T1  P=S_4, Q=S_3, T=S_3 (phi onto Inn): |P| = 24, |Q| = 6, k = 4, |T| = 6, |phi(Q)| = 6, |B| = 1296; subgroups of P: 30 (11 classes), good: 28
    M = 3; max stabiliser of f != 1 (literal) = 12; max order of a good subgroup = 12; equal: True; M_G > M (strict)
    stabiliser orders occurring: [1, 2, 3, 4, 6, 8, 12]; orders of good subgroups: [1, 2, 3, 4, 6, 8, 12]; subset: True
    first half on 1295 elements f: True; second half on 86 pairs (S, t): True; one-coordinate elements have stabiliser Q_t: True   (0.1s)
T2  P=S_4, Q=S_3, T=C_3 (phi(Q)=C_2): |P| = 24, |Q| = 6, k = 4, |T| = 3, |phi(Q)| = 2, |B| = 81; subgroups of P: 30 (11 classes), good: 16
    M = 3; max stabiliser of f != 1 (literal) = 12; max order of a good subgroup = 12; equal: True; M_G > M (strict)
    stabiliser orders occurring: [1, 2, 3, 4, 12]; orders of good subgroups: [1, 2, 3, 4, 12]; subset: True
    first half on 80 elements f: True; second half on 32 pairs (S, t): True; one-coordinate elements have stabiliser Q_t: True   (0.0s)
T3  P=S_4, Q=D_8, T=V_4<=D_8 acting on 4 points (phi(Q)=D_8/Z): |P| = 24, |Q| = 8, k = 3, |T| = 4, |phi(Q)| = 2, |B| = 64; subgroups of P: 30 (11 classes), good: 30
    M = 8; max stabiliser of f != 1 (literal) = 24; max order of a good subgroup = 24; equal: True; M_G > M (strict)
    stabiliser orders occurring: [4, 8, 12, 24]; orders of good subgroups: [1, 2, 3, 4, 6, 8, 12, 24]; subset: True
    first half on 63 elements f: True; second half on 70 pairs (S, t): True; one-coordinate elements have stabiliser Q_t: True   (0.0s)
T4  P=A_5, Q=A_4, T=V_4: |P| = 60, |Q| = 12, k = 5, |T| = 4, |phi(Q)| = 3, |B| = 1024; subgroups of P: 59 (9 classes), good: 45
    M = 4; max stabiliser of f != 1 (literal) = 10; max order of a good subgroup = 10; equal: True; M_G > M (strict)
    stabiliser orders occurring: [1, 2, 4, 6, 10]; orders of good subgroups: [1, 2, 3, 4, 5, 6, 10]; subset: True
    first half on 1023 elements f: True; second half on 135 pairs (S, t): True; one-coordinate elements have stabiliser Q_t: True   (0.1s)
T5  P=A_5, Q=A_4, T=A_4 (phi onto Inn): |P| = 60, |Q| = 12, k = 5, |T| = 12, |phi(Q)| = 12, |B| = 248832; subgroups of P: 59 (9 classes), good: 57
    M = 4; max stabiliser of f != 1 (literal) = 12; max order of a good subgroup = 12; equal: True; M_G > M (strict)
    stabiliser orders occurring: [1, 2, 3, 4, 5, 6, 10, 12]; orders of good subgroups: [1, 2, 3, 4, 5, 6, 10, 12]; subset: True
    first half on 5009 elements f: True; second half on 391 pairs (S, t): True; one-coordinate elements have stabiliser Q_t: True   (1.7s)
T6  P=S_5, Q=S_4, T=V_4: |P| = 120, |Q| = 24, k = 5, |T| = 4, |phi(Q)| = 6, |B| = 1024; subgroups of P: 156 (19 classes), good: 124
    M = 8; max stabiliser of f != 1 (literal) = 20; max order of a good subgroup = 20; equal: True; M_G > M (strict)
    stabiliser orders occurring: [1, 2, 4, 6, 8, 10, 12, 20]; orders of good subgroups: [1, 2, 3, 4, 5, 6, 8, 10, 12, 20]; subset: True
