
print "Simple group TITS represented as a permutation group of degree 1755.";
print "Derived subgroup of the Lie group 2 F(4, 2)   ( twisted F(4, 2) )";
print "Order: 17,971,200 = 2^11 * 3^3 * 5^2 * 13;  Base: 1,2,3,6.";
print "Group: G";

G := PermutationGroup<1755 |
    \[   1,    2,   16,   21,   71,   73,   34,   12,   88,
  10,   11,    8,  946,   56,   18,    3,   33,   15,  201,  518,    4,
 298,  358,  436,  516,  192,  241,  661,   39,   90,  718,   32,   17,
   7,  111,  147,  803,  114,   29,   85,   83,   87,   43,   86,  429,
1032,  589, 1131, 1081,  986,  243,  176,   72,   55,   54,   14,   84,
1130, 1382, 1345,  560,  116, 1489,  224, 1365,  282,  281, 1542,  669,
 922,    5,   53,    6,  357,  474, 1147,  749, 1330,  673,  639,  519,
 578,   41,   57,   40,   44,   42,    9,  110,   30,  992, 1217,  541,
1543,  875,  690,  444,  360,  295,  101,  100,  175,  215,  853, 1485,
 418,  495,  119,  990,   89,   35,  837,  465,   38,  261,   62,  139,
 574,  108, 1557,  672,  671, 1084, 1034,  310,  351,  227, 1180,  568,
 793,  645,  462, 1627,  705, 1295,  160,  738,  380,  117,  231, 1236,
 843,  848, 1733,  145,  213,   36,  710, 1389,  209,  151, 1677,  161,
1251, 1340,  320,  158,  157,  972,  136,  153, 1298, 1057,  759, 1533,
 704,  965,  203,  626,  618,  202,  827,  988,  183,  102,   52,  221,
 933, 1308,  552, 1640,  459,  174,  214,  963,  985,  905,  806,  579,
1432, 1209,   26,  593, 1183, 1706, 1208, 1549,  198,  199,  235,   19,
 171,  168,  449,  317, 1538,  995,  594,  150,  679,  542,  844,  146,
 184,  103, 1397,  217,  693, 1528,  937,  177,  575,  308,   64, 1341,
 466,  127,  234,  647,  242,  140, 1006,  332,  228,  200,  940, 1062,
 446, 1363, 1525,   27,  230,   51,  860,  426,  637,  300,  290,  551,
1681,  316,  798,  253,  869,  904,  297, 1223,  638, 1743,  820,  115,
 947,  625,  731,  976,  781,  885,  435,  667,  309,  712,  774, 1030,
1437, 1087, 1078, 1521,  729, 1388, 1381,   67,   66, 1425, 1267, 1468,
1722,  416,  649,  397,  248, 1154,  485,  335,  494,   99,  927,  256,
  22, 1244,  247, 1232, 1380,  958, 1669, 1409,  703,  975,  223,  270,
 125, 1169, 1431, 1636,  497, 1689,  251,  205, 1143,  613,  156, 1102,
 686,  665,  339, 1412,  751, 1132,  407, 1007, 1018,  668,  233, 1204,
1073,  293,  709,  434,  483,  324,  374, 1378,  743,  633,  726, 1119,
 953,  378, 1026,  652,  950,  126,  948, 1219,  400,  914,  877,   74,
  23,  771,   98,  540,  688, 1522, 1265,  973, 1406, 1405, 1638, 1352,
 804,  916,  581,  938,  340, 1641, 1735, 1322,  347,  931,  138, 1749,
1071,  817, 1569, 1450, 1583,  423, 1716, 1197,  632, 1172, 1597,  484,
 588, 1158, 1159,  289,  410, 1138,  354, 1199,  415,  994, 1466, 1457,
1311,  328, 1033,  666,  398,  919, 1633,  730,  799,  402,  287, 1729,
 106, 1448, 1653, 1058, 1001,  387, 1541, 1494,  245, 1690,  543,   45,
1318, 1561,  447, 1639,  337,  268,   24, 1156, 1016,  911, 1744, 1356,
1534,  641,   97, 1705,  238,  432,  772,  204, 1074, 1288,  627,  453,
1602,  966, 1110, 1072,  662,  182,  460, 1000,  132, 1551, 1210,  113,
