sml768.z

#############################################################################
##
#W  sml768.z               GAP library of groups           Hans Ulrich Besche
##                                               Bettina Eick, Eamonn O'Brien
##

SMALL_GROUP_LIB[ 768 ].pnil := rec( 2syl :=
[ 2, 35, 36, 38, 39, 305, 306, 542, 543, 544, 722, 732, 737, 810, 820, 825,
826, 833, 834, 835, 839, 840, 1087, 1089, 1111, 1114, 1115, 1118, 1119, 1123,
1124, 1304, 1305, 1494, 1497, 1502, 1503, 1518, 1521, 1529, 1533, 1534, 1791,
1792, 1801, 1805, 1806, 3196, 3199, 3288, 3291, 3292, 3304, 3307, 3324, 3327,
3346, 3348, 3378, 3379, 3571, 3574, 3599, 3600, 3661, 3666, 3671, 3678, 3679,
3683, 3686, 3687, 3923, 3924, 4286, 4299, 4300, 4310, 4325, 4326, 4368, 4378,
4379, 4382, 4383, 5525, 5527, 5530, 5667, 5668, 5672, 5760, 5761, 5762, 5765,
5882, 5883, 5886, 5887, 5890, 6366, 6452, 6647, 6723, 6725, 6732, 6732, 6733,
6734, 6735, 6736, 6737, 6738, 6748, 6757, 6760, 6762, 6781, 6782, 6796, 6797,
6798, 6799, 6799, 6799, 6800, 6814, 6815, 6815, 6815, 6815, 6817, 6818, 6822,
6829, 6831, 6837, 6839, 6843, 6844, 6845, 6847, 6848, 6850, 6853, 6854, 7289,
7290, 7309, 7310, 7319, 7321, 7324, 7325, 7337, 7338, 7341, 7342, 7550, 7560,
7589, 7597, 7606, 7608, 7623, 7624, 7625, 7639, 7643, 7644, 7645, 7649, 7653,
7661, 7664, 7666, 7667, 7668, 7671, 7674, 7676, 7680, 7681, 7682, 7698, 7699,
7700, 7701, 7736, 7745, 7815, 7824, 7861, 7862, 7873, 7877, 7887, 7888, 7897,
7898, 8129, 8130, 8142, 8143, 8145, 8146, 8159, 8160, 8164, 8177, 8178, 8186,
8187, 8189, 8190, 8198, 8199, 8202, 8246, 8455, 8468, 8935, 8935, 8974, 9231,
9236, 9285, 10041, 10042, 10060, 10069, 10073, 10079, 10102, 10123, 10137,
10192, 10201, 10204, 10206, 10211, 10214, 10218, 10269, 10283, 10290, 10295,
10296, 10297, 10297, 10297, 10298, 10298, 10298, 10299, 10303, 10304, 10308,
10310, 10320, 10326, 10327, 10331, 10332, 10340, 10341, 10402, 10407, 10413,
10418, 10419, 10420, 10426, 10427, 10495, 10497, 10506, 10508, 10515, 10516,
10537, 10538, 10594, 10599, 10606, 10607, 10621, 10622, 10642, 10643, 10676,
10680, 10681, 10682, 10684, 10708, 10709, 10710, 10711, 10761, 10765, 10770,
10771, 10772, 10776, 10777, 10814, 10816, 10823, 10825, 11966, 11976, 12061,
12071, 12082, 12084, 12580, 12587, 12589, 12721, 12731, 12733, 12741, 13313,
13315, 13316, 13317, 13320, 13324, 13325, 13326, 13327, 13327, 13327, 13328,
13328, 13328, 13329, 13331, 13332, 13336, 13337, 13339, 13340, 13343, 13344,
13346, 13347, 13348, 13357, 13358, 13485, 13486, 13487, 13494, 13495, 13496,
13503, 13510, 13557, 13560, 13565, 13566, 13567, 13568, 13595, 13596, 13597,
13598, 13599, 13600, 13758, 13759, 13760, 13761, 13777, 13778, 13779, 13780,
14426, 14428, 14430, 14432, 14467, 14468, 14469, 14470, 14471, 14472, 14652,
14654, 14656, 14658, 14668, 14669, 14671, 14672, 15496, 15500, 15502, 15504,
15506, 15508, 15516, 15518, 15522, 15524, 15526, 15528, 15530, 15538, 15708,