    first half on 1023 elements f: True; second half on 246 pairs (S, t): True; one-coordinate elements have stabiliser Q_t: True   (0.2s)
T7  P=S_5, Q=A_5 (k=2), T=A_5 (simple; imprimitive datum): |P| = 120, |Q| = 60, k = 2, |T| = 60, |phi(Q)| = 60, |B| = 3600; subgroups of P: 156 (19 classes), good: 112
    M = 5; max stabiliser of f != 1 (literal) = 8; max order of a good subgroup = 8; equal: True; M_G > M (strict)
    stabiliser orders occurring: [1, 2, 3, 4, 5, 6, 8]; orders of good subgroups: [1, 2, 3, 4, 5, 6, 8]; subset: True
    first half on 3599 elements f: True; second half on 928 pairs (S, t): True; one-coordinate elements have stabiliser Q_t: True   (1.1s)
T8  P=PSL(2,5) on 6 points, Q=D_10, T=C_5 (abelian; phi(Q)=C_2): |P| = 60, |Q| = 10, k = 6, |T| = 5, |phi(Q)| = 2, |B| = 15625; subgroups of P: 59 (9 classes), good: 27
    M = 5; max stabiliser of f != 1 (literal) = 5; max order of a good subgroup = 5; equal: True; M_G = M (equality case)
    stabiliser orders occurring: [1, 2, 3, 5]; orders of good subgroups: [1, 2, 3, 5]; subset: True
    first half on 5110 elements f: True; second half on 108 pairs (S, t): True; one-coordinate elements have stabiliser Q_t: True   (0.6s)
T9  P=PGL(2,5) on 6 points, Q=5:4, T=C_5 (phi(Q)=C_4): |P| = 120, |Q| = 20, k = 6, |T| = 5, |phi(Q)| = 4, |B| = 15625; subgroups of P: 156 (19 classes), good: 77
    M = 5; max stabiliser of f != 1 (literal) = 6; max order of a good subgroup = 6; equal: True; M_G > M (strict)
    stabiliser orders occurring: [1, 2, 3, 4, 5, 6]; orders of good subgroups: [1, 2, 3, 4, 5, 6]; subset: True
    first half on 5058 elements f: True; second half on 308 pairs (S, t): True; one-coordinate elements have stabiliser Q_t: True   (1.1s)
T10 P=PGL(3,2), Q=S_4, T=S_3=PGL(2,2) via the 3 lines through the point (analogue of Theorem A, q=2): |P| = 168, |Q| = 24, k = 7, |T| = 6, |phi(Q)| = 6, |B| = 279936; subgroups of P: 179 (15 classes), good: 169
    M = 12; max stabiliser of f != 1 (literal) = 24; max order of a good subgroup = 24; equal: True; M_G > M (strict)
    stabiliser orders occurring: [1, 2, 3, 4, 6, 7, 8, 12, 21, 24]; orders of good subgroups: [1, 2, 3, 4, 6, 7, 8, 12, 21, 24]; subset: True
    first half on 5014 elements f: True; second half on 494 pairs (S, t): True; one-coordinate elements have stabiliser Q_t: True   (10.0s)
T11 P=PGL(3,2), Q=S_4, T=C_3 via the 3 lines through the point: |P| = 168, |Q| = 24, k = 7, |T| = 3, |phi(Q)| = 2, |B| = 2187; subgroups of P: 179 (15 classes), good: 94
    M = 12; max stabiliser of f != 1 (literal) = 21; max order of a good subgroup = 21; equal: True; M_G > M (strict)
    stabiliser orders occurring: [1, 2, 3, 4, 6, 12, 21]; orders of good subgroups: [1, 2, 3, 4, 6, 7, 12, 21]; subset: True
    first half on 2186 elements f: True; second half on 188 pairs (S, t): True; one-coordinate elements have stabiliser Q_t: True   (0.4s)
TOY TESTS ALL PASSED [True, True, True, True, True, True, True, True, True, True, True]