 226, 1500, 1660, 1511, 1508,  605,  611, 1504,   75, 1068, 1109, 1080,
 498,  517,  481,  480, 1423,  338,  393,  292, 1245, 1025, 1709, 1126,
 721,  566,  648,  607,  294,  107,  742,  314,  478, 1552, 1160,  881,
1021,  600,  530,  981,  982,  783, 1391,  537,  813, 1066, 1429,  525,
1235, 1544,   25,  479,   20,   81,  864,  865,  796,  539,  587,  513,
1621, 1200, 1512, 1601,  504, 1671,  706,  547, 1014, 1181,  908,  509,
1020,  523,  361,   93,  211,  428,  915,  694, 1260,  533, 1715,  572,
1048,  249,  180, 1736, 1556, 1241,  839,  614,  558,  776,   61, 1404,
 707,  635,  564, 1483,  491,  928,  129, 1394, 1424,  685,  549,  714,
 118,  222,  677,  802,   82,  189,  822,  372, 1302,  642, 1364,  657,
1694,  524,  394,   47, 1070,  629,  697,  193,  208, 1501, 1255,  763,
 825,  747,  503, 1061,  795, 1589, 1013,  471,  891,  493, 1168, 1275,
1005,  472, 1518,  319,  557, 1524,  858,  800,  170,  993,  754, 1222,
1751,  687, 1623,  263,  169,  452, 1471,  591, 1010, 1004,  390,  343,
 757,  563, 1310,  246,  258,   80, 1094,  443,  583,  814, 1278,  131,
 723,  229,  492,  288,  650,  794,  349, 1082, 1620, 1650, 1273,  585,
 786, 1428, 1134,   28,  458,  906, 1149,  323,  409,  269,  331,   69,
1496,  122,  121,   79, 1092, 1711,  692,  576,  867,  210,  696, 1571,
 699, 1605, 1129,  571,  322,  623,  362, 1329,   96, 1746,  676,  218,
 545,  785,  680,  592, 1105,  682,  732,  872, 1598,  306,  166,  134,
 532,  562, 1012,  336,  148, 1440,  271,  720,  573, 1754,  866, 1656,
  31,  989,  713,  490, 1615,  646, 1676,  811,  344, 1644, 1261,  278,
 413,  264,  700, 1559,  745, 1665,  736,  780,  137,  829, 1319, 1091,
 496,  342, 1710,  734, 1493,  599, 1146,   77, 1433,  326, 1049,  892,
 620,  983,  960,  634,  808,  164,  766, 1083, 1315,  597, 1201, 1395,
 760, 1708,  828, 1474, 1600,  359,  448, 1719,  272,  897,  559, 1426,
1436, 1498,  737,  266,  978,  507, 1452,  695,  658, 1647,  849,  833,
1234, 1624,  792,  130,  651,  602,  522,  818,  252,  414,  617,  826,
 577,   37,  370, 1334,  188, 1085,  758, 1221, 1420,  725, 1306,  510,
 643, 1263, 1248,  383,  797,  856,  260, 1051,  580, 1216,  896,  598,
 801,  172,  768,  739, 1023, 1063, 1213,  789, 1563, 1456, 1324,  112,
1616,  556, 1611, 1286, 1495,  142,  212, 1582, 1325,  880,  143,  788,
1019, 1699, 1477,  104, 1166, 1135,  819, 1121,  616,  918,  244, 1309,
 934,  984,  520,  521,  716,  678, 1503,  254, 1675, 1728,  701, 1539,
1113,   95, 1089,  356,  951, 1355,  847,  501, 1652, 1469, 1490,  267,
1077, 1351, 1499, 1481,  941,  606,  753, 1300, 1537, 1674,  824,  775,
1442, 1730, 1361, 1390, 1717, 1212,  255,  187,  663, 1290,  536, 1737,
1691,  439, 1161, 1594,  355,  544,  371, 1593,  859,  411, 1291, 1667,
  70, 1305, 1573, 1029, 1422,  296,  567,  987, 1555,  379,  932,  178,
 862, 1117, 1532,  220,  373, 1386,  236,  890, 1015, 1376, 1657, 1190,
  13,  262,  352, 1037,  350,  878, 1243,  346, 1003, 1303, 1401,  999,
 303, 1613,  756, 1713, 1124,  185, 1507,  167,  455, 1292, 1167, 1599,
1115, 1281,  159,  365, 1040,  307,  265, 1476,  782,  979, 1622,  505,
 506,  755,  863,  186,   50,  929,  173,  719,  109, 1108,   91,  619,
