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GAP 4.8.9 installation with standard packages -- copy to your CoCalc project to get it

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#############################################################################
##
#W  id768.bta              GAP library of id's             Hans Ulrich Besche
##

ID_GROUP_TREE.next[768].next[2].next[20].next[1]:=
rec(
  fp:= [ 61, 472, 2992, 5032, 5394, 7239, 7601, 8595, 14575, 15107, 15141, 
20078, 22647, 28678, 29791, 30187, 31198, 31761, 37331, 40261, 42781, 44871, 
45233, 45301, 45864, 51844, 52377, 54364, 54550, 56884, 60279, 67423, 67603, 
68467, 69630, 70987, 74963, 75325, 80050, 82570, 84676, 90009, 94153, 99360 ],
  next:= [ rec(
    fp:= [ 57936, 74212, 92235, 98592 ],
    next:= [ 1087334, rec(
      desc:= [ 108003 ],
      fp:= [ 2, 12 ],
      next:= [ 1087342, 1087341 ] ), 1087336, rec(
      desc:= [ 108003 ],
      fp:= [ 2, 12 ],
      next:= [ 1087349, 1087348 ] ) ] ), rec(
    fp:= [ 8405, 15970, 38473, 55539, 84172 ],
    next:= [ 1087120, 1087311, 1087116, 1087109, 1087106 ] ), rec(
    fp:= [ 36484, 77791 ],
    next:= [ 1087209, 1087213 ] ), rec(
    fp:= [ 63670, 93439 ],
    next:= [ 1087517, 1087518 ] ), rec(
    fp:= [ 5528, 6403, 23417, 25407, 32256, 46418, 60882, 82594 ],
    next:= [ 1087492, 1087491, 1087267, 1087266, 1087490, 1087246, 1087248, 
1087265 ] ), rec(
    fp:= [ 26040, 37769 ],
    next:= [ 1087145, rec(
      desc:= [ 209002 ],
      fp:= [ 4, 14 ],
      next:= [ 1087139, 1087149 ] ) ] ), rec(
    fp:= [ 52228, 63774 ],
    next:= [ 1087335, 1087333 ] ), rec(
    fp:= [ 1805, 12593, 24640, 33094, 44347, 59028, 81759, 93272 ],
    next:= [ rec(
      desc:= [ 302009 ],
      fp:= [ 784, 89161 ],
      next:= [ rec(
        desc:= [ 206002 ],
        fp:= [ 4, 14 ],
        next:= [ 1087198, 1087199 ] ), 1087047 ] ), rec(
      desc:= [ 112011 ],
      fp:= [ 16, 818 ],
      next:= [ rec(
        desc:= [ 108003 ],
        fp:= [ 14, 212 ],
        next:= [ 1087040, 1087183 ] ), 1087039 ] ), rec(
      desc:= [ 111007 ],
      fp:= [ 8, 18, 414 ],
      next:= [ rec(
        desc:= [ 108003 ],
        fp:= [ 214, 412 ],
        next:= [ 1087443, 1087368 ] ), 1087308, 1087366 ] ), rec(
      desc:= [ 302007 ],
      fp:= [ 2262, 3321 ],
      next:= [ rec(
        desc:= [ 302005 ],
        fp:= [ 13, 1361 ],
        next:= [ 1087072, rec(
          desc:= [ 302007 ],
          fp:= [ 12, 1581 ],
          next:= [ 1087101, rec(
            desc:= [ 109003 ],
            fp:= [ 4, 14 ],
            next:= [ 1087071, 1087014 ] ) ] ) ] ), 1087013 ] ), rec(
      desc:= [ 111007 ],
      fp:= [ 8, 18, 414 ],
      next:= [ rec(
        desc:= [ 105003 ],
        fp:= [ 4, 14 ],
        next:= [ 1087076, 1087019 ] ), 1087110, 1087078 ] ), rec(
