66,149,151,152,154,155,156,70,159,161,162,163, 74,166,168,169,171,172,173,78,175,79,177,179,180,182,183,184,83,187,188,189,191,192,193,87,195, 88,197,198,90,201,203,204,205,93,207,94,209,211,212,213,97,215,98,217,218,100,221,223,224,226, 227,104,229,105,232,233,107,236,238,239,240,110,242,244,245,113,248,250,251,253,254,117,257,258,259, 119,260,120,263,265,266,268,269,124,271,125,273,274,275,276,277,129,280,281,282,131,284,132,286,287, 134,290,291,293,294,295,138,298,299,300,140,302,141,304,306,307,144,309,145,311,312,313,147,315,148, 317,318,150,321,267,322,153,325,327,329,314,330,157,331,158,333,334,160,337,338,340,341,164,165,345, 167,348,349,350,170,353,355,356,358,359,174,362,363,364,176,366,367,178,369,371,372,373,181,376,378, 379,381,256,185,383,186,386,387,389,390,190,392,394,395,397,398,194,401,402,344,196,303,404,405,199, 406,200,408,202,411,413,414,206,255,417,418,208,421,422,210,425,426,427,428,214,430,431,216,433,435, 436,437,219,439,220,442,357,222,444,445,446,225,449,451,452,228,454,455,230,457,231,459,461,462,463, 234,410,235,467,468,237,470,472,473,474,241,476,477,243,479,480,246,482,247,261,485,249,488,489,490, 252,478,492,493,495,497,374,499,500,501,262,503,264,465,505,506,508,510,511,429,270,514,491,515,272, 518,520,320,519,522,524,525,278,526,279,529,531,532,534,535,536,283,537,285,539,541,542,543,288,545, 289,548,549,292,552,553,555,556,296,558,297,407,560,561,332,562,301,564,565,567,568,305,571,573,574, 308,577,319,310,580,581,583,584,585,559,587,588,316,591,566,592,594,323,582,324,596,326,598,328,601, 377,547,603,546,605,607,608,335,610,336,613,614,615,339,618,619,620,342,420,343,622,346,623,347,625, 627,628,629,351,631,352,633,634,354,611,638,640,641,360,643,361,646,648,649,650,651,652,365,655,656, 657,368,660,661,370,663,664,666,396,375,621,670,671,380,674,400,382,677,678,679,384,680,385,682,563, 683,388,684,685,391,687,688,393,590,690,691,693,695,696,483,399,423,699,403,700,701,702,703,704,705, 409,706,412,708,415,710,416,712,713,715,440,716,419,718,673,720,721,424,723,725,464,668,727,728,432, 730,434,733,735,593,736,737,438,740,617,586,741,441,743,443,745,746,748,749,750,447,752,448,753,450, 504,502,757,758,453,760,762,763,764,456,767,768,458,771,772,460,774,521,775,466,575,570,513,469,777, 778,471,780,672,781,782,475,784,786,788,789,481,494,602,484,636,793,486,794,487,697,589,797,630,799, 496,802,498,804,806,689,742,809,810,812,813,507,815,816,509,785,819,512,821,823,635,824,516,826,517, 734,523,829,830,832,833,834,527,836,528,530,840,841,842,533,845,787,825,717,538,779,848,540,851,853, 751,855,544,857,858,859,861,863,864,550,866,551,868,870,871,872,554,874,669,875,557,878,844,879,769, 827,882,884,642,569,572,888,889,576,612,578,707,579,800,893,894,895,896,897,898,899,900,901,595,686, 891,597,846,599,903,600,905,906,604,908,909,606,911,912,609,914,807,811,744,808,916,917,616,919,639, 828,921,724,624,923,924,626,927,929,930,726,822,931,932,632,935,936,937,938,637,939,940,867,942,943, 644,945,645,947,647,949,950,952,953,954,653,955,654,957,790,959,747,658,961,659,964,965,966,662,969, 970,971,665,667,973,974,675,918,676,976,977,978,681,979,981,982,983,865,986,988,692,694,990,991,698, 993,994,941,975,817,820,997,709,818,999,711,1001,1002,714,907,719,837,1005,722,1007,776,1008,729,1011,1012, 1013,731,1015,732,1018,1019,1021,1022,1023,738,739,1027,773,803,1031,805,1033,1035,1036,1038,1039,1041,1042,1043,754, 1045,755,756,1049,1051,1052,759,1054,761,951,1056,1057,1058,765,766,1062,1063,1064,770,1067,1069,1070,1072,1074,1075, 1076,1046,1078,783,980,1079,801,995,1080,1081,791,992,792,1082,795,796,1085,798,1087,892,962,915,1088,1089,1083, 814,1032,1091,1092,883,1093,1095,1097,1003,1098,831,1101,1103,1104,1105,1106,1107,835,838,1109,839,1110,1112,1113,1114, 1115,843,1071,1061,1117,847,913,849,1119,850,1121,1122,852,1123,1124,854,1125,856,1127,960,886,1129,1130,860,1126, 862,1133,1034,1135,1136,869,996,1139,1140,1141,1142,873,1145,1147,1148,1149,876,1151,877,1153,1094,880,1154,881,904, 885,1077,887,890,1156,1158,1160,1161,1084,987,1163,902,1165,910,1166,1009,1116,1169,1028,920,1170,922,1173,1174,1144, 925,1176,926,1178,928,1181,1182,1099,1184,933,1185,934,1132,1177,1187,1004,1183,1100,1053,1190,944,1180,946,1157,948, 1194,1196,1111,1197,1198,1199,1024,956,1201,958,1204,1205,1164,963,1207,1209,1029,1162,1118,967,1146,968,1214,1216,1217, 1219,1220,972,1168,1188,984,1040,985,1175,989,1000,1223,1224,1225,998,1215,1228,1073,1006,1208,1229,1230,1010,1108,1233, 1202,1025,1014,1232,1037,1016,1017,1030,1020,1128,1203,1026,1193,1237,1239,1235,1131,1155,1050,1240,1044,1047,1048,1192,1244, 1246,1102,1242,1055,1218,1247,1059,1096,1060,1222,1250,1251,1172,1065,1090,1066,1226,1137,1068,1254,1210,1221,1143,1086,1138, 1150,1255,1257,1259,1213,1260,1261,1159,1234,1263,1249,1238,1189,1120,1265,1211,1186,1266,1258,1267,1134,1269,1270,1252,1241, 1271,1236,1272,1152,1273,1274,1167,1200,1171,1264,1179,1276,1191,1231,1195,1278,1279,1253,1206,1280,1212,1268,1227,1275,1256, 1281,1282,1243,1245,1248,1262,1284,1286,1277,1285,1288,1287,1283] >; print "Group G is M24 < Sym(1288)";