15712, 15714, 15720, 15722, 15726, 15728, 15734, 16294, 16297, 16299, 16300,
16343, 16345, 16346, 16347, 16363, 16366, 16368, 16369, 16421, 16422, 16453,
16454, 16455, 16456, 16457, 16458, 16461, 16462, 16551, 16552, 16553, 16554,
16583, 16584, 16585, 16586, 16608, 16609, 16610, 16710, 16711, 16782, 16783,
22644, 22645, 22646, 22647, 22672, 22673, 22674, 22697, 22698, 22699, 23224,
23225, 23226, 23859, 23860, 23861, 24064, 24065, 25694, 25696, 25698, 25703,
25704, 25705, 25784, 25786, 25788, 25789, 25790, 25791, 25792, 25793, 25846,
25848, 25850, 25855, 25856, 25857, 25861, 25862, 25863, 25864, 25865, 25866,
25867, 25869, 25870, 25872, 25873, 25874, 25875, 25882, 25883, 25884, 25885,
25886, 25887, 25888, 25889, 25914, 25915, 25916, 25917, 25918, 25919, 25920,
25921, 25922, 25935, 25936, 25937, 25963, 25964, 25965, 26066, 26067, 26070,
26071, 26076, 26077, 26080, 26081, 26148, 26149, 26150, 26151, 26154, 26155,
26156, 26157, 26253, 26254, 26255, 26259, 26260, 26261, 26288, 26289, 26290,
26295, 26296, 26297, 26308, 26309, 26313, 26314, 26315, 26317, 26318, 26322,
26323, 26325, 26326, 26328, 26329, 26330, 26337, 26339, 26340, 26341, 26348,
26350, 26351, 26352, 26359, 26361, 26362, 26363, 26369, 26370, 26371, 26373,
26374, 26376, 26377, 26378, 26380, 26381, 26382, 26386, 26387, 26389, 26390,
26392, 26393, 26394, 26398, 26399, 26400, 26402, 26460, 26465, 26466, 26473,
26484, 26486, 26490, 26493, 26550, 26552, 26554, 26555, 26913, 26914, 26917,
26918, 26933, 26934, 26937, 26946, 26947, 26950, 26959, 26960, 26961, 26962,
26963, 26964, 26965, 26970, 26971, 26972, 26973, 26973, 26973, 26974, 26974,
26974, 26975, 26975, 26975, 26976, 26977, 26979, 26980, 26980, 26980, 26981,
26981, 26981, 26982, 26984, 26985, 26986, 26986, 26986, 26987, 26987, 26987,
26989, 26990, 26991, 26991, 26991, 26992, 26993, 26995, 26996, 26996, 26996,
26998, 26998, 26998, 27000, 27001, 27002, 27003, 27004, 27006, 27007, 27009,
27015, 27021, 27024, 27084, 27088, 27089, 27090, 27100, 27101, 27102, 27112,
27113, 27116, 27117, 27146, 27148, 27149, 27157, 27158, 27158, 27161, 27162,
27163, 27170, 27171, 27172, 27180, 27181, 27184, 27185, 27237, 27238, 27245,
27246, 27247, 27250, 27251, 27279, 27281, 27282, 27283, 27299, 27300, 27301,
27323, 27324, 27325, 27326, 27332, 27337, 27339, 27341, 27341, 27341, 27343,
27500, 27512, 27514, 27517, 27518, 27519, 27519, 27519, 27520, 27520, 27520,
27521, 27522, 27522, 27522, 27523, 27524, 27524, 27524, 27525, 27526, 27528,
27528, 27528, 27529, 27532, 27536, 27536, 27536, 27537, 27539, 27540, 27553,
27559, 27586, 27593, 27598, 27605, 27606, 27610, 27618, 27620, 27627, 27629,
28334, 28357, 28378, 28403, 28420, 28426, 28432, 28434, 28444, 28451, 28469,
28486, 28492, 28498, 28675, 28688, 28699, 28711, 28725, 28736, 28745, 28759,
28774, 28789, 28804, 28819, 28833, 28842, 28856, 28871, 28886, 28898, 28902,
28906, 28908, 28908, 28908, 28909, 28912, 28915, 28915, 28915, 28925, 28936,
