G := sub; involutions := [ [ G!(1, 1217)(2, 1140)(3, 666)(4, 905)(5, 1333)(6, 1249)(7, 175)(8, 815)(9, 998)(10, 1021)(11, 170)(12, 431)(13, 1133)(14, 371)(15, 1424)(16, 68)(17, 787)(18, 49)(19, 422)(20, 354)(21, 1049)(22, 656)(23, 756)(24, 763)(25, 1487)(26, 1221)(27, 1189)(28, 960)(29, 894)(30, 406)(31, 883)(32, 1003)(33, 1539)(34, 1423)(35, 596)(36, 1115)(37, 54)(38, 1485)(39, 1310)(40, 137)(41, 114)(42, 478)(43, 1578)(44, 991)(45, 517)(46, 583)(47, 195)(48, 119)(50, 1567)(51, 391)(52, 1404)(53, 1515)(55, 597)(56, 618)(57, 822)(58, 1063)(59, 142)(60, 1375)(61, 253)(62, 1034)(63, 530)(64, 1570)(65, 957)(66, 248)(67, 1328)(69, 88)(70, 811)(71, 481)(72, 363)(73, 446)(74, 180)(75, 1262)(76, 450)(77, 1258)(78, 987)(79, 1458)(80, 1163)(81, 282)(82, 1087)(83, 106)(84, 550)(85, 1154)(86, 677)(87, 1377)(89, 318)(90, 294)(91, 1017)(92, 277)(93, 1205)(94, 1107)(95, 801)(96, 463)(97, 1551)(98, 737)(99, 1382)(100, 1356)(101, 1280)(102, 730)(103, 1372)(104, 1386)(105, 879)(107, 1127)(108, 1547)(109, 1499)(110, 951)(111, 241)(112, 172)(113, 524)(115, 1353)(116, 218)(117, 1138)(118, 1257)(120, 900)(121, 224)(122, 289)(123, 1057)(124, 1300)(125, 673)(126, 762)(127, 1044)(128, 1534)(129, 1175)(130, 874)(131, 1273)(132, 865)(133, 1069)(134, 531)(135, 1582)(136, 1432)(138, 982)(139, 631)(140, 1047)(141, 1564)(143, 906)(144, 194)(145, 362)(146, 477)(147, 922)(148, 1368)(149, 295)(150, 759)(151, 160)(152, 382)(153, 1591)(154, 1479)(155, 1070)(156, 589)(157, 489)(158, 1254)(159, 844)(161, 1083)(162, 1093)(163, 1078)(164, 892)(165, 1149)(166, 555)(167, 196)(168, 783)(169, 866)(171, 1157)(173, 491)(174, 757)(176, 1108)(177, 769)(178, 829)(179, 1090)(181, 1293)(182, 1145)(183, 1523)(184, 1075)(185, 387)(186, 1324)(187, 705)(188, 336)(189, 302)(190, 591)(191, 1490)(192, 621)(193, 1241)(197, 1374)(198, 1099)(199, 398)(200, 576)(201, 358)(202, 817)(203, 919)(204, 728)(205, 402)(206, 897)(207, 945)(208, 798)(209, 688)(210, 335)(211, 1346)(212, 623)(213, 538)(214, 1366)(215, 444)(216, 689)(217, 544)(219, 246)(220, 1102)(221, 993)(222, 553)(223, 678)(225, 1051)(226, 1177)(227, 675)(228, 485)(229, 1004)(230, 433)(231, 861)(232, 1186)(233, 832)(234, 792)(235, 862)(236, 1104)(237, 1071)(238, 372)(239, 1311)(240, 536)(242, 421)(243, 1306)(244, 311)(245, 966)(247, 1559)(249, 749)(250, 1105)(251, 379)(252, 1252)(254, 635)(255, 853)(256, 1452)(257, 483)(258, 447)(259, 799)(260, 1390)(261, 1216)(262, 649)(263, 1448)(264, 603)(265, 970)(266, 1525)(267, 1045)(268, 1014)(269, 1165)(270, 1416)(271, 965)(272, 1188)(273, 