== L2_7: |S| = 168, |A| = 336, 179 subgroups in 15 S-classes
  coset d^1 f^0    r=2 p=2  : WITNESS EXISTS; 1 classes, e.g. |X|=7 b1(q=7) |N_S(X)|=21 |F*|=7
  coset d^1 f^0    r=2 p=3  : WITNESS EXISTS; 1 classes, e.g. |X|=7 b1(q=7) |N_S(X)|=21 |F*|=7
  coset d^1 f^0    r=2 p=7  : NO WITNESS among all 7 Aut-invariant classes
  coset d^1 f^0    r=2 p=11 : WITNESS EXISTS; 1 classes, e.g. |X|=7 b1(q=7) |N_S(X)|=21 |F*|=7
  (time 0.0s)
== L2_9: |S| = 360, |A| = 1440, 501 subgroups in 22 S-classes
  coset d^1 f^0    r=2 p=2  : WITNESS EXISTS; 1 classes, e.g. |X|=9 b1(q=3) |N_S(X)|=36 |F*|=9
  coset d^1 f^0    r=2 p=3  : NO WITNESS among all 8 Aut-invariant classes
  coset d^1 f^0    r=2 p=5  : WITNESS EXISTS; 1 classes, e.g. |X|=9 b1(q=3) |N_S(X)|=36 |F*|=9
  coset d^1 f^0    r=2 p=7  : WITNESS EXISTS; 1 classes, e.g. |X|=9 b1(q=3) |N_S(X)|=36 |F*|=9
  coset d^0 f^1    r=2 p=2  : WITNESS EXISTS; 4 classes, e.g. |X|=5 b1(q=5) |N_S(X)|=10 |F*|=5; |X|=9 b1(q=3) |N_S(X)|=36 |F*|=9; |X|=18 b2 |N_S(X)|=36 |F*|=9; |X|=36 b2 |N_S(X)|=36 |F*|=9
  coset d^0 f^1    r=2 p=3  : WITNESS EXISTS; 1 classes, e.g. |X|=5 b1(q=5) |N_S(X)|=10 |F*|=5
  coset d^0 f^1    r=2 p=5  : WITNESS EXISTS; 3 classes, e.g. |X|=9 b1(q=3) |N_S(X)|=36 |F*|=9; |X|=18 b2 |N_S(X)|=36 |F*|=9; |X|=36 b2 |N_S(X)|=36 |F*|=9
  coset d^0 f^1    r=2 p=7  : WITNESS EXISTS; 4 classes, e.g. |X|=5 b1(q=5) |N_S(X)|=10 |F*|=5; |X|=9 b1(q=3) |N_S(X)|=36 |F*|=9; |X|=18 b2 |N_S(X)|=36 |F*|=9; |X|=36 b2 |N_S(X)|=36 |F*|=9
  coset d^1 f^1    r=2 p=2  : WITNESS EXISTS; 4 classes, e.g. |X|=5 b1(q=5) |N_S(X)|=10 |F*|=5; |X|=9 b1(q=3) |N_S(X)|=36 |F*|=9; |X|=18 b2 |N_S(X)|=36 |F*|=9; |X|=36 b2 |N_S(X)|=36 |F*|=9
  coset d^1 f^1    r=2 p=3  : WITNESS EXISTS; 1 classes, e.g. |X|=5 b1(q=5) |N_S(X)|=10 |F*|=5
  coset d^1 f^1    r=2 p=5  : WITNESS EXISTS; 3 classes, e.g. |X|=9 b1(q=3) |N_S(X)|=36 |F*|=9; |X|=18 b2 |N_S(X)|=36 |F*|=9; |X|=36 b2 |N_S(X)|=36 |F*|=9
  coset d^1 f^1    r=2 p=7  : WITNESS EXISTS; 4 classes, e.g. |X|=5 b1(q=5) |N_S(X)|=10 |F*|=5; |X|=9 b1(q=3) |N_S(X)|=36 |F*|=9; |X|=18 b2 |N_S(X)|=36 |F*|=9; |X|=36 b2 |N_S(X)|=36 |F*|=9
  (time 0.1s)
== L2_8: |S| = 504, |A| = 1512, 386 subgroups in 12 S-classes
