== L2_23: |S| = 6072, |A| = 12144, 5915 subgroups in 23 S-classes (non-soluble search skipped: none exist by Dickson)
  coset d^1 f^0    r=2 p=2  : WITNESS EXISTS; 1 classes, e.g. |X|=23 b1(q=23) |N_S(X)|=253 |F*|=23
  coset d^1 f^0    r=2 p=3  : WITNESS EXISTS; 1 classes, e.g. |X|=23 b1(q=23) |N_S(X)|=253 |F*|=23
  coset d^1 f^0    r=2 p=11 : WITNESS EXISTS; 1 classes, e.g. |X|=23 b1(q=23) |N_S(X)|=253 |F*|=23
  coset d^1 f^0    r=2 p=23 : NO WITNESS among all 11 Aut-invariant classes
  coset d^1 f^0    r=2 p=7  : WITNESS EXISTS; 1 classes, e.g. |X|=23 b1(q=23) |N_S(X)|=253 |F*|=23
  (time 0.4s)
== L2_16: |S| = 4080, |A| = 16320, 3455 subgroups in 21 S-classes
  coset frob^2     r=2 p=2  : WITNESS EXISTS; 1 classes, e.g. |X|=17 b1(q=17) |N_S(X)|=34 |F*|=17
  coset frob^2     r=2 p=3  : WITNESS EXISTS; 5 classes, e.g. |X|=16 b2 |N_S(X)|=240 |F*|=16; |X|=17 b1(q=17) |N_S(X)|=34 |F*|=17; |X|=48 b2 |N_S(X)|=240 |F*|=16; |X|=80 b2 |N_S(X)|=240 |F*|=16
  coset frob^2     r=2 p=5  : WITNESS EXISTS; 5 classes, e.g. |X|=16 b2 |N_S(X)|=240 |F*|=16; |X|=17 b1(q=17) |N_S(X)|=34 |F*|=17; |X|=48 b2 |N_S(X)|=240 |F*|=16; |X|=80 b2 |N_S(X)|=240 |F*|=16
  coset frob^2     r=2 p=17 : WITNESS EXISTS; 4 classes, e.g. |X|=16 b2 |N_S(X)|=240 |F*|=16; |X|=48 b2 |N_S(X)|=240 |F*|=16; |X|=80 b2 |N_S(X)|=240 |F*|=16; |X|=240 b2 |N_S(X)|=240 |F*|=16
  coset frob^2     r=2 p=7  : WITNESS EXISTS; 5 classes, e.g. |X|=16 b2 |N_S(X)|=240 |F*|=16; |X|=17 b1(q=17) |N_S(X)|=34 |F*|=17; |X|=48 b2 |N_S(X)|=240 |F*|=16; |X|=80 b2 |N_S(X)|=240 |F*|=16
  (time 41.8s)
== A7: |S| = 2520, |A| = 5040, 3786 subgroups in 40 S-classes
  coset odd        r=2 p=2  : WITNESS EXISTS; 4 classes, e.g. |X|=7 b1(q=7) |N_S(X)|=21 |F*|=7; |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 odd        r=2 p=3  : WITNESS EXISTS; 1 classes, e.g. |X|=7 b1(q=7) |N_S(X)|=21 |F*|=7
  coset odd        r=2 p=5  : WITNESS EXISTS; 4 classes, e.g. |X|=7 b1(q=7) |N_S(X)|=21 |F*|=7; |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 odd        r=2 p=7  : 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 odd        r=2 p=11 : WITNESS EXISTS; 4 classes, e.g. |X|=7 b1(q=7) |N_S(X)|=21 |F*|=7; |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 5.8s)
