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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  id27300.z              GAP library of id's             Hans Ulrich Besche
##

ID_GROUP_TREE.next[27300]:=
rec(
  fp:= [ 557, 4049, 7399, 8308, 8434, 10106, 11643, 15027, 18447, 20310, 
20369, 21536, 22260, 23260, 24725, 25585, 25611, 25650, 25925, 27789, 28332, 
29036, 29409, 32965, 33368, 33482, 34075, 35419, 39682, 40917, 44572, 45430, 
45953, 51990, 54080, 55586, 55943, 60730, 61558, 61808, 63422, 64669, 66886, 
68598, 71333, 73570, 74451, 77786, 78090, 81063, 81170, 85000, 86724, 88403, 
89613, 94475, 95552, 96376, 97510 ],
  next:= [ rec(
    fp:= [ 58544, 98551 ],
    level:= 4,
    next:= [ 538, rec(
      desc:= [ 105002 ],
      fp:= [ 16, 412 ],
      next:= [ 596, 604 ] ) ] ), rec(
    fp:= [ 11229, 14948, 26510, 27165, 28437, 30407, 41684, 48069, 50401, 
56194, 62348, 94312, 94771 ],
    level:= 4,
    next:= [ 405, 631, rec(
      desc:= [ 120004 ],
      fp:= [ 12, 22 ],
      next:= [ 403, 402 ] ), 441, rec(
      desc:= [ 119003 ],
      fp:= [ 12, 22 ],
      next:= [ 399, 400 ] ), 131, 406, 404, 126, rec(
      desc:= [ 118009 ],
      fp:= [ 12, 22 ],
      next:= [ 397, 398 ] ), rec(
      desc:= [ 120003 ],
      fp:= [ 6, 16 ],
      next:= [ 123, 124 ] ), 401, rec(
      desc:= [ 116009 ],
      fp:= [ 24, 34 ],
      next:= [ 627, 628 ] ) ] ), rec(
    fp:= [ 5729, 30882, 40011, 56619, 80504 ],
    level:= 4,
    next:= [ 572, rec(
      desc:= [ 121008 ],
      fp:= [ 72, 6022 ],
      next:= [ 540, 539 ] ), rec(
      desc:= [ 116008 ],
      fp:= [ 72, 82, 6022 ],
      next:= [ 598, 597, 605 ] ), 541, rec(
      desc:= [ 105002 ],
      fp:= [ 16, 412 ],
      next:= [ 599, 606 ] ) ] ), rec(
    fp:= [ 23278, 29454, 42358, 45338, 74731, 77237, 77602, 81846, 82579, 
93077 ],
    level:= 4,
    next:= [ 568, 588, 576, 592, 565, 558, 550, 584, 554, 650 ] ), 611, rec(
    fp:= [ 17875, 30094, 45223, 93363 ],
    level:= 4,
    next:= [ 372, 111, 17, 112 ] ), rec(
    fp:= [ 25223, 35094, 55697, 74878, 90007 ],
    level:= 4,
    next:= [ 503, 643, 501, 505, 504 ] ), rec(
    fp:= [ 69431, 70975 ],
    level:= 4,
    next:= [ 644, 514 ] ), rec(
    fp:= [ 23533, 44132, 66229, 84555 ],
    level:= 4,
    next:= [ 636, 375, 466, 620 ] ), rec(
    fp:= [ 25404, 76631, 78566 ],
    level:= 4,
    next:= [ 395, 625, 629 ] ), rec(
    fp:= [ 21758, 40064 ],
    level:= 4,
    next:= [ 642, 502 ] ), rec(
    fp:= [ 33700, 51534, 58076, 59199, 65142, 67782, 77899, 81427, 85698, 
90334 ],
    level:= 4,
    next:= [ 374, 116, 115, 21, 119, 118, 23, 114, 22, 19 ] ), rec(
    fp:= [ 2490, 5401, 16251, 16895, 22138, 23452, 25435, 25633, 35450, 
36702, 41777, 44196, 44746, 47621, 53788, 55312, 56212, 59179, 59401, 72228, 