28945, 28959, 28971, 28984, 28993, 29006, 29017, 29028, 29037, 29041, 29045,
29047, 29047, 29047, 29048, 29051, 29054, 29054, 29054, 29064, 29066, 29070,
29070, 29070, 29072, 29073, 29078, 29079, 29079, 29079, 29080, 29094, 29107,
29140, 29154, 29167, 29416, 29417, 29418, 29419, 29420, 29421, 29422, 29423,
29432, 29433, 29434, 29435, 29436, 29443, 29444, 29445, 29446, 29453, 29454,
29455, 29462, 29463, 29470, 29471, 29528, 29528, 29528, 29529, 29530, 29531,
29536, 29537, 29538, 29538, 29538, 29545, 29545, 29545, 29546, 29556, 29560,
29561, 29563, 29563, 29563, 29564, 29565, 29566, 29571, 29572, 29573, 29573,
29573, 29580, 29580, 29580, 29581, 29591, 29595, 29596, 29598, 29599, 29600,
29602, 29605, 29610, 29617, 29621, 29629, 29630, 29631, 29632, 29634, 29644,
29645, 29651, 29659, 29659, 29659, 29659, 29660, 29662, 29663, 29663, 29663,
29663, 29664, 29670, 29673, 29676, 29677, 29678, 29682, 29684, 29689, 30463,
30516, 30551, 30552, 30591, 30592, 30599, 30601, 30630, 30631, 38427, 38446,
38467, 38482, 38497, 38958, 38970, 38980, 38990, 38998, 39008, 39312, 39315,
39316, 39318, 39321, 39420, 39830, 39984, 40006, 40184, 40551, 40692, 40694,
40721, 40722, 40763, 40764, 40780, 40781, 40790, 40792, 40802, 40803, 40806,
40812, 45081, 45086, 45159, 45186, 45215, 45247, 45259, 45274, 45274, 45274,
45275, 45279, 45282, 45287, 45289, 45293, 45295, 45295, 45295, 45386, 45460,
45730, 45753, 45902, 45913, 45946, 45976, 45981, 45992, 46003, 46031, 46053,
46066, 46073, 46078, 46146, 46156, 46157, 46167, 46228, 46243, 46284, 46288,
46290, 46291, 46292, 46295, 46330, 46343, 46352, 46361, 46368, 46371, 46376,
46377, 46481, 47682, 48232, 48756, 49332, 50105, 50388, 50657, 51157, 51248,
51448, 51711, 51738, 51837, 51906, 51932, 51963, 51969, 51975, 51977, 51978,
52180, 52584, 52765, 52804, 52863, 52912, 53014, 53015, 53020, 53025, 53033,
53036, 53037, 53038, 53039, 53040, 53041, 53043, 53044, 53045, 53046, 53047,
53048, 53049, 53051, 53052, 53053, 53054, 53055, 53057, 53058, 53059, 53060,
53061, 53062, 53063, 53064, 53065, 53066, 53067, 53068, 53069, 53070, 53072,
53073, 53074, 53075, 53076, 53077, 53078, 53079, 53080, 53081, 53082, 53083,
53084, 53086, 53087, 53088, 53089, 53090, 53091, 53092, 53094, 53095, 53096,
53097, 53098, 53099, 53100, 53101, 53102, 53103, 53104, 53115, 53116, 53117,
53118, 53119, 53120, 53133, 53134, 53135, 53136, 53137, 53138, 53140, 53141,
53142, 53159, 53160, 53161, 53162, 53163, 53164, 53165, 53166, 53171, 53172,
53173, 53173, 53173, 53174, 53178, 53179, 53182, 53182, 53182, 53183, 53184,
53191, 53201, 53206, 53230, 53232, 53236, 53241, 53243, 53246, 53251, 53262,
53264, 53266, 53271, 53272, 53289, 53291, 53291, 53292, 53295, 53296, 53296,
53313, 53316, 53317, 53319, 53321, 53323, 53331, 53333, 53335, 53336, 53337,
53338, 53339, 53340, 53360, 53361, 53362, 53363, 53364, 53365, 53366, 53367,
53368, 53369, 53376, 53377, 53378, 53379, 53380, 53380, 53380, 53381, 53381,
53381, 53382, 53383, 53384, 53385, 53386, 53387, 53388, 53388, 53388, 53389,