  coset frob^1     r=3 p=2  : WITNESS EXISTS; 1 classes, e.g. |X|=7 b1(q=7) |N_S(X)|=14 |F*|=7
  coset frob^1     r=3 p=3  : WITNESS EXISTS; 4 classes, e.g. |X|=4 b1(q=2) |N_S(X)|=8 |F*|=8; |X|=7 b1(q=7) |N_S(X)|=14 |F*|=7; |X|=8 b1(q=2) |N_S(X)|=56 |F*|=8; |X|=56 b2 |N_S(X)|=56 |F*|=8
  coset frob^1     r=3 p=7  : WITNESS EXISTS; 3 classes, e.g. |X|=4 b1(q=2) |N_S(X)|=8 |F*|=8; |X|=8 b1(q=2) |N_S(X)|=56 |F*|=8; |X|=56 b2 |N_S(X)|=56 |F*|=8
  coset frob^1     r=3 p=11 : WITNESS EXISTS; 4 classes, e.g. |X|=4 b1(q=2) |N_S(X)|=8 |F*|=8; |X|=7 b1(q=7) |N_S(X)|=14 |F*|=7; |X|=8 b1(q=2) |N_S(X)|=56 |F*|=8; |X|=56 b2 |N_S(X)|=56 |F*|=8
  coset frob^2     r=3 p=2  : WITNESS EXISTS; 1 classes, e.g. |X|=7 b1(q=7) |N_S(X)|=14 |F*|=7
  coset frob^2     r=3 p=3  : WITNESS EXISTS; 4 classes, e.g. |X|=4 b1(q=2) |N_S(X)|=8 |F*|=8; |X|=7 b1(q=7) |N_S(X)|=14 |F*|=7; |X|=8 b1(q=2) |N_S(X)|=56 |F*|=8; |X|=56 b2 |N_S(X)|=56 |F*|=8
  coset frob^2     r=3 p=7  : WITNESS EXISTS; 3 classes, e.g. |X|=4 b1(q=2) |N_S(X)|=8 |F*|=8; |X|=8 b1(q=2) |N_S(X)|=56 |F*|=8; |X|=56 b2 |N_S(X)|=56 |F*|=8
  coset frob^2     r=3 p=11 : WITNESS EXISTS; 4 classes, e.g. |X|=4 b1(q=2) |N_S(X)|=8 |F*|=8; |X|=7 b1(q=7) |N_S(X)|=14 |F*|=7; |X|=8 b1(q=2) |N_S(X)|=56 |F*|=8; |X|=56 b2 |N_S(X)|=56 |F*|=8
  (time 0.3s)
== L2_11: |S| = 660, |A| = 1320, 620 subgroups in 16 S-classes
  coset d^1 f^0    r=2 p=2  : WITNESS EXISTS; 1 classes, e.g. |X|=11 b1(q=11) |N_S(X)|=55 |F*|=11
  coset d^1 f^0    r=2 p=3  : WITNESS EXISTS; 3 classes, e.g. |X|=4 b2 |N_S(X)|=12 |F*|=4; |X|=11 b1(q=11) |N_S(X)|=55 |F*|=11; |X|=12 b2 |N_S(X)|=12 |F*|=4
  coset d^1 f^0    r=2 p=5  : WITNESS EXISTS; 3 classes, e.g. |X|=4 b2 |N_S(X)|=12 |F*|=4; |X|=11 b1(q=11) |N_S(X)|=55 |F*|=11; |X|=12 b2 |N_S(X)|=12 |F*|=4
  coset d^1 f^0    r=2 p=11 : WITNESS EXISTS; 2 classes, e.g. |X|=4 b2 |N_S(X)|=12 |F*|=4; |X|=12 b2 |N_S(X)|=12 |F*|=4
  coset d^1 f^0    r=2 p=7  : WITNESS EXISTS; 3 classes, e.g. |X|=4 b2 |N_S(X)|=12 |F*|=4; |X|=11 b1(q=11) |N_S(X)|=55 |F*|=11; |X|=12 b2 |N_S(X)|=12 |F*|=4
  (time 0.4s)
== L2_13: |S| = 1092, |A| = 2184, 942 subgroups in 16 S-classes
  coset d^1 f^0    r=2 p=2  : WITNESS EXISTS; 1 classes, e.g. |X|=13 b1(q=13) |N_S(X)|=78 |F*|=13