834)(274, 622)(275, 516)(276, 1181)(278, 324)(279, 885)(280, 494)(281, 628)(283, 567)(284, 1548)(285, 1600)(286, 956)(287, 1574)(288, 1287)(290, 359)(291, 1303)(292, 400)(293, 1536)(296, 1097)(297, 857)(298, 1222)(299, 1497)(300, 755)(301, 859)(303, 766)(304, 964)(305, 442)(306, 744)(307, 1247)(308, 563)(309, 1460)(310, 1106)(312, 1139)(313, 830)(314, 1506)(315, 1122)(316, 435)(317, 521)(319, 534)(320, 1362)(321, 424)(322, 1594)(323, 708)(325, 972)(326, 1270)(327, 361)(328, 396)(329, 723)(330, 1313)(331, 552)(332, 617)(333, 624)(334, 1550)(337, 1388)(338, 935)(339, 671)(340, 1535)(341, 1440)(342, 1409)(343, 794)(344, 1179)(345, 1348)(346, 860)(347, 512)(348, 1520)(349, 1586)(350, 916)(351, 1173)(352, 1174)(353, 930)(355, 370)(356, 717)(357, 753)(360, 1264)(364, 738)(365, 388)(366, 1164)(367, 911)(368, 1089)(369, 1396)(373, 790)(374, 633)(375, 404)(376, 907)(377, 428)(378, 929)(380, 912)(381, 1237)(383, 1599)(384, 648)(385, 572)(386, 1503)(389, 952)(390, 850)(392, 1469)(393, 539)(394, 1068)(395, 967)(397, 1419)(399, 1562)(401, 961)(403, 508)(405, 1504)(407, 1342)(408, 1583)(409, 771)(410, 1369)(411, 802)(412, 1064)(413, 1123)(414, 1398)(415, 1517)(416, 1456)(417, 777)(418, 1024)(419, 1537)(420, 1399)(423, 1028)(425, 1347)(426, 1309)(427, 1441)(429, 697)(430, 527)(432, 686)(434, 1555)(436, 582)(437, 882)(438, 1152)(439, 1204)(440, 1079)(441, 729)(443, 806)(445, 462)(448, 1092)(449, 1085)(451, 1481)(452, 1238)(453, 1581)(454, 812)(455, 641)(456, 1355)(457, 1284)(458, 754)(459, 910)(460, 937)(461, 781)(464, 1590)(465, 734)(466, 1483)(467, 1032)(468, 722)(469, 592)(470, 558)(471, 1524)(472, 1200)(473, 1538)(474, 1308)(475, 574)(476, 963)(479, 1245)(480, 1471)(482, 1006)(484, 1117)(486, 627)(487, 1554)(488, 1260)(490, 752)(492, 719)(493, 499)(495, 694)(496, 1373)(497, 507)(498, 943)(500, 547)(501, 514)(502, 1307)(503, 852)(504, 1429)(505, 1597)(506, 580)(509, 918)(510, 581)(511, 1415)(513, 1202)(515, 869)(518, 793)(519, 718)(520, 1401)(522, 1367)(523, 889)(525, 1332)(526, 1444)(528, 1201)(529, 959)(532, 914)(533, 1475)(535, 768)(537, 1119)(540, 1561)(541, 668)(542, 1210)(543, 1433)(545, 1531)(546, 598)(548, 657)(549, 784)(551, 557)(554, 816)(556, 1527)(559, 841)(560, 609)(561, 928)(562, 1511)(564, 1026)(565, 1080)(566, 1297)(568, 988)(569, 1061)(570, 1379)(571, 579)(573, 913)(575, 1454)(577, 1019)(578, 796)(584, 1365)(585, 880)(586, 813)(587, 873)(588, 824)(590, 595)(593, 1579)(594, 1439)(599, 629)(600, 854)(601, 979)(602, 1016)(604, 1156)(605, 1343)(606, 807)(607, 1421)(608, 915)(610, 1275)(611, 