53390, 53390, 53390, 53391, 53392, 53393, 53394, 53395, 53396, 53416, 53417,
53418, 53419, 53420, 53421, 53422, 53423, 53424, 53426, 53427, 53428, 53445,
53446, 53447, 53448, 53449, 53450, 53451, 53452, 53453, 53458, 53459, 53460,
53461, 53462, 53463, 53464, 53465, 53466, 53482, 53483, 53484, 53485, 53486,
53487, 53488, 53489, 53490, 53491, 53492, 53493, 53509, 53510, 53511, 53512,
53513, 53514, 53590, 53591, 53592, 53594, 53595, 53596, 53610, 53611, 53612,
53613, 53614, 53615, 53616, 53617, 53618, 53619, 53621, 53622, 53634, 53635,
53636, 53637, 53638, 53639, 53640, 53641, 53642, 53644, 53653, 53654, 53655,
53656, 54283, 54284, 54287, 54288, 54291, 54305, 54307, 54309, 54310, 54339,
54340, 54343, 54345, 54354, 54356, 54375, 54376, 54379, 54381, 54390, 54392,
54413, 54414, 54417, 54422, 54423, 54424, 54453, 54454, 54457, 54458, 54805,
54806, 54808, 54809, 54811, 54812, 54825, 54826, 54828, 54831, 54832, 54834,
54868, 54869, 54871, 54872, 54874, 54875, 54888, 54889, 54891, 54894, 54895,
54897, 54935, 54936, 54939, 54940, 54945, 54946, 54987, 54988, 54989, 54990,
54991, 54993, 55083, 55084, 55087, 55088, 55093, 55094, 55135, 55136, 55137,
55138, 55139, 55141, 55345, 55347, 55348, 55350, 55351, 55352, 55381, 55382,
55385, 55386, 55401, 55403, 55404, 55408, 55441, 55442, 55457, 55459, 55460,
55464, 55497, 55498, 55513, 55514, 55517, 55518, 55522, 55576, 55577, 55582,
55583, 55608, 55608, 55609, 55610, 55610, 55610, 55611, 55612, 55612, 55613,
55614, 55615, 55616, 55617, 55618, 55620, 55621, 55622, 55623, 55624, 55625,
55626, 55626, 55626, 55626, 55626, 55627, 55627, 55628, 55628, 55629, 55630,
55631, 55631, 55631, 55632, 55632, 55632, 55633, 55634, 55634, 55634, 55635,
55635, 55635, 55636, 55637, 55637, 55638, 55639, 55639, 55640, 55640, 55641,
55642, 55642, 55643, 55643, 55643, 55644, 55645, 55646, 55647, 55648, 55649,
55650, 55650, 55650, 55651, 55652, 55652, 55652, 55653, 55654, 55655, 55656,
55657, 55658, 55658, 55658, 55659, 55660, 55661, 55662, 55663, 55664, 55665,
55666, 55668, 55669, 55672, 55674, 55675, 55675, 55675, 55676, 55676, 55676,
55676, 55676, 55676, 55676, 55677, 55678, 55679, 55680, 55680, 55680, 55682,
55682, 55682, 55683, 55684, 55684, 55684, 55685, 55686, 55686, 55686, 55687,
55688, 55688, 55688, 55689, 55690, 55691, 55692, 55693, 55694, 55695, 55697,
55697, 55697, 55698, 55699, 55700, 55700, 55700, 55700, 55700, 55701, 55701,
55701, 55703, 55704, 55704, 55705, 55705, 55706, 55724, 55725, 55745, 55748,
55770, 55771, 55772, 55773, 55774, 55775, 55776, 55777, 55778, 55779, 55780,
55781, 55782, 55783, 55784, 55788, 55789, 55790, 55793, 55794, 55795, 55798,
55799, 55800, 55801, 55804, 55805, 55805, 55805, 55814, 55820, 55827, 55828,
55829, 55831, 55832, 55833, 55836, 55837, 55837, 55837, 55838, 55839, 55840,
55841, 55842, 55845, 55846, 55847, 55849, 55859, 55881, 55882, 55883, 55883,
55883, 55885, 55887, 55891, 55892, 55893, 55901, 55904, 55905, 55907, 55910,
