prop384.z

#############################################################################
##
#W  prop384.z              GAP library of groups           Hans Ulrich Besche
##                                               Bettina Eick, Eamonn O'Brien
##

PROPERTIES_SMALL_GROUPS[ 384 ] := rec(
isNilpotent := [ 2, 406, -567, 4723, -5555, 16705, -17857, 19878, -20046,
20153, -20161, 20169 ], 
isSupersolvable := [ 1, -2, 7, -567, 621, -5555, 5872, -17857, 18243, -20046,
20128, -20161, 20168, -20169 ], 
isAbelian := [ 2, 446, 532, 563, 4738, 5015, 5396, 5547, 16705, 17309, 17844,
19878, 20029, 20153, 20169 ], 
lgLength := rec( lgLength := [ 2, 3, 4, 5, 6, 7, 8 ], pos := [ [ 20168,
-20169 ], [ 1976, -2005, 4109, -4113, 4120, -4126, 4139, -4146, 4703, 4707,
4710, 4723, -4737, 5859, -11014, 14627, -14693, 14695, -14707, 14719, -14776,
14798, -14841, 14843, -14864, 14892, -14999, 15025, -15080, 15153, -15178,
15180, -15188, 15208, -15299, 15319, -15467, 15469, -15488, 15528, -15584,
15598, -15696, 15747, -15768, 15802, -15845, 16599, -16609, 16617, -16630,
16637, -16645, 16662, -16674, 16703, -17308, 17948, 18158, 18199, 18221,
18243, -19720, 19790, -19799, 19803, -19815, 19819, -19827, 19834, -19851,
19855, -19861, 19865, -19871, 19876, -20028, 20125, -20167 ], [ 3, -6, 53,
-56, 187, -197, 199, -202, 204, -207, 209, -210, 214, -215, 218, 229, -232,
235, -238, 241, -246, 250, -256, 258, -264, 278, -284, 286, -292, 312, -335,
406, -445, 584, 591, -592, 609, -612, 617, -618, 621, -1619, 1961, -1975,
2006, -2314, 2323, -2377, 2379, -2439, 2441, -2456, 2463, -2589, 2596, -2631,
2638, -2668, 2672, -2702, 2706, -2720, 2727, -3125, 3128, -3169, 3180, -3223,
3233, -3257, 3267, -3298, 3301, -3431, 3435, -3458, 3469, -3482, 3506, -3523,
3526, -3559, 3580, -3643, 3676, -3863, 3872, -3885, 3902, -3925, 3935, -3956,
3967, -3970, 4101, -4108, 4114, -4119, 4127, -4138, 4147, -4243, 4245, -4278,
4280, -4291, 4293, -4307, 4310, -4345, 4347, -4371, 4373, -4394, 4397, -4422,
4424, -4434, 4439, -4445, 4450, -4484, 4486, -4497, 4499, -4505, 4507, -4517,
4519, -4521, 4524, -4525, 4528, -4533, 4536, -4537, 4540, -4553, 4555, -4579,
4584, -4607, 4613, -4635, 4641, -4650, 4660, -4687, 4690, -4697, 4702, 4704,
-4706, 4708, -4709, 4711, -4722, 4738, -5395, 5559, -5567, 5571, -5582, 5601,
-5608, 5655, -5657, 5678, 5718, 5735, -5737, 5741, -5742, 5744, 5747, 5754,
5757, -5780, 5783, -5788, 5790, -5792, 5833, -5838, 11015, -14573, 14618,
-14626, 14694, 14708, -14718, 14777, -14797, 14842, 14865, -14891, 15000,
-15024, 15081, -15152, 15179, 15189, -15207, 15300, -15318, 15468, 15489,
-15527, 15585, -15597, 15697, -15746, 15769, -15801, 15846, -16297, 16300,
-16354, 16357, -16393, 16397, -16444, 16448, -16467, 16472, -16582, 16585,