      desc:= [ 306010 ],
      fp:= [ 484, 762, 1021 ],
      next:= [ 1087191, rec(
        desc:= [ 302006 ],
        fp:= [ 961, 62341 ],
        next:= [ 1087074, rec(
          desc:= [ 107003 ],
          fp:= [ 8, 414 ],
          next:= [ 1087044, 1087043 ] ) ] ), 1087016 ] ), rec(
      desc:= [ 302008 ],
      fp:= [ 54781, 64921 ],
      next:= [ rec(
        desc:= [ 111003 ],
        fp:= [ 214, 412 ],
        next:= [ 1087448, rec(
          desc:= [ 302007, 212002 ],
          fp:= [ 4, 212 ],
          next:= [ 1087375, 1087377 ] ) ] ), 1087458 ] ), rec(
      desc:= [ 112007 ],
      fp:= [ 12, 418, 814 ],
      next:= [ 1087370, 1087451, rec(
        desc:= [ 107003 ],
        fp:= [ 416, 812 ],
        next:= [ 1087319, 1087372 ] ) ] ) ] ), rec(
    fp:= [ 10599, 47007, 58192, 71345, 94561 ],
    next:= [ 1087226, 1087496, rec(
      desc:= [ 105003 ],
      fp:= [ 4, 14 ],
      next:= [ 1087503, 1087499 ] ), 1087231, 1087223 ] ), rec(
    fp:= [ 79093, 88387 ],
    next:= [ 1087469, 1087471 ] ), rec(
    fp:= [ 3376, 16386, 40481, 60306 ],
    next:= [ 1087523, 1087521, 1087337, 1087344 ] ), rec(
    fp:= [ 51190, 78961 ],
    next:= [ 1087413, 1087414 ] ), rec(
    fp:= [ 49093, 95513 ],
    next:= [ 1087476, 1087475 ] ), rec(
    fp:= [ 7881, 16565, 18184, 29715, 34372, 34930, 57278, 65899, 74081, 
79829, 81498, 84660, 93398, 94389, 95356, 97124 ],
    next:= [ rec(
      desc:= [ 112003 ],
      fp:= [ 8, 414 ],
      next:= [ 1087194, 1087200 ] ), 1087112, 1087184, 1086989, 1086997, 
1087117, 1087143, rec(
      desc:= [ 210002 ],
      fp:= [ 8, 414 ],
      next:= [ 1087005, 1087000 ] ), 1087103, 1087192, 1087307, 1087118, rec(
      desc:= [ 108003 ],
      fp:= [ 8, 414 ],
      next:= [ 1087456, 1087321 ] ), rec(
      desc:= [ 112003 ],
      fp:= [ 8, 18, 414 ],
      next:= [ rec(
        desc:= [ 107003 ],
        fp:= [ 4, 212 ],
        next:= [ 1087440, 1087445 ] ), 1087310, 1087459 ] ), rec(
      desc:= [ 212003 ],
      fp:= [ 6, 214 ],
      next:= [ 1087144, 1087142 ] ), 1087318 ] ), 1087332, rec(
    fp:= [ 12912, 93914 ],
    next:= [ 1087468, 1087474 ] ), rec(
    fp:= [ 40640, 55412 ],
    next:= [ 1087210, 1087214 ] ), rec(
    fp:= [ 15408, 18772, 45874, 69725, 92890 ],
    next:= [ 1086990, 1086991, 1086998, rec(
      desc:= [ 210002 ],
      fp:= [ 8, 414 ],
      next:= [ 1087007, 1087001 ] ), 1087006 ] ), rec(
    fp:= [ 3068, 12568, 14874, 24452, 31456, 37301, 48405, 91355, 92425 ],
    next:= [ rec(
      desc:= [ 210002 ],
      fp:= [ 16, 412 ],
      next:= [ 1087147, 1087098 ] ), 1087325, rec(
      desc:= [ 210003 ],
      fp:= [ 6, 214 ],
      next:= [ 1087140, 1087114 ] ), 1087148, rec(
      desc:= [ 114003 ],
      fp:= [ 12, 814 ],
      next:= [ 1087113, 1087100 ] ), 1087324, 1087322, 1087099, 1087097 ] ), 