 403,  207, 1178, 1116, 1294,  957,  461,  422, 1370,  954,  631,  610,
 232,  329, 1218, 1246,  630, 1011,  708,  604,  534,  942,  438, 1035,
 330,  850,  538,  502, 1182,  830, 1136,  487,  348, 1702, 1698,  925,
 273, 1410,   46,  408,  124, 1017, 1458,  949, 1357, 1400,  974, 1414,
1171, 1287, 1527, 1186, 1755, 1739,  550,  752, 1059,  821, 1449, 1701,
1054, 1259, 1252,  163,  421, 1050, 1645,  601,  237,  831, 1323, 1595,
 511, 1545,  475, 1227,  590,  382,  457,  334,  450, 1193, 1393,  886,
 276, 1455,  477,   49,  653,  761,  123,  807, 1459,  275, 1225,  876,
1712,  741,  674, 1531,  640, 1107, 1262, 1214, 1282, 1337, 1747, 1301,
 321, 1625, 1591,  698, 1562, 1095,  991,  476,  456, 1475, 1462,  874,
1478,  970,  997,  935, 1118,  345, 1467,  857, 1629, 1240,  962, 1362,
 489, 1369, 1666,  684,   58,   48,  327, 1416,  660,  855, 1024, 1177,
 399, 1628, 1492, 1150, 1399,  318, 1662, 1343,  748,   76, 1320,  664,
1141, 1385, 1725, 1643,  291, 1604,  437, 1373,  395,  396,  500,  912,
1297, 1618, 1164, 1384,  854,  968,  608,  311, 1237, 1042,  391, 1451,
1576, 1727, 1327, 1137,  996, 1651,  128,  535, 1022,  194, 1607, 1634,
1045, 1570, 1202, 1279,  945, 1637, 1194, 1075, 1192, 1238, 1577,  389,
1354,  401,  527,  764, 1188, 1686,  333, 1578, 1587, 1372,  196,  191,
 464, 1731,  903,  832, 1097, 1421,  823,   92, 1008,  353, 1430,  809,
 621,  257, 1585, 1088, 1732, 1069, 1326, 1396, 1566, 1461,  301, 1497,
 790,  514,  141, 1170, 1195, 1415, 1123,  555, 1284,  952,  299,  486,
1009, 1358,  816, 1411, 1724,  154, 1056, 1392, 1520,  596, 1700, 1687,
1546, 1055,  546,  728, 1096,  815, 1454,  364, 1672,  284, 1443, 1673,
1314, 1631, 1742,  656, 1703,  609, 1417, 1567,  644, 1189, 1664,  971,
1098, 1649, 1242, 1506,  841, 1043,  451, 1632,  907,  920,  967, 1603,
 998,  135, 1316, 1162,  162, 1402,  893, 1101,  582,  955, 1484,  923,
 812, 1684,  179,  861,  636,  406, 1670, 1646, 1270,  762, 1296, 1346,
 430,  740, 1148, 1547,  377, 1064,  836,  846, 1228, 1176, 1720,  689,
  78, 1612, 1661, 1516,  805, 1679, 1554, 1099, 1734, 1366,  155,  225,
1685, 1145, 1572,   60, 1317, 1592, 1374, 1444, 1740,  887,  369, 1502,
1198,  879,  441, 1038, 1247, 1359, 1482,  900, 1125,  239,  584,   65,
1339, 1574, 1692, 1127, 1002, 1548, 1207, 1157, 1348, 1704,  943, 1513,
 341, 1564,  302,  280,   59, 1435, 1165, 1151,  939, 1718,  279,  149,
 901,  508, 1253, 1076,  569,  765, 1229,  216, 1614, 1142, 1039,  956,
1299, 1486,  561,  367,  366, 1678, 1753,  305, 1031, 1249,  325, 1565,
1041, 1239, 1133, 1276, 1439, 1658,  810, 1215,  926,  482,  570,  283,
 777, 1472,  659,  512, 1220,  312,  190,  750, 1752, 1383,  778,  274,
1560, 1418,  711, 1619,  898, 1268, 1349, 1663, 1655, 1488,  419, 1052,
 385, 1173,  784, 1487, 1264, 1079,  835,  405, 1036, 1086, 1540, 1231,
1112, 1480, 1473, 1610,  404, 1120,  285,  883, 1550,  628, 1427, 1464,
 769, 1111,  977,  852, 1114, 1697, 1463,  889, 1360,  565, 1304,  105,
1403, 1453, 1447,   63,  884, 1606, 1140,  746,  425,  842,  670, 1233,
 779,  888,  467,  595, 1353,  868,  473, 1683, 1285,  964,  470, 1514,
