prop640.z

#############################################################################
##
#W  prop640.z              GAP library of groups           Hans Ulrich Besche
##                                               Bettina Eick, Eamonn O'Brien
##

PROPERTIES_SMALL_GROUPS[ 640 ] := rec(
isNilpotent := [ 2, 403, -564, 5022, -5854, 17942, -19094, 21285, -21453,
21527, -21535, 21541 ], 
isSupersolvable := [ 1, -19094, 19105, -21453, 21475, -21535, 21539, -21541 ]
, 
isAbelian := [ 2, 443, 529, 560, 5037, 5314, 5695, 5846, 17942, 18546, 19081,
21285, 21436, 21527, 21541 ], 
lgLength := rec( lgLength := [ 2, 3, 4, 5, 6, 7, 8 ], pos := [ [ 21540,
-21541 ], [ 2275, -2304, 4408, -4412, 4419, -4425, 4438, -4445, 5002, 5006,
5009, 5022, -5036, 5881, -5886, 6278, -6280, 6334, -6337, 6424, -6427, 6991,
7036, 7070, 7109, -12251, 15864, -15930, 15932, -15944, 15956, -16013, 16035,
-16078, 16080, -16101, 16129, -16236, 16262, -16317, 16390, -16415, 16417,
-16425, 16445, -16536, 16556, -16704, 16706, -16725, 16765, -16821, 16835,
-16933, 16984, -17005, 17039, -17082, 17836, -17846, 17854, -17867, 17874,
-17882, 17899, -17911, 17940, -18545, 19122, -19130, 19148, -19154, 19179,
-19186, 19208, -19216, 19253, -19264, 19289, -19296, 19303, -19306, 19331,
-19338, 19363, -19370, 19385, -19390, 19405, -19410, 19425, -19430, 19439,
-19442, 19449, -19452, 19467, -19472, 19558, -19562, 19586, -19590, 19608,
-19610, 19637, -19640, 19649, -21127, 21197, -21206, 21210, -21222, 21226,
-21234, 21241, -21258, 21262, -21268, 21272, -21278, 21283, -21435, 21478,
-21480, 21483, -21484, 21487, -21488, 21492, -21494, 21496, 21498, 21501,
-21535, 21537, -21539 ], [ 50, -53, 184, -194, 196, -199, 201, -204, 206,
-207, 211, -212, 215, 226, -229, 232, -235, 238, -243, 247, -253, 255, -261,
275, -281, 283, -289, 309, -332, 403, -442, 585, -592, 608, -615, 625, -648,
665, -680, 774, 777, -779, 787, -790, 794, -797, 802, -804, 807, 846, -849,
853, -858, 867, -871, 875, -877, 903, 906, 910, 920, -1918, 2260, -2274, 2305
, -2613, 2622, -2676, 2678, -2738, 2740, -2755, 2762, -2888, 2895, -2930,
2937, -2967, 2971, -3001, 3005, -3019, 3026, -3424, 3427, -3468, 3479, -3522,
3532, -3556, 3566, -3597, 3600, -3730, 3734, -3757, 3768, -3781, 3805, -3822,
3825, -3858, 3879, -3942, 3975, -4162, 4171, -4184, 4201, -4224, 4234, -4255,
4266, -4269, 4400, -4407, 4413, -4418, 4426, -4437, 4446, -4542, 4544, -4577,
4579, -4590, 4592, -4606, 4609, -4644, 4646, -4670, 4672, -4693, 4696, -4721,
4723, -4733, 4738, -4744, 4749, -4783, 4785, -4796, 4798, -4804, 4806, -4816,
4818, -4820, 4823, -4824, 4827, -4832, 4835, -4836, 4839, -4852, 4854, -4878,
4883, -4906, 4912, -4934, 4940, -4949, 4959, -4986, 4989, -4996, 5001, 5003,
-5005, 5007, -5008, 5010, -5021, 5037, -5694, 5855, -5880, 5887, -5903, 5918,
-5949, 5958, -5984, 5989, -6080, 6083, -6102, 6109, -6164, 6167, -6174, 6238,
-6277, 6281, -6292, 6296, -6333, 6338, -6423, 6428, -6434, 6441, -6447, 6454,
-6462, 6466, -6493, 6497, -6528, 6531, -6538, 6543, -6610, 6615, -6625, 6634,
-6681, 6686, -6721, 6726, -6762, 6765, -6781, 6798, -6822, 6835, -6855, 6859,
-6864, 6873, -6910, 6919, -6934, 6945, -6952, 6956, -6967, 6970, -6990, 6992,
-6998, 7003, -7020, 7023, -7035, 7037, -7043, 7048, -7061, 7063, -7069, 7071,
-7077, 7082, -7088, 7093, -7104, 7106, -7108, 12252, -15810, 15855, -15863,
15931, 15945, -15955, 16014, -16034, 16079, 16102, -16128, 16237, -16261,
16318, -16389, 16416, 16426, -16444, 16537, -16555, 16705, 16726, -16764,