79933, 82424, 89134, 90525, 92569, 96304, 97258, 98205 ],
    level:= 4,
    next:= [ 651, 551, 591, 595, 561, 577, 578, 559, 571, 555, 570, 566, 
590, 594, 557, 579, 585, 569, 587, 560, 589, 556, 553, 575, 593, 567, 552, 
586 ] ), rec(
    fp:= [ 28277, 66119, 70880, 75014 ],
    level:= 4,
    next:= [ 373, 113, 117, 20 ] ), rec(
    desc:= [ 113009 ],
    fp:= [ 24, 34 ],
    next:= [ 613, 614 ] ),, 64, rec(
    fp:= [ 40802, 53132, 76984 ],
    level:= 4,
    next:= [ 630, 396, 626 ] ), rec(
    fp:= [ 9384, 21787, 24849, 31330, 37676, 41927, 42157, 49830, 51882, 
52298, 56290, 63759, 64185, 65252, 74229, 74740, 82430, 94221 ],
    level:= 4,
    next:= [ 425, 473, 243, 385, 34, 252, 276, 480, 358, 231, 52, 622, 367, 
638, 431, 379, 391, 469 ] ), rec(
    fp:= [ 44877, 74172, 79061, 81996, 93135 ],
    level:= 4,
    next:= [ 634, 140, 409, 446, 415 ] ), rec(
    fp:= [ 2925, 17495, 18825, 83475, 91773 ],
    level:= 4,
    next:= [ 526, 510, 522, 646, 518 ] ), rec(
    fp:= [ 781, 7868, 14209, 16873, 17621, 18570, 22064, 26077, 33738, 
36187, 44611, 46332, 55554, 63221, 65138, 78947, 95401, 97145 ],
    level:= 4,
    next:= [ 269, 423, 477, 378, 27, 376, 230, 357, 621, 467, 424, 468, 25, 
377, 356, 228, 637, 229 ] ), rec(
    fp:= [ 41399, 61965, 63525, 88609, 92237 ],
    level:= 4,
    next:= [ 516, 515, 645, 517, 507 ] ), rec(
    fp:= [ 104, 420, 1833, 2018, 3783, 9057, 9892, 10759, 11882, 14809, 
27222, 30035, 40778, 44548, 46678, 62557, 66470, 68158, 70422, 74205, 75920, 
77260, 79364, 82492, 87620, 90943, 92640, 92895, 93370 ],
    level:= 4,
    next:= [ 149, 151, 447, 150, rec(
      desc:= [ 130003 ],
      fp:= [ 12, 22 ],
      next:= [ 147, 148 ] ), 445, 421, rec(
      desc:= [ 133004 ],
      fp:= [ 12, 22 ],
      next:= [ 155, 154 ] ), 160, 139, rec(
      desc:= [ 130009 ],
      fp:= [ 24, 34 ],
      next:= [ 418, 419 ] ), 448, rec(
      desc:= [ 127003 ],
      fp:= [ 6, 16 ],
      next:= [ 136, 137 ] ), 162, rec(
      desc:= [ 126003 ],
      fp:= [ 12, 22 ],
      next:= [ 412, 413 ] ), rec(
      desc:= [ 128004 ],
      fp:= [ 12, 22 ],
      next:= [ 417, 416 ] ), 635, 449, rec(
      desc:= [ 124009 ],
      fp:= [ 12, 22 ],
      next:= [ 410, 411 ] ), 159, 157, rec(
      desc:= [ 128003 ],
      fp:= [ 6, 16 ],
      next:= [ 145, 146 ] ), rec(
      desc:= [ 128009 ],
      fp:= [ 12, 22 ],
      next:= [ 143, 144 ] ), 422, 420, 161, 163, 414, rec(
      desc:= [ 127003 ],
      fp:= [ 6, 16 ],
      next:= [ 141, 142 ] ) ] ), rec(
    fp:= [ 11635, 64918, 90071 ],
    level:= 4,
    next:= [ 537, 508, rec(
      desc:= [ 121008 ],
      fp:= [ 72, 6022 ],
      next:= [ 536, 535 ] ) ] ), rec(
    fp:= [ 13293, 27616, 54666, 58127, 67018, 90371, 94938 ],