  coset d^1 f^0    r=2 p=3  : WITNESS EXISTS; 3 classes, e.g. |X|=4 b2 |N_S(X)|=12 |F*|=4; |X|=12 b2 |N_S(X)|=12 |F*|=4; |X|=13 b1(q=13) |N_S(X)|=78 |F*|=13
  coset d^1 f^0    r=2 p=7  : WITNESS EXISTS; 3 classes, e.g. |X|=4 b2 |N_S(X)|=12 |F*|=4; |X|=12 b2 |N_S(X)|=12 |F*|=4; |X|=13 b1(q=13) |N_S(X)|=78 |F*|=13
  coset d^1 f^0    r=2 p=13 : WITNESS EXISTS; 2 classes, e.g. |X|=4 b2 |N_S(X)|=12 |F*|=4; |X|=12 b2 |N_S(X)|=12 |F*|=4
  coset d^1 f^0    r=2 p=11 : WITNESS EXISTS; 3 classes, e.g. |X|=4 b2 |N_S(X)|=12 |F*|=4; |X|=12 b2 |N_S(X)|=12 |F*|=4; |X|=13 b1(q=13) |N_S(X)|=78 |F*|=13
  (time 1.4s)
== L2_17: |S| = 2448, |A| = 4896, 2420 subgroups in 22 S-classes
  coset d^1 f^0    r=2 p=2  : WITNESS EXISTS; 1 classes, e.g. |X|=17 b1(q=17) |N_S(X)|=136 |F*|=17
  coset d^1 f^0    r=2 p=3  : WITNESS EXISTS; 1 classes, e.g. |X|=17 b1(q=17) |N_S(X)|=136 |F*|=17
  coset d^1 f^0    r=2 p=17 : NO WITNESS among all 12 Aut-invariant classes
  coset d^1 f^0    r=2 p=7  : WITNESS EXISTS; 1 classes, e.g. |X|=17 b1(q=17) |N_S(X)|=136 |F*|=17
  (time 8.9s)
== L2_19: |S| = 3420, |A| = 6840, 2912 subgroups in 19 S-classes
  coset d^1 f^0    r=2 p=2  : WITNESS EXISTS; 1 classes, e.g. |X|=19 b1(q=19) |N_S(X)|=171 |F*|=19
  coset d^1 f^0    r=2 p=3  : WITNESS EXISTS; 3 classes, e.g. |X|=4 b2 |N_S(X)|=12 |F*|=4; |X|=12 b2 |N_S(X)|=12 |F*|=4; |X|=19 b1(q=19) |N_S(X)|=171 |F*|=19
  coset d^1 f^0    r=2 p=5  : WITNESS EXISTS; 3 classes, e.g. |X|=4 b2 |N_S(X)|=12 |F*|=4; |X|=12 b2 |N_S(X)|=12 |F*|=4; |X|=19 b1(q=19) |N_S(X)|=171 |F*|=19
  coset d^1 f^0    r=2 p=19 : WITNESS EXISTS; 2 classes, e.g. |X|=4 b2 |N_S(X)|=12 |F*|=4; |X|=12 b2 |N_S(X)|=12 |F*|=4
  coset d^1 f^0    r=2 p=7  : WITNESS EXISTS; 3 classes, e.g. |X|=4 b2 |N_S(X)|=12 |F*|=4; |X|=12 b2 |N_S(X)|=12 |F*|=4; |X|=19 b1(q=19) |N_S(X)|=171 |F*|=19
  (time 19.7s)
== L2_27: |S| = 9828, |A| = 58968, 5286 subgroups in 16 S-classes
  coset d^1 f^0    r=2 p=2  : WITNESS EXISTS; 3 classes, e.g. |X|=3 b1(q=3) |N_S(X)|=27 |F*|=27; |X|=9 b1(q=3) |N_S(X)|=27 |F*|=27; |X|=27 b1(q=3) |N_S(X)|=351 |F*|=27
  coset d^1 f^0    r=2 p=3  : WITNESS EXISTS; 2 classes, e.g. |X|=4 b2 |N_S(X)|=12 |F*|=4; |X|=12 b2 |N_S(X)|=12 |F*|=4