1087327, rec(
    fp:= [ 2697, 19218, 28395, 32371, 54095, 54698, 92671 ],
    next:= [ rec(
      desc:= [ 107003 ],
      fp:= [ 4, 212 ],
      next:= [ 1087160, 1087228 ] ), rec(
      desc:= [ 302008 ],
      fp:= [ 54781, 64582, 64921, 75061, 98821 ],
      next:= [ 1087421, rec(
        desc:= [ 107003 ],
        fp:= [ 4, 14 ],
        next:= [ 1087504, 1087418 ] ), rec(
        desc:= [ 108003 ],
        fp:= [ 4, 212 ],
        next:= [ 1087501, 1087429 ] ), 1087502, 1087426 ] ), rec(
      desc:= [ 111003 ],
      fp:= [ 818, 1214 ],
      next:= [ 1087155, rec(
        desc:= [ 108003 ],
        fp:= [ 4, 212 ],
        next:= [ 1087158, 1087225 ] ) ] ), rec(
      desc:= [ 111003 ],
      fp:= [ 8, 18, 414 ],
      next:= [ rec(
        desc:= [ 106003 ],
        fp:= [ 4, 212 ],
        next:= [ 1087162, 1087230 ] ), 1087163, rec(
        desc:= [ 106003 ],
        fp:= [ 4, 212 ],
        next:= [ 1087166, 1087229 ] ) ] ), rec(
      desc:= [ 302007 ],
      fp:= [ 54781, 64582, 64921 ],
      next:= [ 1087425, 1087422, 1087498 ] ), rec(
      desc:= [ 302005 ],
      fp:= [ 483, 58261 ],
      next:= [ 1087401, rec(
        desc:= [ 110003 ],
        fp:= [ 6, 412 ],
        next:= [ 1087286, 1087400 ] ) ] ), rec(
      desc:= [ 113011 ],
      fp:= [ 12, 22, 814 ],
      next:= [ rec(
        desc:= [ 106003 ],
        fp:= [ 4, 212 ],
        next:= [ 1087393, 1087397 ] ), 1087297, rec(
        desc:= [ 106003 ],
        fp:= [ 4, 14, 212 ],
        next:= [ 1087392, 1087290, 1087396 ] ) ] ) ] ), rec(
    fp:= [ 40786, 77679, 87485 ],
    next:= [ 1087247, 1087245, 1087329 ] ), rec(
    fp:= [ 9694, 32002, 76522, 84494 ],
    next:= [ 1087519, 1087524, rec(
      desc:= [ 107003 ],
      fp:= [ 14, 212 ],
      next:= [ 1087345, 1087347 ] ), rec(
      desc:= [ 107003 ],
      fp:= [ 14, 212 ],
      next:= [ 1087338, 1087340 ] ) ] ), rec(
    fp:= [ 22001, 25741 ],
    next:= [ 1087361, 1087360 ] ), rec(
    fp:= [ 16497, 81317, 84846 ],
    next:= [ 1087283, 1087293, 1087296 ] ), rec(
    fp:= [ 1937, 29862, 47513, 60891 ],
    next:= [ 1087111, 1087316, 1087102, 1087305 ] ), rec(
    fp:= [ 14201, 25307, 46831, 53847, 59935, 72052, 72205, 97506 ],
    next:= [ 1087217, 1087218, 1087205, 1087465, 1087462, 1087203, rec(
      desc:= [ 111003, 119003, 119005, 304011, 311020, 41104007 ],
      fp:= [ 1, 161 ],
      next:= [ 1087206, 1087207 ] ), rec(
      desc:= [ 117003, 117005, 308015, 219008 ],
      fp:= [ 216, 612 ],
      next:= [ 1087463, 1087466 ] ) ] ), rec(
    fp:= [ 52803, 67104 ],
    next:= [ 1087211, 1087215 ] ), rec(
    fp:= [ 85690, 92601 ],
    next:= [ 1087350, 1087343 ] ), rec(
    fp:= [ 1423, 4183, 7065, 12272, 17336, 31973, 36993, 42163, 45133, 59567, 
60080, 63126, 69802, 72421, 73702, 91876, 96117 ],