    level:= 4,
    next:= [ rec(
      desc:= [ 123002 ],
      fp:= [ 24, 2014 ],
      next:= [ 165, 164 ] ), 442, 167, rec(
      desc:= [ 124008 ],
      fp:= [ 72, 6022 ],
      next:= [ 452, 451 ] ), 453, 166, 132 ] ), rec(
    fp:= [ 26295, 46912, 49018, 97328 ],
    level:= 4,
    next:= [ 562, 648, 580, 546 ] ), 616, rec(
    fp:= [ 6841, 20013, 24401, 88609, 89733, 96055 ],
    level:= 4,
    next:= [ rec(
      desc:= [ 120002 ],
      fp:= [ 6, 16 ],
      next:= [ 128, 127 ] ), 125, rec(
      desc:= [ 119004 ],
      fp:= [ 6, 16 ],
      next:= [ 122, 121 ] ), 130, 129, 440 ] ), rec(
    fp:= [ 7281, 8248, 12362, 14521, 15355, 25841, 72046, 83418, 84687, 
89204 ],
    level:= 4,
    next:= [ 547, 582, 548, 549, 563, 573, 649, 581, 583, 564 ] ), 498, 632, 
615, 640, rec(
    fp:= [ 29480, 40300, 41137 ],
    level:= 4,
    next:= [ rec(
      desc:= [ 105002 ],
      fp:= [ 16, 412 ],
      next:= [ 484, 492 ] ), 458, 70 ] ), rec(
    desc:= [ 114009 ],
    fp:= [ 24, 34 ],
    next:= [ 618, 619 ] ), rec(
    fp:= [ 51987, 67278 ],
    level:= 4,
    next:= [ 120, 439 ] ), 610, rec(
    fp:= [ 29294, 30566, 35907, 36464, 43305, 58752, 68311, 88039, 93667 ],
    level:= 4,
    next:= [ 200, rec(
      desc:= [ 105002 ],
      fp:= [ 16, 412 ],
      next:= [ 316, 344 ] ), rec(
      desc:= [ 105002 ],
      fp:= [ 16, 412 ],
      next:= [ 304, 335 ] ), 212, rec(
      desc:= [ 105002 ],
      fp:= [ 16, 412 ],
      next:= [ 488, 495 ] ), 102, 462, 78, 90 ] ), rec(
    fp:= [ 457, 70499 ],
    level:= 4,
    next:= [ 110, 371 ] ), rec(
    fp:= [ 21252, 47888, 96181 ],
    level:= 4,
    next:= [ 454, 168, 180 ] ), rec(
    fp:= [ 810, 7883, 15076, 22557, 24749, 25270, 30368, 32166, 32527, 
35217, 43425, 50889, 58242, 64466, 64747, 66536, 88012, 89783, 95337, 95540, 
98523 ],
    level:= 4,
    next:= [ rec(
      desc:= [ 116008 ],
      fp:= [ 24, 34 ],
      next:= [ 75, 74 ] ), 476, 2, rec(
      desc:= [ 117008 ],
      fp:= [ 72, 82, 6022 ],
      next:= [ 486, 485, 493 ] ), rec(
      desc:= [ 105002 ],
      fp:= [ 16, 412 ],
      next:= [ 487, 494 ] ), rec(
      desc:= [ 105002 ],
      fp:= [ 16, 412 ],
      next:= [ 303, 334 ] ), 76, rec(
      desc:= [ 116002 ],
      fp:= [ 24, 34, 2014 ],
      next:= [ 301, 300, 332 ] ), 77, rec(
      desc:= [ 115008 ],
      fp:= [ 24, 34 ],
      next:= [ 72, 71 ] ), 26, rec(
      desc:= [ 105002 ],
      fp:= [ 16, 412 ],
      next:= [ 302, 333 ] ), 198, 24, 461, 199, rec(
      desc:= [ 122008 ],
      fp:= [ 72, 6022 ],
      next:= [ 460, 459 ] ), 73, 268, rec(
      desc:= [ 121002 ],
      fp:= [ 24, 2014 ],
      next:= [ 197, 196 ] ), 1 ] ), rec(
    fp:= [ 21703, 28200, 29660, 57639, 63540, 63673, 68571, 73674, 73922, 