  coset d^1 f^0    r=2 p=7  : WITNESS EXISTS; 5 classes, e.g. |X|=3 b1(q=3) |N_S(X)|=27 |F*|=27; |X|=4 b2 |N_S(X)|=12 |F*|=4; |X|=9 b1(q=3) |N_S(X)|=27 |F*|=27; |X|=12 b2 |N_S(X)|=12 |F*|=4
  coset d^1 f^0    r=2 p=13 : WITNESS EXISTS; 5 classes, e.g. |X|=3 b1(q=3) |N_S(X)|=27 |F*|=27; |X|=4 b2 |N_S(X)|=12 |F*|=4; |X|=9 b1(q=3) |N_S(X)|=27 |F*|=27; |X|=12 b2 |N_S(X)|=12 |F*|=4
  coset d^1 f^0    r=2 p=11 : WITNESS EXISTS; 5 classes, e.g. |X|=3 b1(q=3) |N_S(X)|=27 |F*|=27; |X|=4 b2 |N_S(X)|=12 |F*|=4; |X|=9 b1(q=3) |N_S(X)|=27 |F*|=27; |X|=12 b2 |N_S(X)|=12 |F*|=4
  coset d^0 f^1    r=3 p=2  : WITNESS EXISTS; 4 classes, e.g. |X|=7 b1(q=7) |N_S(X)|=28 |F*|=14; |X|=13 b1(q=13) |N_S(X)|=26 |F*|=13; |X|=27 b2 |N_S(X)|=351 |F*|=27; |X|=351 b2 |N_S(X)|=351 |F*|=27
  coset d^0 f^1    r=3 p=3  : WITNESS EXISTS; 2 classes, e.g. |X|=7 b1(q=7) |N_S(X)|=28 |F*|=14; |X|=13 b1(q=13) |N_S(X)|=26 |F*|=13
  coset d^0 f^1    r=3 p=7  : WITNESS EXISTS; 3 classes, e.g. |X|=13 b1(q=13) |N_S(X)|=26 |F*|=13; |X|=27 b2 |N_S(X)|=351 |F*|=27; |X|=351 b2 |N_S(X)|=351 |F*|=27
  coset d^0 f^1    r=3 p=13 : WITNESS EXISTS; 3 classes, e.g. |X|=7 b1(q=7) |N_S(X)|=28 |F*|=14; |X|=27 b2 |N_S(X)|=351 |F*|=27; |X|=351 b2 |N_S(X)|=351 |F*|=27
  coset d^0 f^1    r=3 p=11 : WITNESS EXISTS; 4 classes, e.g. |X|=7 b1(q=7) |N_S(X)|=28 |F*|=14; |X|=13 b1(q=13) |N_S(X)|=26 |F*|=13; |X|=27 b2 |N_S(X)|=351 |F*|=27; |X|=351 b2 |N_S(X)|=351 |F*|=27
  coset d^0 f^2    r=3 p=2  : WITNESS EXISTS; 4 classes, e.g. |X|=7 b1(q=7) |N_S(X)|=28 |F*|=14; |X|=13 b1(q=13) |N_S(X)|=26 |F*|=13; |X|=27 b2 |N_S(X)|=351 |F*|=27; |X|=351 b2 |N_S(X)|=351 |F*|=27
  coset d^0 f^2    r=3 p=3  : WITNESS EXISTS; 2 classes, e.g. |X|=7 b1(q=7) |N_S(X)|=28 |F*|=14; |X|=13 b1(q=13) |N_S(X)|=26 |F*|=13
  coset d^0 f^2    r=3 p=7  : WITNESS EXISTS; 3 classes, e.g. |X|=13 b1(q=13) |N_S(X)|=26 |F*|=13; |X|=27 b2 |N_S(X)|=351 |F*|=27; |X|=351 b2 |N_S(X)|=351 |F*|=27
  coset d^0 f^2    r=3 p=13 : WITNESS EXISTS; 3 classes, e.g. |X|=7 b1(q=7) |N_S(X)|=28 |F*|=14; |X|=27 b2 |N_S(X)|=351 |F*|=27; |X|=351 b2 |N_S(X)|=351 |F*|=27
  coset d^0 f^2    r=3 p=11 : WITNESS EXISTS; 4 classes, e.g. |X|=7 b1(q=7) |N_S(X)|=28 |F*|=14; |X|=13 b1(q=13) |N_S(X)|=26 |F*|=13; |X|=27 b2 |N_S(X)|=351 |F*|=27; |X|=351 b2 |N_S(X)|=351 |F*|=27
  (time 248.5s)