    next:= [ 1087067, rec(
      desc:= [ 112003 ],
      fp:= [ 4, 14, 212 ],
      next:= [ rec(
        desc:= [ 111003 ],
        fp:= [ 8, 414 ],
        next:= [ 1087369, 1087367 ] ), 1087444, rec(
        desc:= [ 302008 ],
        fp:= [ 64681, 74821 ],
        next:= [ rec(
          desc:= [ 110003 ],
          fp:= [ 8, 414 ],
          next:= [ rec(
            desc:= [ 111003 ],
            fp:= [ 214, 412 ],
            next:= [ 1087447, rec(
              desc:= [ 302007, 212002 ],
              fp:= [ 4, 212 ],
              next:= [ 1087376, 1087374 ] ) ] ), 1087314 ] ), 
1087457 ] ) ] ), 1087050, rec(
      desc:= [ 302007 ],
      fp:= [ 64681, 74821 ],
      next:= [ rec(
        desc:= [ 113003 ],
        fp:= [ 12, 814 ],
        next:= [ 1087371, 1087373 ] ), 1087452 ] ), rec(
      desc:= [ 302009 ],
      fp:= [ 784, 89161 ],
      next:= [ rec(
        desc:= [ 112003 ],
        fp:= [ 8, 414 ],
        next:= [ 1087201, 1087195 ] ), 1087048 ] ), 1087051, rec(
      desc:= [ 302008 ],
      fp:= [ 1462, 2521 ],
      next:= [ rec(
        desc:= [ 302006 ],
        fp:= [ 283, 382 ],
        next:= [ 1087018, rec(
          desc:= [ 208003 ],
          fp:= [ 4, 14 ],
          next:= [ 1087105, 1087075 ] ) ] ), 1087017 ] ), 1087049, rec(
      desc:= [ 302008 ],
      fp:= [ 784, 1462 ],
      next:= [ rec(
        desc:= [ 108003 ],
        fp:= [ 2, 12 ],
        next:= [ 1087193, 1087045 ] ), 1087046 ] ), rec(
      desc:= [ 106003 ],
      fp:= [ 8, 414 ],
      next:= [ 1087073, 1087015 ] ), rec(
      desc:= [ 302009 ],
      fp:= [ 89161, 99541 ],
      next:= [ rec(
        desc:= [ 215002 ],
        fp:= [ 22, 418, 814 ],
        next:= [ 1087079, 1087108, rec(
          desc:= [ 113003 ],
          fp:= [ 8, 18 ],
          next:= [ 1087077, 1087080 ] ) ] ), 1087020 ] ), rec(
      desc:= [ 302009 ],
      fp:= [ 784, 1462 ],
      next:= [ rec(
        desc:= [ 109003 ],
        fp:= [ 2, 12 ],
        next:= [ 1087185, 1087041 ] ), 1087042 ] ), rec(
      desc:= [ 108003 ],
      fp:= [ 4, 14 ],
      next:= [ 1087066, 1087023 ] ), 1087021, 1087022, rec(
      desc:= [ 108003 ],
      fp:= [ 12, 418 ],
      next:= [ rec(
        desc:= [ 109003 ],
        fp:= [ 4, 14 ],
        next:= [ 1087065, 1087115 ] ), 1087064 ] ), rec(
      desc:= [ 110003, 210002 ],
      fp:= [ 4, 14 ],
      next:= [ 1087119, 1087068 ] ) ] ), rec(
    fp:= [ 7556, 89784 ],
    next:= [ rec(
      desc:= [ 109003 ],
      fp:= [ 10, 416, 812 ],
      next:= [ 1087473, rec(
        desc:= [ 113003 ],
        fp:= [ 4, 14 ],
        next:= [ 1087410, 1087407 ] ), rec(
        desc:= [ 113003 ],
        fp:= [ 4, 14 ],
        next:= [ 1087409, 1087408 ] ) ] ), rec(
      desc:= [ 302009 ],
      fp:= [ 243, 34581 ],