1076)(612, 1453)(613, 936)(614, 1545)(615, 1422)(616, 1482)(619, 1246)(620, 842)(625, 1417)(626, 634)(630, 1532)(632, 707)(636, 1286)(637, 1170)(638, 1103)(639, 1158)(640, 1040)(642, 1215)(643, 1466)(644, 1198)(645, 1214)(646, 653)(647, 1129)(650, 658)(651, 1405)(652, 732)(654, 1277)(655, 836)(659, 1018)(660, 1336)(661, 855)(662, 1120)(663, 1116)(664, 1261)(665, 810)(667, 1589)(669, 740)(670, 884)(672, 1371)(674, 1533)(676, 904)(679, 1437)(680, 1462)(681, 1162)(682, 875)(683, 1557)(684, 1144)(685, 1055)(687, 1418)(690, 1050)(691, 1478)(692, 1046)(693, 1445)(695, 1101)(696, 1502)(698, 1447)(699, 1125)(700, 1350)(701, 1148)(702, 780)(703, 1592)(704, 1315)(706, 1001)(709, 1271)(710, 955)(711, 1265)(712, 1180)(713, 1143)(714, 1484)(715, 969)(716, 1059)(720, 1253)(721, 835)(724, 1197)(725, 1541)(726, 949)(727, 932)(731, 1066)(733, 1560)(735, 1384)(736, 1020)(739, 1549)(741, 1393)(742, 1126)(743, 1233)(745, 925)(746, 821)(747, 1394)(748, 1338)(750, 1190)(751, 1330)(758, 1301)(760, 1224)(761, 1320)(764, 782)(765, 1176)(767, 1263)(770, 1027)(772, 938)(773, 788)(774, 1477)(775, 1131)(776, 1025)(778, 1413)(779, 1312)(785, 980)(786, 948)(789, 1015)(791, 1110)(795, 1294)(797, 1474)(800, 1100)(803, 978)(804, 1546)(805, 1153)(808, 1305)(809, 1359)(814, 846)(818, 1113)(819, 858)(820, 1269)(823, 1584)(825, 827)(826, 1302)(828, 975)(831, 1403)(833, 1569)(837, 881)(838, 996)(839, 1509)(840, 1449)(843, 1184)(845, 876)(847, 891)(848, 1408)(849, 1335)(851, 994)(856, 1425)(863, 947)(864, 977)(867, 1410)(868, 1067)(870, 1081)(871, 1508)(872, 992)(877, 1334)(878, 908)(886, 893)(887, 1380)(888, 1406)(890, 1518)(895, 1288)(896, 1414)(898, 1035)(899, 1543)(901, 1513)(902, 1208)(903, 1283)(909, 941)(917, 1058)(920, 1183)(921, 1358)(923, 946)(924, 1521)(926, 1376)(927, 1426)(931, 1407)(933, 1211)(934, 1168)(939, 1442)(940, 1580)(942, 1530)(944, 986)(950, 1563)(953, 1282)(954, 1065)(958, 1150)(962, 1219)(968, 1299)(971, 1255)(973, 1542)(974, 1593)(976, 1457)(981, 1461)(983, 1436)(984, 1522)(985, 1230)(989, 1451)(990, 1147)(995, 1236)(997, 1268)(999, 1553)(1000, 1295)(1002, 1234)(1005, 1240)(1007, 1470)(1008, 1195)(1009, 1395)(1010, 1043)(1011, 1194)(1012, 1323)(1013, 1206)(1022, 1041)(1023, 1360)(1029, 1278)(1030, 1171)(1031, 1096)(1033, 1155)(1036, 1354)(1037, 1389)(1038, 1159)(1039, 1199)(1042, 1572)(1048, 1121)(1052, 1178)(1053, 1248)(1054, 1118)(1056, 1494)(1060, 1427)(1062, 1420)(1072, 1516)(1073, 1568)(1074, 1577)(1077, 1392)(1082, 1259)(1084, 1235)(1086, 1397)(1088, 1137)(1091, 1209)(1094, 1289)(1095, 