55911, 55931, 55934, 55935, 55937, 55940, 55941, 55960, 55961, 55964, 55967,
55968, 55968, 55969, 55969, 55970, 55970, 55970, 55970, 55970, 55972, 55973,
55974, 55974, 55974, 55975, 55975, 55976, 55976, 55977, 55977, 55981, 55982,
55983, 55984, 55985, 55985, 55985, 55986, 55987, 55987, 55987, 55988, 55989,
55989, 55989, 55990, 55991, 55992, 55993, 55994, 55995, 55996, 55997, 55998,
55999, 56002, 56003, 56004, 56007, 56008, 56010, 56014, 56020, 56021, 56022,
56023, 56024, 56025, 56025, 56026, 56026, 56027, 56027, 56027, 56028, 56028,
56028, 56028, 56032, 56033, 56034, 56035, 56036, 56036, 56036, 56040, 56045,
56049, 56054, 56058, 56059, 56059, 56060, 56060, 56061, 56061, 56061, 56062,
56062, 56062, 56063, 56063, 56064, 56064, 56065, 56065, 56066, 56066, 56067,
56067, 56068, 56069, 56070, 56071, 56072, 56072, 56072, 56073, 56073, 56073,
56074, 56074, 56074, 56075, 56076, 56077, 56078, 56079, 56079, 56080, 56080,
56081, 56081, 56082, 56082, 56082, 56083, 56083, 56084, 56084, 56084, 56084,
56084, 56085, 56085, 56085, 56085, 56085, 56086, 56086, 56086, 56086, 56086,
56087, 56087, 56087, 56088, 56088, 56088, 56088, 56088, 56089, 56089, 56090,
56090, 56090, 56091, 56091, 56091, 56092, 56092, 56092, 56092 ], oper :=
[ 17456517598002657319, 16634755920641191944, 18036248863449215237,
6360085275270923443, 18847100477745468931, 7917752869889846741,
8580753434709990351, 10994519239187364493, 18778209959236008718,
16263083912320217331, 10822241396294244174, 11044680769386539088,
9952901325278621811, 9859004524630111807, 11045263769930928728,
10748479494725131087, 6947304738084466563, 5538911073839372923,
6572149489147778921, 9476856671601008089, 15602935583218623979,
7541153611747299482, 5176130046036054409, 6738428010312511442,
16704771860692737757, 5393407626397200531, 8058649555992786848,
9473998856503612647, 15515918262986361531, 5694493777289005449,
7773112706944607686, 18467339502747995629, 16597093863158498996,
17727127247098232047, 14671760351823263637, 12543534881395181200,
18082726125900316641, 14471750868856608960, 13932103085277810046,
11932719522512549212, 18085600771391610084, 16229435781370996154,
9717237864921392976, 10402414930204634782, 15198483413958847156,
12847524819098326448, 16023088409741910719, 2784058605458844722,
3371019068930762046, 6158232530213511999, 3148559519412795945,
7124921433363064145, 5051774860978183476, 7047408147521782336,
2629611662113877518, 3001046927840342836, 14404003928337267103,
6501272358041838198, 15518509251723612340, 4943024005290224717,
14482084518520420519, 14632789046815190204, 17818140367679641847,
6141687717069871524, 8652226002525674935, 17826779969818682892,
8351972869701181844, 12942100965518326073, 9502959360948815314,
14932756272309227756, 15822781720697848035, 16700446436407291335,
14602021154027482020, 16697913786529128453, 14970572809384723882,
17875243024414832380, 15339385680694968745, 14012513422325735069,