      next:= [ 1087412, rec(
        desc:= [ 109003 ],
        fp:= [ 4, 212 ],
        next:= [ 1087411, 1087467 ] ) ] ) ] ), rec(
    fp:= [ 25421, 31848, 33390, 43486, 45039, 74180, 74612, 82694, 90491, 
94514 ],
    next:= [ rec(
      desc:= [ 109003 ],
      fp:= [ 8, 414 ],
      next:= [ 1087031, 1087070 ] ), 1087380, rec(
      desc:= [ 209002 ],
      fp:= [ 8, 18, 414 ],
      next:= [ 1087030, 1087034, 1087082 ] ), rec(
      desc:= [ 302008 ],
      fp:= [ 1161, 49161, 59541 ],
      next:= [ 1087138, 1087150, 1087035 ] ), 1087378, rec(
      desc:= [ 109003 ],
      fp:= [ 8, 414 ],
      next:= [ 1087083, 1087069 ] ), 1087379, 1087084, 1087081, rec(
      desc:= [ 302007 ],
      fp:= [ 1462, 2521 ],
      next:= [ rec(
        desc:= [ 108003 ],
        fp:= [ 8, 414 ],
        next:= [ 1087032, 1087146 ] ), 1087033 ] ) ] ), rec(
    fp:= [ 14595, 42215 ],
    next:= [ 1086985, 1086979 ] ), rec(
    fp:= [ 14339, 43535, 60995, 88278 ],
    next:= [ 1087300, 1087328, 1087303, 1087302 ] ), rec(
    fp:= [ 32956, 59093 ],
    next:= [ 1087339, 1087346 ] ), rec(
    fp:= [ 29914, 64541, 77694, 84948, 85655 ],
    next:= [ rec(
      desc:= [ 302007 ],
      fp:= [ 784, 1462 ],
      next:= [ rec(
        desc:= [ 107003 ],
        fp:= [ 4, 212 ],
        next:= [ 1087159, 1087260 ] ), rec(
        desc:= [ 206002 ],
        fp:= [ 18, 414 ],
        next:= [ rec(
          desc:= [ 105003, 205002 ],
          fp:= [ 18, 414 ],
          next:= [ 1087258, 1087259 ] ), 1087227 ] ) ] ), rec(
      desc:= [ 302007 ],
      fp:= [ 54781, 64582, 64921, 98821 ],
      next:= [ rec(
        desc:= [ 303010 ],
        fp:= [ 3, 483, 582, 681, 1161, 59061 ],
        next:= [ 1087427, 1087395, 1087485, 1087489, 1087399, 
1087487 ] ), rec(
        desc:= [ 302010 ],
        fp:= [ 583, 682, 781, 1261, 1741, 69061 ],
        next:= [ 1087428, rec(
          desc:= [ 110003 ],
          fp:= [ 416, 812 ],
          next:= [ 1087398, 1087486 ] ), rec(
          desc:= [ 107003 ],
          fp:= [ 4, 14 ],
          next:= [ 1087488, 1087484 ] ), rec(
          desc:= [ 110003 ],
          fp:= [ 416, 812 ],
          next:= [ 1087394, 1087483 ] ), 1087356, rec(
          desc:= [ 108003 ],
          fp:= [ 4, 14 ],
          next:= [ 1087358, 1087500 ] ) ] ), rec(
        desc:= [ 107003 ],
        fp:= [ 4, 212 ],
        next:= [ 1087419, 1087505 ] ), rec(
        desc:= [ 107003 ],
        fp:= [ 4, 14 ],
        next:= [ 1087420, 1087357 ] ) ] ), rec(
      desc:= [ 110007 ],
      fp:= [ 8, 18, 414 ],
      next:= [ rec(
        desc:= [ 302008 ],
        fp:= [ 784, 89161 ],
        next:= [ 1087161, rec(
          desc:= [ 107003, 207003 ],
          fp:= [ 2, 12 ],
          next:= [ 1087262, 1087264 ] ) ] ), 1087165, rec(
        desc:= [ 302008 ],
        fp:= [ 784, 89161 ],