1659,  469,  528, 1377, 1509, 1654, 1333, 1630,  612, 1581, 1254,  277,
 363, 1526,  615,  240, 1523, 1044,  219, 1596, 1748, 1093,  936,  165,
 442, 1580, 1695,  894,  206,  873, 1460,  424,   68,   94,  515, 1067,
1258, 1321, 1371,  197, 1470,  463,  499, 1648, 1336,  930,  554,  120,
1579,  733, 1438,  431, 1106,  834, 1379, 1413, 1230, 1277, 1688,  384,
1187,  681, 1344,  924, 1367, 1693, 1174, 1196, 1205, 1558, 1535, 1519,
 845,  386, 1635, 1224, 1609, 1206, 1714,  603, 1707, 1104, 1347,  917,
 913, 1065, 1529,  392,  702,  969,  770,  529,  454, 1293, 1155,  683,
1491, 1184, 1745, 1586, 1465,  840, 1331,  959, 1398,  722,  838, 1741,
1163, 1441,  654,  526,  980,  624,  791, 1103, 1668,  133, 1139, 1122,
1517, 1271, 1289,  412, 1185, 1584,  313, 1191,  368,  433,  181,  375,
1721, 1153,  727, 1060, 1313,  787, 1553, 1283,  655, 1179,  882,  420,
1515, 1446,  717,  944, 1419, 1510,  468, 1332, 1144, 1445, 1280,  735,
1128,  921, 1626,  304, 1312,  531, 1266, 1269,  895,  870,  724,  152,
1407, 1335, 1750,  250, 1726, 1505, 1307, 1342, 1203, 1257, 1568,  315,
 427,  910, 1368, 1575,  586, 1536, 1696, 1479, 1028,  851, 1256, 1053,
1027, 1274, 1375,  445,  195, 1590,  767,  488,  744,  675, 1090,  961,
1588,  548,  388,  902, 1387,  773, 1328, 1642,  286, 1738, 1250, 1152,
1682, 1175,  871,  417,  899, 1211, 1226,  144, 1338,  376,  553,  909,
1723, 1047, 1350, 1617, 1272,  259,  440, 1608,  691, 1100, 1530,  381,
1680,  622, 1434, 1408,  715, 1046],
    \[   1,    2,    3,   17,   41,  110,   90,   12,   72,
  32,   11,    8,  431,   18,   56,   16,    4,   14,   86,   45,   33,
 292,  353,  273,  317,  551,  241,   55,   85,   34,  627,   10,   21,
  30,   84,  351,  799,  539,   40,   39,    5,   42,  253,  201,   20,
 588, 1158, 1018, 1007,  232,  140,  176,   88,  661,   28,   15,  111,
 486, 1380, 1280,  352,  465,  847,  678,  384, 1406, 1405,  816,  681,
 746,   83,    9,   89,  269,  666,  419,  660,  664,  906,  577,  202,
 244,   71,   35,   29,   19,   87,   53,   73,    7, 1294, 1301, 1102,
 989, 1303, 1484, 1487, 1199,  402,  310,  125,  175,  542,  844,  378,
 632, 1204,  135,  167,    6,   57,  139,  116,  523,  716,  113,  837,
1732, 1295,  136,  159, 1105, 1562,  994,  101,  147,  227,  376,  870,
1256,  819,  264,  732,  811,  108,  120,  863,  796,  112,   51, 1652,
 604,  148,  222,  792,  963,  126,  143,  945, 1501, 1696, 1529, 1319,
 312,  619,  226,  697,  592,  121, 1557,  740, 1731,  557,  356,  822,
 190,  109, 1062,  940,  813,  519, 1063,  735,  183,  102,   52,  428,
 266, 1074,  512, 1747, 1685,  174,  184,  213,  942,  187,  807,  941,
 166, 1737,  249,  593,  194, 1695, 1197, 1539,  217,  650,  647,   44,
  81,  237,  314,  516, 1276,  995,  208,  595,  982,  215,  853,  185,
 214,  211, 1165,  198,  824, 1500, 1051,  543,  144, 1663,  867, 1519,
 156,  127,  228,  235,  230,  243,   50,  287,  234,  229,  626,  203,
 363, 1603, 1292,   27,  242,  231,   82, 1271,  505,  709,  337,  192,
 836, 1172,  662,   43, 1552,  692,  288, 1089,  911, 1491,  884,  866,