-16591, 16594, -16598, 16610, -16616, 16631, -16636, 16646, -16661, 16675,
-16702, 17309, -17843, 17858, -17889, 17949, 18054, -18062, 18066, -18072,
18078, 18080, 18082, 18084, 18121, -18136, 18144, -18150, 18159, -18169,
18198, 18218, 18222, -18239, 19721, -19789, 19800, -19802, 19816, -19818,
19828, -19833, 19852, -19854, 19862, -19864, 19872, -19875, 20029, -20124 ],
[ 12, -35, 40, -52, 57, -82, 87, -94, 96, -113, 130, -150, 198, 203, 208, 211
, -213, 216, -217, 219, -228, 233, -234, 239, -240, 247, -249, 257, 265, -277
, 285, 293, -311, 336, -345, 350, -357, 359, 361, 363, 366, -367, 369, -370,
372, 375, -378, 380, -384, 386, -398, 446, -531, 568, -570, 572, -574, 576,
-579, 583, 585, -590, 593, -595, 597, -603, 605, 607, -608, 613, -615, 1620,
-1939, 2315, -2322, 2378, 2440, 2457, -2462, 2590, -2595, 2632, -2637, 2669,
-2671, 2703, -2705, 2721, -2726, 3126, -3127, 3170, -3179, 3224, -3232, 3258,
-3266, 3299, -3300, 3432, -3434, 3459, -3468, 3483, -3505, 3524, -3525, 3560,
-3579, 3644, -3675, 3864, -3871, 3886, -3901, 3926, -3934, 3957, -3966, 3973,
-4026, 4028, -4032, 4036, -4067, 4071, -4083, 4087, -4100, 4244, 4279, 4292,
4308, -4309, 4346, 4372, 4395, -4396, 4423, 4435, -4438, 4446, -4449, 4485,
4498, 4506, 4518, 4522, -4523, 4526, -4527, 4534, -4535, 4538, -4539, 4554,
4580, -4583, 4608, -4612, 4636, -4640, 4651, -4659, 4688, -4689, 4698, -4701,
5396, -5546, 5556, -5558, 5568, -5570, 5619, -5629, 5634, -5643, 5646, 5649,
-5654, 5658, -5660, 5677, 5681, -5693, 5696, -5708, 5717, 5719, -5734, 5738,
-5740, 5743, 5745, -5746, 5748, -5753, 5755, -5756, 5781, -5782, 5789, 5793,
-5824, 14574, -14617, 16298, -16299, 16355, -16356, 16394, -16396, 16445,
-16447, 16468, -16471, 16583, -16584, 16592, -16593, 17844, -17857, 17890,
-17947, 17950, -18053, 18063, -18065, 18073, -18077, 18079, 18081, 18083,
18085, -18120, 18137, -18143, 18151, -18157, 18170, -18197, 18200, -18217,
18219, -18220, 18240, -18242 ], [ 36, -39, 83, -86, 95, 114, -129, 151, -161,
164, -182, 346, -349, 358, 360, 362, 364, -365, 368, 371, 373, -374, 379, 385
, 399, -405, 532, -562, 571, 575, 596, 604, 606, 1940, -1960, 3971, -3972,
4027, 4033, -4035, 4068, -4070, 4084, -4086, 5547, -5555, 5583, -5600, 5609,
-5618, 5630, -5633, 5644, -5645, 5647, -5648, 5661, -5676, 5679, -5680, 5694,
-5695, 5709, -5716, 5825, -5832, 5839, -5858 ], [ 7, -11, 162, -163, 183,
-186, 563, -567, 580, -582, 616, 619, -620 ], [ 1, -2 ] ] ),
frattFacs := rec( frattFacs := [ 8, 15, 23, 30, 37, 87, 94, 101, 108, 340,
347, 354, 361, 368, 1587, 1594, 1601, 1608, 1615, 1622, 10765, 10772, 10779,
10786, 10793, 10800, 10807 ], pos := [ 1, 2, 6, 405, 567, 582, 620, 4722,
5555, 5733, 5858, 5871, 16704, 17857, 18122, 18143, 18217, 18242, 19877,
20046, 20077, 20100, 20113, 20124, 20127, 20152, 20161 ] ) );