rank 4, subsets of B_4 with 7, 8, 9 hyperplanes: (n, status, exponents, supersolvable): count
   (7, 'free', (1, 2, 2, 2), True) 2052
   (7, 'nonessential', None, None) 144
   (7, 'notfree', None, False) 6740
   (7, 'reducible', None, None) 2504
   (8, 'free', (1, 2, 2, 3), True) 1968
   (8, 'nonessential', None, None) 36
   (8, 'notfree', None, False) 9855
   (8, 'reducible', None, None) 1011
   (9, 'free', (1, 2, 3, 3), False) 180
   (9, 'free', (1, 2, 3, 3), True) 2204
   (9, 'nonessential', None, None) 4
   (9, 'notfree', None, False) 8800
   (9, 'reducible', None, None) 252
free and NOT supersolvable: 180
   e.g. (1, 2, 3, 3) [(1, 0, 0, 0), (0, 1, 0, 0), (1, 1, 0, 0), (1, 0, 1, 0), (1, 0, -1, 0), (1, 0, 0, 1), (1, 0, 0, -1), (0, 0, 1, 1), (0, 0, 1, -1)]
   e.g. (1, 2, 3, 3) [(1, 0, 0, 0), (0, 1, 0, 0), (1, 1, 0, 0), (0, 1, 1, 0), (0, 1, -1, 0), (0, 1, 0, 1), (0, 1, 0, -1), (0, 0, 1, 1), (0, 0, 1, -1)]
   e.g. (1, 2, 3, 3) [(1, 0, 0, 0), (0, 1, 0, 0), (1, -1, 0, 0), (1, 0, 1, 0), (1, 0, -1, 0), (1, 0, 0, 1), (1, 0, 0, -1), (0, 0, 1, 1), (0, 0, 1, -1)]
   e.g. (1, 2, 3, 3) [(1, 0, 0, 0), (0, 1, 0, 0), (1, -1, 0, 0), (0, 1, 1, 0), (0, 1, -1, 0), (0, 1, 0, 1), (0, 1, 0, -1), (0, 0, 1, 1), (0, 0, 1, -1)]
   e.g. (1, 2, 3, 3) [(1, 0, 0, 0), (0, 0, 1, 0), (1, 1, 0, 0), (1, -1, 0, 0), (1, 0, 1, 0), (1, 0, 0, 1), (1, 0, 0, -1), (0, 1, 0, 1), (0, 1, 0, -1)]
time 632.5s