1111)(1098, 1337)(1109, 1318)(1112, 1381)(1114, 1434)(1124, 1166)(1128, 1250)(1130, 1467)(1132, 1266)(1134, 1361)(1135, 1391)(1136, 1291)(1141, 1438)(1142, 1223)(1146, 1585)(1151, 1226)(1160, 1228)(1161, 1473)(1167, 1272)(1169, 1339)(1172, 1203)(1182, 1464)(1185, 1364)(1187, 1251)(1191, 1468)(1192, 1239)(1193, 1383)(1196, 1344)(1207, 1489)(1212, 1387)(1213, 1455)(1218, 1267)(1220, 1505)(1225, 1507)(1227, 1496)(1229, 1443)(1231, 1501)(1232, 1540)(1242, 1510)(1243, 1571)(1244, 1430)(1256, 1331)(1274, 1329)(1276, 1556)(1279, 1528)(1281, 1491)(1285, 1428)(1290, 1385)(1292, 1402)(1296, 1500)(1298, 1529)(1304, 1493)(1314, 1321)(1316, 1352)(1317, 1495)(1319, 1450)(1322, 1573)(1325, 1327)(1326, 1400)(1340, 1465)(1341, 1514)(1345, 1351)(1349, 1575)(1357, 1370)(1363, 1526)(1378, 1476)(1411, 1431)(1412, 1598)(1435, 1498)(1446, 1488)(1459, 1480)(1463, 1595)(1472, 1512)(1486, 1552)(1492, 1519)(1544, 1558)(1565, 1588)(1566, 1576)(1587, 1596), G!(1, 736)(2, 240)(3, 1091)(4, 543)(5, 186)(6, 161)(7, 1011)(8, 990)(9, 226)(10, 713)(11, 1264)(12, 610)(13, 1498)(14, 373)(15, 712)(16, 766)(17, 539)(18, 224)(19, 96)(20, 1489)(21, 52)(22, 422)(23, 318)(24, 1486)(25, 622)(26, 1596)(27, 619)(28, 484)(29, 1569)(30, 229)(31, 1148)(32, 1078)(33, 55)(34, 1573)(35, 1069)(36, 560)(37, 868)(38, 1385)(39, 1000)(40, 895)(41, 194)(42, 632)(43, 1061)(44, 1155)(45, 1116)(46, 88)(47, 796)(48, 1119)(49, 211)(50, 912)(51, 349)(53, 1334)(54, 688)(56, 1323)(57, 1462)(58, 128)(59, 511)(60, 1550)(61, 1312)(62, 155)(63, 1278)(64, 698)(65, 337)(66, 1404)(67, 1084)(68, 102)(69, 979)(70, 615)(71, 348)(72, 84)(73, 1131)(74, 1353)(75, 411)(76, 815)(77, 280)(78, 1187)(79, 849)(80, 678)(81, 1584)(82, 1226)(83, 747)(85, 1025)(86, 496)(87, 812)(89, 465)(90, 1337)(91, 1509)(92, 1508)(93, 1379)(94, 446)(95, 661)(97, 1266)(98, 580)(99, 1150)(100, 491)(101, 106)(103, 1357)(104, 266)(105, 830)(107, 262)(108, 1551)(109, 204)(110, 1272)(111, 136)(112, 690)(113, 290)(114, 521)(115, 325)(116, 770)(117, 1243)(118, 844)(119, 1545)(120, 244)(121, 1318)(122, 1419)(123, 272)(124, 1598)(125, 554)(126, 1465)(127, 327)(129, 592)(130, 1406)(131, 1068)(132, 1102)(133, 439)(134, 1397)(135, 1432)(137, 694)(138, 1002)(139, 954)(140, 586)(141, 909)(142, 243)(143, 385)(144, 742)(145, 1041)(146, 1015)(147, 1270)(148, 1314)(149, 545)(150, 252)(151, 1504)(152, 1045)(153, 370)(154, 1558)(156, 376)(157, 374)(158, 159)(160, 384)(162, 426)(163, 173)(164, 1429)(165, 297)(166, 1600)(167, 675)(168, 1118)(169, 354)(170, 449)(171, 504)(172, 1154)(174, 1261)(175, 1407)(176, 