(Z1) |S|                           ok  |S| = 29120 (q^2(q-1)(q^2+1) = 29120)
(Z1) S perfect                     ok  |S'| = 29120
(Z1) S simple                      ok  11 conjugacy classes, sizes [1, 455, 1820, 1820, 2240, 2240, 2240, 4160, 4160, 4160, 5824]
(Z1) sigma normalizes S, |S<sigma>| ok  |A| = 87360
(Z2) |U|, |H|                      ok  |U| = 64, |h| = 7
(Z2) B = N_S(U)                    ok  |B| = 448, |C_S(U)| = 8 (inside U: True)
(Z2) F(B) = U, O_p(B) = 1 (p odd)  ok  H fixed-point-free on U: True; Fitting series orders [1, 64, 448]; O_p(B) orders {3: 1, 5: 1, 7: 1, 13: 1}
(Z3) t=5                           ok  |C_S(z)| = 5 cyclic: True, |N_S(<z>)| = 20 soluble: True
(Z3) t=7                           ok  |C_S(z)| = 7 cyclic: True, |N_S(<z>)| = 14 soluble: True
(Z3) t=13                          ok  |C_S(z)| = 13 cyclic: True, |N_S(<z>)| = 52 soluble: True
(Z4) j=1                           ok  |C_S(sigma)| = 20 (|Sz(2)| = 20), #order-3 in S sigma^1 = 1456 (|S|/20 = 1456)
(Z4) j=2                           ok  |C_S(sigma)| = 20 (|Sz(2)| = 20), #order-3 in S sigma^2 = 1456 (|S|/20 = 1456)
Lemma 3.1 j=1                      ok  beta normalizing U: 448, trivial on B/U: 0
Lemma 3.1 j=2                      ok  beta normalizing U: 448, trivial on B/U: 0
Lemma 3.2 j=1                      ok  beta in S sigma^1 centralizing Q_t: {5: 5, 7: 0, 13: 0}
Lemma 3.2 j=2                      ok  beta in S sigma^2 centralizing Q_t: {5: 5, 7: 0, 13: 0}
Sz(8): ALL OK  [2.5s]
nice -n 10 python3 -u -I   2.54s user 0.01s system 99% cpu 2.556 total