== L2_25: |S| = 7800, |A| = 31200, 9559 subgroups in 37 S-classes
  coset d^1 f^0    r=2 p=2  : WITNESS EXISTS; 1 classes, e.g. |X|=25 b1(q=5) |N_S(X)|=300 |F*|=25
  coset d^1 f^0    r=2 p=3  : WITNESS EXISTS; 1 classes, e.g. |X|=25 b1(q=5) |N_S(X)|=300 |F*|=25
  coset d^1 f^0    r=2 p=5  : NO WITNESS among all 15 Aut-invariant classes
  coset d^1 f^0    r=2 p=13 : WITNESS EXISTS; 1 classes, e.g. |X|=25 b1(q=5) |N_S(X)|=300 |F*|=25
  coset d^1 f^0    r=2 p=7  : WITNESS EXISTS; 1 classes, e.g. |X|=25 b1(q=5) |N_S(X)|=300 |F*|=25
  coset d^0 f^1    r=2 p=2  : WITNESS EXISTS; 7 classes, e.g. |X|=13 b1(q=13) |N_S(X)|=26 |F*|=13; |X|=25 b1(q=5) |N_S(X)|=300 |F*|=25; |X|=50 b2 |N_S(X)|=300 |F*|=25; |X|=75 b2 |N_S(X)|=300 |F*|=25
  coset d^0 f^1    r=2 p=3  : WITNESS EXISTS; 7 classes, e.g. |X|=13 b1(q=13) |N_S(X)|=26 |F*|=13; |X|=25 b1(q=5) |N_S(X)|=300 |F*|=25; |X|=50 b2 |N_S(X)|=300 |F*|=25; |X|=75 b2 |N_S(X)|=300 |F*|=25
  coset d^0 f^1    r=2 p=5  : WITNESS EXISTS; 1 classes, e.g. |X|=13 b1(q=13) |N_S(X)|=26 |F*|=13
  coset d^0 f^1    r=2 p=13 : WITNESS EXISTS; 6 classes, e.g. |X|=25 b1(q=5) |N_S(X)|=300 |F*|=25; |X|=50 b2 |N_S(X)|=300 |F*|=25; |X|=75 b2 |N_S(X)|=300 |F*|=25; |X|=100 b2 |N_S(X)|=300 |F*|=25
  coset d^0 f^1    r=2 p=7  : WITNESS EXISTS; 7 classes, e.g. |X|=13 b1(q=13) |N_S(X)|=26 |F*|=13; |X|=25 b1(q=5) |N_S(X)|=300 |F*|=25; |X|=50 b2 |N_S(X)|=300 |F*|=25; |X|=75 b2 |N_S(X)|=300 |F*|=25
  coset d^1 f^1    r=2 p=2  : WITNESS EXISTS; 7 classes, e.g. |X|=13 b1(q=13) |N_S(X)|=26 |F*|=13; |X|=25 b1(q=5) |N_S(X)|=300 |F*|=25; |X|=50 b2 |N_S(X)|=300 |F*|=25; |X|=75 b2 |N_S(X)|=300 |F*|=25
  coset d^1 f^1    r=2 p=3  : WITNESS EXISTS; 7 classes, e.g. |X|=13 b1(q=13) |N_S(X)|=26 |F*|=13; |X|=25 b1(q=5) |N_S(X)|=300 |F*|=25; |X|=50 b2 |N_S(X)|=300 |F*|=25; |X|=75 b2 |N_S(X)|=300 |F*|=25
  coset d^1 f^1    r=2 p=5  : WITNESS EXISTS; 1 classes, e.g. |X|=13 b1(q=13) |N_S(X)|=26 |F*|=13
  coset d^1 f^1    r=2 p=13 : WITNESS EXISTS; 6 classes, e.g. |X|=25 b1(q=5) |N_S(X)|=300 |F*|=25; |X|=50 b2 |N_S(X)|=300 |F*|=25; |X|=75 b2 |N_S(X)|=300 |F*|=25; |X|=100 b2 |N_S(X)|=300 |F*|=25
  coset d^1 f^1    r=2 p=7  : WITNESS EXISTS; 7 classes, e.g. |X|=13 b1(q=13) |N_S(X)|=26 |F*|=13; |X|=25 b1(q=5) |N_S(X)|=300 |F*|=25; |X|=50 b2 |N_S(X)|=300 |F*|=25; |X|=75 b2 |N_S(X)|=300 |F*|=25