1282)(177, 1403)(178, 993)(179, 797)(180, 519)(181, 1052)(182, 443)(183, 980)(184, 1511)(185, 420)(187, 328)(188, 548)(189, 1333)(190, 813)(191, 947)(192, 1206)(193, 1125)(195, 487)(196, 633)(197, 877)(198, 476)(199, 1188)(200, 360)(201, 989)(202, 793)(203, 247)(205, 1316)(206, 1290)(207, 925)(208, 1065)(209, 1140)(210, 486)(212, 1136)(213, 1593)(214, 1089)(215, 239)(216, 594)(217, 547)(218, 699)(219, 1160)(220, 841)(221, 1184)(222, 1494)(223, 642)(225, 959)(227, 1528)(228, 399)(230, 1228)(231, 1095)(232, 570)(233, 1474)(234, 407)(235, 1097)(236, 1477)(237, 628)(238, 1305)(241, 762)(242, 460)(245, 283)(246, 1326)(248, 935)(249, 1062)(250, 741)(251, 1430)(253, 1591)(254, 967)(255, 462)(256, 1523)(257, 1348)(258, 754)(259, 819)(260, 734)(261, 585)(263, 1412)(264, 709)(265, 876)(267, 475)(268, 522)(269, 1141)(270, 1005)(271, 577)(273, 361)(274, 1200)(275, 1114)(276, 1042)(277, 1425)(278, 1595)(279, 358)(281, 834)(282, 1162)(284, 700)(285, 597)(286, 1235)(287, 684)(288, 710)(289, 1567)(291, 525)(292, 1421)(293, 523)(294, 515)(295, 644)(296, 1454)(298, 646)(299, 609)(300, 1351)(301, 971)(302, 1075)(303, 1019)(304, 1541)(305, 1066)(306, 780)(307, 1017)(308, 1021)(309, 776)(310, 1112)(311, 1304)(312, 584)(313, 992)(314, 472)(315, 714)(316, 761)(317, 1103)(319, 1038)(320, 510)(321, 433)(322, 664)(323, 1592)(324, 1409)(326, 1215)(329, 665)(330, 546)(331, 334)(332, 1386)(333, 654)(335, 905)(336, 1280)(338, 837)(339, 972)(340, 421)(341, 724)(342, 658)(343, 920)(344, 1375)(345, 490)(346, 944)(347, 369)(350, 379)(351, 1105)(352, 964)(353, 1408)(355, 527)(356, 1145)(357, 1418)(359, 1124)(362, 1461)(363, 1134)(364, 757)(365, 696)(366, 903)(367, 542)(368, 798)(371, 1564)(372, 827)(375, 1597)(377, 768)(378, 1438)(380, 1250)(381, 501)(382, 933)(383, 1572)(386, 1127)(387, 419)(388, 1578)(389, 848)(390, 952)(391, 635)(392, 497)(393, 436)(394, 737)(395, 1524)(396, 498)(397, 1128)(398, 997)(400, 847)(401, 927)(402, 680)(403, 453)(404, 1471)(405, 1117)(406, 1197)(408, 1480)(409, 750)(410, 1082)(412, 1008)(413, 839)(414, 1417)(415, 1585)(416, 1363)(417, 938)(418, 1413)(423, 660)(424, 1400)(425, 1496)(427, 1218)(428, 551)(429, 432)(430, 779)(431, 1258)(434, 1174)(435, 1410)(437, 459)(438, 1217)(440, 1293)(441, 928)(442, 1548)(444, 937)(445, 1566)(447, 518)(448, 918)(450, 1405)(451, 1106)(452, 1221)(454, 976)(455, 1521)(456, 1555)(457, 669)(458, 1032)(461, 1111)(463, 739)(464, 792)(466, 1212)(467, 817)(468, 1231)(469, 764)(470, 1346)(471, 1586)(473, 1057)(474, 808)(477, 1047)(478, 1581)(479, 1130)(480, 