prop896.z

#############################################################################
##
#W  prop896.z              GAP library of groups           Hans Ulrich Besche
##                                               Bettina Eick, Eamonn O'Brien
##

PROPERTIES_SMALL_GROUPS[ 896 ] := rec(
isNilpotent := [ 2, 402, -563, 4667, -5499, 16340, -17492, 19136, -19304,
19335, -19343, 19349 ], 
isSupersolvable := [ 1, -563, 565, -5499, 5507, -17492, 17501, -19304, 19310,
-19343, 19348, -19349 ], 
isAbelian := [ 2, 442, 528, 559, 4682, 4959, 5340, 5491, 16340, 16944, 17479,
19136, 19287, 19335, 19349 ], 
lgLength := rec( lgLength := [ 2, 3, 4, 5, 6, 7, 8 ], pos := [ [ 19348,
-19349 ], [ 1920, -1949, 4053, -4057, 4064, -4070, 4083, -4090, 4647, 4651,
4654, 4667, -4681, 5502, 5507, -10649, 14262, -14328, 14330, -14342, 14354,
-14411, 14433, -14476, 14478, -14499, 14527, -14634, 14660, -14715, 14788,
-14813, 14815, -14823, 14843, -14934, 14954, -15102, 15104, -15123, 15163,
-15219, 15233, -15331, 15382, -15403, 15437, -15480, 16234, -16244, 16252,
-16265, 16272, -16280, 16297, -16309, 16338, -16943, 17501, -18978, 19048,
-19057, 19061, -19073, 19077, -19085, 19092, -19109, 19113, -19119, 19123,
-19129, 19134, -19286, 19309, -19347 ], [ 49, -52, 183, -193, 195, -198, 200,
-203, 205, -206, 210, -211, 214, 225, -228, 231, -234, 237, -242, 246, -252,
254, -260, 274, -280, 282, -288, 308, -331, 402, -441, 564, -1563, 1905,
-1919, 1950, -2258, 2267, -2321, 2323, -2383, 2385, -2400, 2407, -2533, 2540,
-2575, 2582, -2612, 2616, -2646, 2650, -2664, 2671, -3069, 3072, -3113, 3124,
-3167, 3177, -3201, 3211, -3242, 3245, -3375, 3379, -3402, 3413, -3426, 3450,
-3467, 3470, -3503, 3524, -3587, 3620, -3807, 3816, -3829, 3846, -3869, 3879,
-3900, 3911, -3914, 4045, -4052, 4058, -4063, 4071, -4082, 4091, -4187, 4189,
-4222, 4224, -4235, 4237, -4251, 4254, -4289, 4291, -4315, 4317, -4338, 4341,
-4366, 4368, -4378, 4383, -4389, 4394, -4428, 4430, -4441, 4443, -4449, 4451,
-4461, 4463, -4465, 4468, -4469, 4472, -4477, 4480, -4481, 4484, -4497, 4499,
-4523, 4528, -4551, 4557, -4579, 4585, -4594, 4604, -4631, 4634, -4641, 4646,
4648, -4650, 4652, -4653, 4655, -4666, 4682, -5339, 5500, -5501, 5503, -5505,
10650, -14208, 14253, -14261, 14329, 14343, -14353, 14412, -14432, 14477,
14500, -14526, 14635, -14659, 14716, -14787, 14814, 14824, -14842, 14935,
-14953, 15103, 15124, -15162, 15220, -15232, 15332, -15381, 15404, -15436,
15481, -15932, 15935, -15989, 15992, -16028, 16032, -16079, 16083, -16102,
16107, -16217, 16220, -16226, 16229, -16233, 16245, -16251, 16266, -16271,
16281, -16296, 16310, -16337, 16944, -17478, 17493, -17495, 18979, -19047,
19058, -19060, 19074, -19076, 19086, -19091, 19110, -19112, 19120, -19122,
19130, -19133, 19287, -19308 ], [ 8, -31, 36, -48, 53, -78, 83, -90, 92, -109
, 126, -146, 194, 199, 204, 207, -209, 212, -213, 215, -224, 229, -230, 235,
-236, 243, -245, 253, 261, -273, 281, 289, -307, 332, -341, 346, -353, 355,
357, 359, 362, -363, 365, -366, 368, 371, -374, 376, -380, 382, -394, 442,
-527, 1564, -1883, 2259, -2266, 2322, 2384, 2401, -2406, 2534, -2539, 2576,
-2581, 2613, -2615, 2647, -2649, 2665, -2670, 3070, -3071, 3114, -3123, 3168,
-3176, 3202, -3210, 3243, -3244, 3376, -3378, 3403, -3412, 3427, -3449, 3468,
-3469, 3504, -3523, 3588, -3619, 3808, -3815, 3830, -3845, 3870, -3878, 3901,
-3910, 3917, -3970, 3972, -3976, 3980, -4011, 4015, -4027, 4031, -4044, 4188,
4223, 4236, 4252, -4253, 4290, 4316, 4339, -4340, 4367, 4379, -4382, 4390,
-4393, 4429, 4442, 4450, 4462, 4466, -4467, 4470, -4471, 4478, -4479, 4482,
-4483, 4498, 4524, -4527, 4552, -4556, 4580, -4584, 4595, -4603, 4632, -4633,
4642, -4645, 5340, -5490, 14209, -14252, 15933, -15934, 15990, -15991, 16029,
-16031, 16080, -16082, 16103, -16106, 16218, -16219, 16227, -16228, 17479,
-17492, 17496, -17500 ], [ 32, -35, 79, -82, 91, 110, -125, 147, -157, 160,
-178, 342, -345, 354, 356, 358, 360, -361, 364, 367, 369, -370, 375, 381, 395
, -401, 528, -558, 1884, -1904, 3915, -3916, 3971, 3977, -3979, 4012, -4014,
4028, -4030, 5491, -5499, 5506 ], [ 3, -7, 158, -159, 179, -182, 559, -563 ],
[ 1, -2 ] ] ),
frattFacs := rec( frattFacs := [ 8, 15, 23, 30, 80, 87, 94, 291, 298, 305,
1370, 1377, 1384, 9750, 9764, 9771, 9778 ], pos := [ 1, 2, 401, 563, 564,
4666, 5499, 5506, 16339, 17492, 17500, 19135, 19304, 19308, 19309, 19334,
19343 ] ) );