83052, 83711, 87347, 88756, 89648 ],
    level:= 4,
    next:= [ 519, 527, 647, 520, 528, 513, 511, 525, 529, 512, 524, 523, 
521, 509 ] ), rec(
    fp:= [ 716, 2300, 19454, 20082, 23284, 24217, 25625, 29533, 30882, 
48052, 50869, 58853, 62785, 63067, 65428, 68114, 75709, 77620, 90914, 91276, 
95623 ],
    level:= 4,
    next:= [ rec(
      desc:= [ 121008 ],
      fp:= [ 72, 6022 ],
      next:= [ 176, 175 ] ), rec(
      desc:= [ 123004 ],
      fp:= [ 6, 16 ],
      next:= [ 135, 134 ] ), 457, 195, 179, rec(
      desc:= [ 125004 ],
      fp:= [ 12, 22 ],
      next:= [ 186, 185 ] ), rec(
      desc:= [ 122002 ],
      fp:= [ 24, 2014 ],
      next:= [ 193, 192 ] ), rec(
      desc:= [ 120002 ],
      fp:= [ 24, 2014 ],
      next:= [ rec(
        desc:= [ 122004 ],
        fp:= [ 6, 16 ],
        next:= [ 172, 171 ] ), rec(
        desc:= [ 123004 ],
        fp:= [ 6, 16 ],
        next:= [ 170, 169 ] ) ] ), 156, rec(
      desc:= [ 122008 ],
      fp:= [ 72, 6022 ],
      next:= [ 188, 187 ] ), 194, 191, rec(
      desc:= [ 125003 ],
      fp:= [ 12, 22 ],
      next:= [ 177, 178 ] ), rec(
      desc:= [ 124009 ],
      fp:= [ 12, 22 ],
      next:= [ 173, 174 ] ), rec(
      desc:= [ 126009 ],
      fp:= [ 24, 34 ],
      next:= [ 189, 190 ] ), 444, 158, 138, rec(
      desc:= [ 121002 ],
      fp:= [ 24, 2014 ],
      next:= [ rec(
        desc:= [ 123002 ],
        fp:= [ 6, 16 ],
        next:= [ 184, 182 ] ), rec(
        desc:= [ 124002 ],
        fp:= [ 6, 16 ],
        next:= [ 183, 181 ] ) ] ), rec(
      desc:= [ 126002 ],
      fp:= [ 6, 16 ],
      next:= [ 153, 152 ] ), rec(
      desc:= [ 123008 ],
      fp:= [ 72, 6022 ],
      next:= [ 456, 455 ] ) ] ), 612, rec(
    fp:= [ 1260, 29804, 62484 ],
    level:= 4,
    next:= [ 66, 65, 16 ] ), rec(
    fp:= [ 37144, 78925 ],
    level:= 4,
    next:= [ 542, rec(
      desc:= [ 105002 ],
      fp:= [ 16, 412 ],
      next:= [ 600, 607 ] ) ] ), 500, rec(
    fp:= [ 4002, 81753 ],
    level:= 4,
    next:= [ 499, 641 ] ), 450, 530, rec(
    fp:= [ 50889, 85912, 88352 ],
    level:= 4,
    next:= [ 69, 68, 18 ] ), 67, rec(
    fp:= [ 29287, 41798, 56832, 71875, 99580 ],
    level:= 4,
    next:= [ rec(
      desc:= [ 120008 ],
      fp:= [ 72, 6022 ],
      next:= [ 544, 543 ] ), rec(
      desc:= [ 105002 ],
      fp:= [ 16, 412 ],
      next:= [ 603, 609 ] ), 574, rec(
      desc:= [ 115008 ],
      fp:= [ 72, 82, 6022 ],
      next:= [ 602, 601, 608 ] ), 545 ] ),, 534, rec(
    fp:= [ 19953, 51216, 80502 ],
    level:= 4,
    next:= [ 533, 506, rec(
      desc:= [ 122008 ],
      fp:= [ 72, 6022 ],
      next:= [ 532, 531 ] ) ] ), 617, rec(
    fp:= [ 38074, 77600, 87715, 88922, 97982 ],
    level:= 4,
    next:= [ 408, 443, 133, 407, 633 ] ) ] );