1372)(481, 824)(482, 1153)(483, 1526)(485, 857)(488, 1147)(489, 1279)(492, 1433)(493, 1074)(494, 1360)(495, 1294)(499, 1399)(500, 1392)(502, 902)(503, 1059)(505, 1370)(506, 864)(507, 1580)(508, 901)(509, 835)(512, 771)(513, 1256)(514, 1087)(516, 640)(517, 561)(520, 1390)(524, 821)(526, 1491)(528, 746)(529, 1022)(530, 1483)(531, 1414)(532, 1376)(533, 1317)(534, 717)(535, 777)(536, 1067)(537, 852)(538, 1328)(540, 676)(541, 1006)(544, 1367)(549, 1416)(550, 1028)(552, 818)(553, 1378)(555, 988)(556, 1530)(557, 772)(558, 1109)(559, 845)(562, 1324)(563, 1063)(564, 1331)(565, 836)(566, 878)(567, 1276)(568, 1539)(569, 893)(571, 795)(572, 1371)(573, 1427)(574, 1315)(575, 949)(576, 600)(578, 1177)(579, 1288)(581, 1499)(582, 1033)(583, 603)(587, 1589)(588, 898)(589, 943)(590, 613)(591, 789)(593, 866)(595, 1223)(596, 1565)(598, 1249)(599, 731)(601, 1271)(602, 1037)(604, 697)(605, 748)(606, 1132)(607, 1080)(608, 1054)(611, 1241)(612, 910)(614, 716)(616, 1151)(617, 1343)(618, 1470)(620, 1495)(621, 887)(623, 1302)(624, 1094)(625, 861)(626, 1092)(627, 719)(629, 1350)(630, 1107)(631, 1366)(634, 978)(636, 1420)(637, 1451)(638, 1126)(639, 1435)(641, 1156)(643, 1515)(645, 1434)(647, 1225)(648, 960)(649, 1129)(650, 1253)(651, 1260)(652, 1490)(653, 1518)(655, 891)(656, 985)(657, 1394)(659, 1527)(662, 1321)(663, 1359)(666, 936)(667, 672)(668, 759)(670, 1436)(671, 718)(673, 727)(674, 1529)(677, 942)(679, 786)(681, 1473)(682, 1203)(683, 1517)(685, 1426)(686, 924)(687, 1238)(689, 1198)(691, 838)(692, 850)(693, 703)(695, 1443)(701, 1227)(702, 1298)(704, 1211)(705, 907)(706, 829)(707, 1513)(708, 1467)(711, 1485)(715, 822)(720, 1463)(721, 803)(722, 1186)(723, 1115)(725, 1355)(726, 1341)(728, 1540)(729, 809)(730, 965)(732, 1167)(733, 1532)(735, 1283)(738, 820)(740, 1458)(743, 1520)(744, 1053)(745, 1344)(749, 1369)(751, 1178)(752, 1456)(753, 1587)(755, 784)(756, 1401)(758, 917)(760, 1307)(763, 966)(765, 833)(767, 790)(769, 1590)(773, 1079)(774, 1575)(775, 1560)(778, 1557)(781, 1398)(782, 1246)(783, 1447)(785, 1303)(787, 991)(788, 1330)(791, 1247)(794, 882)(799, 1472)(800, 1176)(801, 1020)(802, 1510)(804, 825)(805, 1252)(806, 1159)(807, 1325)(810, 1497)(811, 1576)(814, 1043)(816, 1234)(823, 1039)(826, 983)(828, 1588)(831, 1342)(832, 1388)(840, 1466)(842, 1101)(843, 1402)(846, 872)(851, 1335)(853, 1422)(854, 1085)(855, 1152)(856, 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geometries := [* *]; for i in [1..#involutions] do G1 := sub; G2 := sub; G3 := sub; Append(~geometries,CosetGeometry(G,{G1,G2,G3})); end for;