        next:= [ 1087164, rec(
          desc:= [ 302007 ],
          fp:= [ 282, 381 ],
          next:= [ 1087232, rec(
            desc:= [ 108003, 208003 ],
            fp:= [ 2, 12 ],
            next:= [ 1087263, 1087261 ] ) ] ) ] ) ] ), rec(
      desc:= [ 302006 ],
      fp:= [ 54781, 64582, 64921, 75061, 98821 ],
      next:= [ rec(
        desc:= [ 108003 ],
        fp:= [ 416, 812 ],
        next:= [ 1087403, 1087482 ] ), rec(
        desc:= [ 109003 ],
        fp:= [ 6, 214, 412 ],
        next:= [ 1087355, rec(
          desc:= [ 113003 ],
          fp:= [ 12, 418 ],
          next:= [ 1087481, 1087480 ] ), 1087402 ] ), 1087423, 1087497, rec(
        desc:= [ 106003 ],
        fp:= [ 22, 814 ],
        next:= [ 1087354, 1087424 ] ) ] ), rec(
      desc:= [ 110003 ],
      fp:= [ 16, 818, 1214 ],
      next:= [ rec(
        desc:= [ 302008 ],
        fp:= [ 784, 1462 ],
        next:= [ 1087157, rec(
          desc:= [ 207002 ],
          fp:= [ 8, 18 ],
          next:= [ 1087224, 1087256 ] ) ] ), 1087255, rec(
        desc:= [ 107003 ],
        fp:= [ 4, 212 ],
        next:= [ 1087156, 1087257 ] ) ] ) ] ), rec(
    fp:= [ 7378, 12694, 27007, 29973, 37663, 43516, 61461, 76053, 80465, 
87314, 98708 ],
    next:= [ 1087233, 1087331, 1087251, 1087508, 1087249, 1087250, 1087507, 
1087235, 1087234, 1087506, 1087244 ] ), rec(
    fp:= [ 76605, 84910 ],
    next:= [ 1087522, 1087520 ] ), rec(
    fp:= [ 2816, 13110, 26854, 29296, 30282, 30969, 36588, 45278, 47805, 
60583, 62035, 65787, 71212, 74500, 75956, 79345, 80290, 93064, 93127 ],
    next:= [ 1087181, 1087107, 1087141, rec(
      desc:= [ 107003 ],
      fp:= [ 18, 414 ],
      next:= [ 1087104, 1087189 ] ), 1086995, 1087312, 1087003, 1086980, 
1086982, rec(
      desc:= [ 302009 ],
      fp:= [ 54781, 64921 ],
      next:= [ 1087460, rec(
        desc:= [ 111003 ],
        fp:= [ 416, 812 ],
        next:= [ 1087313, 1087446 ] ) ] ), 1087455, 1086993, 1086986, rec(
      desc:= [ 213002 ],
      fp:= [ 4, 14 ],
      next:= [ 1086996, 1086999 ] ), rec(
      desc:= [ 213003 ],
      fp:= [ 8, 18, 414 ],
      next:= [ 1087008, 1087009, 1087004 ] ), 1087002, rec(
      desc:= [ 110003, 302006, 211002 ],
      fp:= [ 14, 212 ],
      next:= [ 1087197, 1087196 ] ), 1087439, 1086988 ] ), rec(
    fp:= [ 39382, 39461 ],
    next:= [ 1087216, 1087212 ] ), rec(
    fp:= [ 13409, 76350 ],
    next:= [ 1087472, 1087470 ] ), rec(
    fp:= [ 5757, 6599, 20219, 38394, 38600, 43941, 53696, 59392, 81696, 
81863 ],
    next:= [ 1087405, 1087167, 1087431, 1087430, 1087170, 1087432, 1087169, 
1087168, 1087406, 1087404 ] ), rec(
    fp:= [ 51998, 65497, 96526 ],
    next:= [ rec(
      desc:= [ 302010 ],
      fp:= [ 883, 99061 ],
      next:= [ 1087295, 1087294 ] ), 1087285, 1087289 ] ), 1087330 ] );