14916662150310377682, 12679305539468190604, 9587550571553129339,
17358874953266887402, 18918585278911635750, 13790658170932725936,
14235527952257616302, 16838218490709320904, 9953192781875385958,
9564831453714266952, 10173031110566211423, 10768627830179346818,
10178535981108095886, 17504961440145339104, 15931209700955752873,
15265035164015216030, 18545137566294650366, 11339453683921551183,
10154638494881881666, 16671155108669409191, 16102041262811373266,
9586978786920140670, 15588819117326145194, 6128435648767081842,
14420996151777286854, 9562505057361569064, 9581486209701024074,
4694699312035244557, 6241081029884808586, 8058367064288088481,
18936404945115675177, 12761031217664312431, 12692453518870812545,
15287204906773360086, 10250858284741991562, 15561532506115310764,
9570313936024104297, 15730059968443481797, 10469553052909281162,
17112320938574233097, 3507382063081584786, 16467067060343301578,
15574419217572409773, 16240590434655932861, 9261496597704015040,
12829751102455524267, 15037321110238542458, 14745438515500249219,
8096571721647720938, 9319240428510071773, 12459354209350366807,
14707996121386952153, 17151655362343428845, 8502658478063407814,
9873317388295801147, 18947852630206379677, 18615745654717970418,
15585973652416139973, 9583808156452470897, 9858439497091059519,
10181970095910802312, 18160237221440710099, 6378936459958985020,
6284307571272102015, 15298951264037269687, 9317811889623643053,
16705056642471749071, 9918614157546512635, 14335131391862698922,
15445612933962500292, 14780090878649996804, 14706827864832945332,
7024524363925562018, 14483247217134104016, 5761622917819142501,
5616976041761206655, 6578792410142415009, 16114675517903865306,
15448576146345376279, 16181114035710999621, 15855734560928098422,
4663090954203489340, 4589320061582879788, 4143865059233140266,
3702443919838975022, 4068374345543874093, 9880288616132131695,
10159844086510911349, 10180826500470005652, 9585820594585748088,
10453454389664345199, 9860759166564796508, 1796007867069286464,
2316671043350300999, 10830244770997843617, 10906605452896947617,
2020466413949154629, 2242619918718542414, 9567434819017756007,
9719488135944528180, 10451414974014109252, 16689537616442185655,
10154266606994168629, 11952576348969167494, 10016279172979447371,
9573079982261449262, 9868132081882414640, 9573082194033942569,
13644738945142947162, 10990746640153869690, 15192421350925476749,
11935026937467568229, 16990075518230070230, 12451090032672251497,
9864781887788005214, 16823288014167807667, 9562248334636107085,
13861237196240721042, 17430920392734144982, 12898565373589161337,
14450174207835806583, 15134753654156419753, 14746090726604259710,
14160017109723187083, 14450174225285688187, 12601784461848042867,
9862171839179927876, 17339041722971585966, 16839654633398303164,
18009550679628444379, 10471843554905915001, 17283961651662019536,
12828858719822568868, 17359753921117754840, 13569053028302985618,
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