Sz(8), modulus x^3+x+1, generator of GF(8)^*: 2
form preserved by all U(a,b), M(c), T: True
order of the group generated: 29120 (expected q^2(q^2+1)(q-1) = 29120)
classes: 11, sizes [1, 455, 1820, 1820, 2240, 2240, 2240, 4160, 4160, 4160, 5824], sum 29120
   y of order  1, class size     1: max tail 1
   y of order  2, class size   455: max tail 2
   y of order  4, class size  1820: max tail 8
   y of order  4, class size  1820: max tail 11
   y of order  5, class size  5824: max tail 62
   y of order  7, class size  4160: max tail 56
   y of order  7, class size  4160: max tail 56
   y of order  7, class size  4160: max tail 56
   y of order 13, class size  2240: max tail 27
   y of order 13, class size  2240: max tail 27
   y of order 13, class size  2240: max tail 27
mu(Sz(8)) = 62; witness: tail 62, period of the cycle reached 90
   periods of the cycles reached by all pairs (class representatives y) with tail 62: [90]
   witness re-iterated with tuples: tail 62, period 90
   witness x = (6, 2, 0, 1, 2, 0, 1, 0, 7, 5, 0, 2, 7, 7, 2, 6)
   witness y = (0, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 1, 1, 0, 1, 1)   [1.6s]
Proposition 5.1 (q = 8): 43552 double cosets <y>x<y> over the 11 class representatives y; orders of the proper subgroups <x,y> met: [1, 2, 4, 5, 7, 8, 10, 13, 14, 20, 26, 32, 52, 56, 448]; max tail(x,y) over pairs with <x,y> proper: 3; pairs with tail >= 4: 202617, of which not generating: 0   [341.4s]
Section 5.2 (q = 8, y = M(c), c != 1, all x, column and row action): pairs with some a_j exchanging the two fixed points: 61824; of these with tail = j+2: 61824; with more than one such j: 0   [0.4s]
exit=0