 927,  908,  132,  954,  178, 1249,  289,   74, 1124,  457, 1066,   24,
1723, 1098, 1337, 1356, 1592, 1661, 1638,  367,  366,  387, 1605, 1279,
 464,  233,  256,  268,  434,  576,   22,  299,  952,  415,  947,  649,
 485,  293,  336,  483, 1382, 1043,  629, 1686, 1387, 1410, 1445,  962,
 100, 1668,  154, 1727,  204, 1558,  391,   25, 1502,  581,  466,  541,
1213, 1115, 1455, 1091,  377,  331,  653, 1081, 1131,  327,  416,  495,
 850, 1244,  300,  248, 1232, 1079, 1754, 1392,  346,  633,  726,  496,
 342, 1485, 1446, 1414, 1565,   36,   61,   23,  359,  797,  164,  667,
1219,  354,  401,  408,  654,  238,  445, 1135,  282,  281, 1381, 1064,
 617,  602,  613,  917,  715,  711,  128,  326,  105,  783,  522,  913,
1393,  915,   65, 1314,  612,  283, 1433, 1208,  418,  316,  396,  437,
1032,  589,  392,  435,  475, 1045,  771,  360,   99, 1034,  488, 1422,
1305, 1082,  361,  474, 1068, 1439, 1684,  968,  803,  295,  332,  724,
 390,   76,  675, 1061, 1400, 1425, 1133, 1460, 1631,  605,  177,  518,
1666,   13,  477, 1375,  290,  397, 1030,  393, 1221,  638, 1628, 1521,
1613, 1278, 1453,  364, 1522, 1080,  478,  497, 1308, 1290,  718,  932,
1010, 1328, 1025,  271,  798, 1342,  979, 1095,  731, 1140,  286,   62,
 320, 1528, 1044, 1504,  472, 1690,  470, 1511,  409,  398, 1122,  432,
 448,  481,  517,  479,  974,  301, 1156,  298,   58, 1110,  404, 1467,
 745,  528, 1601, 1635, 1243,  333,  345,  449,  772,  869,  610, 1503,
1247,  530,  600,  246,  679,  931, 1168, 1111,  618,  774,  180,  548,
1097,  646,  205,  480,  429,  171,  939,  587,  380,  114,  865, 1715,
 549,  571,  491,  648,  503,  861,  573, 1077, 1035, 1050,  625, 1475,
1246,   38, 1033,  321,  103,  221,  817,  849, 1667,  886,  513,  526,
1585,   26, 1429, 1730, 1702,  760, 1578,  163, 1054, 1053,  948,  835,
 778,  960, 1359,  878, 1512, 1470, 1675, 1586,  786,  527, 1621,  532,
1226, 1733,  291,   80,  860,  890, 1533,  319, 1008, 1161,  840,  657,
 791,  521,   46,  395, 1263, 1669,  158,  193,  594,  209, 1622,  597,
 826,  805,  504, 1058,  371, 1338,  142,  427, 1092, 1584, 1391, 1343,
 500, 1508,  386,  372, 1057,  901,  785,  370,  510,  155,  620, 1362,
1464,  925,  782,  536,  236,   31, 1329,  304, 1602, 1604,  106,  343,
 634,  756, 1513,  981,  439,  802, 1452,  644,  912, 1216,  641,  856,
 515,  200,  529,  297,  199,  808, 1041,  328,  362, 1103, 1610,  585,
1424,  910,   77,   54,  252,  673,   78,  970,   75,  357, 1132, 1571,
 682,  698,  972,  663,  891,  420,  904, 1154,   64,  506, 1316,   69,
 670, 1267, 1297, 1200,  832, 1029, 1620, 1471, 1304, 1136,  255,  896,
 788,  858, 1296,  157,  671, 1496, 1627, 1673,  773, 1718, 1432,  725,
 714, 1436, 1498,  247,  848,  375, 1072,  733,  706,  374,  115, 1713,
 452, 1543, 1559,  734,  744, 1544,  417,  705,  344, 1176, 1326, 1347,
1167,  462,  133,  713,  721,  173, 1011,  983,  984, 1259,  161, 1412,
1119,  953,  722,  490,   70, 1334, 1321, 1134, 1716, 1322, 1336, 1726,
 754,  780,  635,  757,  794,  877,  555,  764, 1315,  763,  761, 1659,
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AssertAttribute(G, "Order", 2^11 * 3^3 * 5^2 * 13);