16822, -16834, 16934, -16983, 17006, -17038, 17083, -17534, 17537, -17591,
17594, -17630, 17634, -17681, 17685, -17704, 17709, -17819, 17822, -17828,
17831, -17835, 17847, -17853, 17868, -17873, 17883, -17898, 17912, -17939,
18546, -19080, 19095, -19096, 19101, -19102, 19105, -19121, 19131, -19147,
19155, -19178, 19187, -19207, 19217, -19252, 19265, -19288, 19297, -19302,
19307, -19330, 19339, -19362, 19371, -19384, 19391, -19404, 19411, -19424,
19431, -19438, 19443, -19448, 19453, -19466, 19476, -19484, 19487, -19493,
19496, -19535, 19538, -19557, 19563, -19585, 19591, -19607, 19613, -19636,
19641, -19648, 21128, -21196, 21207, -21209, 21223, -21225, 21235, -21240,
21259, -21261, 21269, -21271, 21279, -21282, 21436, -21453, 21457, -21477,
21481, -21482, 21485, -21486, 21489, -21491, 21495, 21497, 21499, -21500,
21536 ], [ 9, -32, 37, -49, 54, -79, 84, -91, 93, -110, 127, -147, 195, 200,
205, 208, -210, 213, -214, 216, -225, 230, -231, 236, -237, 244, -246, 254,
262, -274, 282, 290, -308, 333, -342, 347, -354, 356, 358, 360, 363, -364,
366, -367, 369, 372, -375, 377, -381, 383, -395, 443, -528, 577, -584, 593,
-597, 604, -607, 649, -652, 655, -656, 659, -664, 681, -714, 717, -733, 741,
-750, 752, -759, 768, -773, 775, -776, 780, -786, 791, -793, 798, -801, 805,
-806, 808, -819, 826, -828, 832, -834, 838, -839, 842, -845, 850, -852, 859,
-866, 872, -874, 878, -879, 881, -902, 904, -905, 907, -909, 911, -914, 919,
1919, -2238, 2614, -2621, 2677, 2739, 2756, -2761, 2889, -2894, 2931, -2936,
2968, -2970, 3002, -3004, 3020, -3025, 3425, -3426, 3469, -3478, 3523, -3531,
3557, -3565, 3598, -3599, 3731, -3733, 3758, -3767, 3782, -3804, 3823, -3824,
3859, -3878, 3943, -3974, 4163, -4170, 4185, -4200, 4225, -4233, 4256, -4265,
4272, -4325, 4327, -4331, 4335, -4366, 4370, -4382, 4386, -4399, 4543, 4578,
4591, 4607, -4608, 4645, 4671, 4694, -4695, 4722, 4734, -4737, 4745, -4748,
4784, 4797, 4805, 4817, 4821, -4822, 4825, -4826, 4833, -4834, 4837, -4838,
4853, 4879, -4882, 4907, -4911, 4935, -4939, 4950, -4958, 4987, -4988, 4997,
-5000, 5695, -5845, 5904, -5917, 5950, -5957, 5985, -5988, 6081, -6082, 6103,
-6108, 6165, -6166, 6178, -6192, 6194, -6237, 6293, -6295, 6435, -6440, 6448,
-6453, 6463, -6465, 6494, -6496, 6529, -6530, 6539, -6542, 6611, -6614, 6626,
-6633, 6682, -6685, 6722, -6725, 6782, -6797, 6823, -6834, 6857, -6858, 6865,
-6872, 6911, -6918, 6935, -6944, 6953, -6955, 6968, -6969, 6999, -7002, 7021,
-7022, 7044, -7047, 7062, 7078, -7081, 7089, -7092, 7105, 15811, -15854,
17535, -17536, 17592, -17593, 17631, -17633, 17682, -17684, 17705, -17708,
17820, -17821, 17829, -17830, 19081, -19094, 19097, -19100, 19103, -19104,
19473, -19475, 19485, -19486, 19494, -19495, 19536, -19537, 19611, -19612,
21454, -21456 ], [ 33, -36, 80, -83, 92, 111, -126, 148, -158, 161, -179, 343
, -346, 355, 357, 359, 361, -362, 365, 368, 370, -371, 376, 382, 396, -402,
529, -559, 567, -576, 598, -603, 616, -624, 653, -654, 657, -658, 734, -740,
751, 760, -767, 820, -825, 829, -831, 835, -837, 840, -841, 880, 915, -918,
2239, -2259, 4270, -4271, 4326, 4332, -4334, 4367, -4369, 4383, -4385, 5846,
-5854, 6175, -6177, 6193, 6763, -6764, 6856 ], [ 4, -8, 159, -160, 180, -183,
560, -566, 715, -716 ], [ 1, -3 ] ] ),
frattFacs := rec( frattFacs := [ 8, 15, 23, 30, 37, 87, 94, 101, 354, 361,
368, 1643, 1650, 1657, 1664, 1671, 11451, 11458, 11465, 11472, 11479, 11486 ]
, pos := [ 1, 2, 3, 402, 564, 919, 5021, 5854, 7108, 17941, 19094, 19099,
19104, 19649, 21284, 21453, 21456, 21467, 21474, 21501, 21526, 21535 ] ) );