  (time 146.6s)
== L2_32: |S| = 32736, |A| = 163680, 22328 subgroups in 24 S-classes (non-soluble search skipped: none exist by Dickson)
  coset frob^1     r=5 p=2  : WITNESS EXISTS; 2 classes, e.g. |X|=11 b1(q=11) |N_S(X)|=66 |F*|=33; |X|=31 b1(q=31) |N_S(X)|=62 |F*|=31
  coset frob^1     r=5 p=3  : WITNESS EXISTS; 5 classes, e.g. |X|=11 b1(q=11) |N_S(X)|=66 |F*|=33; |X|=16 b1(q=2) |N_S(X)|=32 |F*|=32; |X|=31 b1(q=31) |N_S(X)|=62 |F*|=31; |X|=32 b1(q=2) |N_S(X)|=992 |F*|=32
  coset frob^1     r=5 p=11 : WITNESS EXISTS; 4 classes, e.g. |X|=16 b1(q=2) |N_S(X)|=32 |F*|=32; |X|=31 b1(q=31) |N_S(X)|=62 |F*|=31; |X|=32 b1(q=2) |N_S(X)|=992 |F*|=32; |X|=992 b2 |N_S(X)|=992 |F*|=32
  coset frob^1     r=5 p=31 : WITNESS EXISTS; 4 classes, e.g. |X|=11 b1(q=11) |N_S(X)|=66 |F*|=33; |X|=16 b1(q=2) |N_S(X)|=32 |F*|=32; |X|=32 b1(q=2) |N_S(X)|=992 |F*|=32; |X|=992 b2 |N_S(X)|=992 |F*|=32
  coset frob^1     r=5 p=7  : WITNESS EXISTS; 5 classes, e.g. |X|=11 b1(q=11) |N_S(X)|=66 |F*|=33; |X|=16 b1(q=2) |N_S(X)|=32 |F*|=32; |X|=31 b1(q=31) |N_S(X)|=62 |F*|=31; |X|=32 b1(q=2) |N_S(X)|=992 |F*|=32
  coset frob^2     r=5 p=2  : WITNESS EXISTS; 2 classes, e.g. |X|=11 b1(q=11) |N_S(X)|=66 |F*|=33; |X|=31 b1(q=31) |N_S(X)|=62 |F*|=31
  coset frob^2     r=5 p=3  : WITNESS EXISTS; 5 classes, e.g. |X|=11 b1(q=11) |N_S(X)|=66 |F*|=33; |X|=16 b1(q=2) |N_S(X)|=32 |F*|=32; |X|=31 b1(q=31) |N_S(X)|=62 |F*|=31; |X|=32 b1(q=2) |N_S(X)|=992 |F*|=32
  coset frob^2     r=5 p=11 : WITNESS EXISTS; 4 classes, e.g. |X|=16 b1(q=2) |N_S(X)|=32 |F*|=32; |X|=31 b1(q=31) |N_S(X)|=62 |F*|=31; |X|=32 b1(q=2) |N_S(X)|=992 |F*|=32; |X|=992 b2 |N_S(X)|=992 |F*|=32
  coset frob^2     r=5 p=31 : WITNESS EXISTS; 4 classes, e.g. |X|=11 b1(q=11) |N_S(X)|=66 |F*|=33; |X|=16 b1(q=2) |N_S(X)|=32 |F*|=32; |X|=32 b1(q=2) |N_S(X)|=992 |F*|=32; |X|=992 b2 |N_S(X)|=992 |F*|=32
  coset frob^2     r=5 p=7  : WITNESS EXISTS; 5 classes, e.g. |X|=11 b1(q=11) |N_S(X)|=66 |F*|=33; |X|=16 b1(q=2) |N_S(X)|=32 |F*|=32; |X|=31 b1(q=31) |N_S(X)|=62 |F*|=31; |X|=32 b1(q=2) |N_S(X)|=992 |F*|=32
  coset frob^3     r=5 p=2  : WITNESS EXISTS; 2 classes, e.g. |X|=11 b1(q=11) |N_S(X)|=66 |F*|=33; |X|=31 b1(q=31) |N_S(X)|=62 |F*|=31
  coset frob^3     r=5 p=3  : WITNESS EXISTS; 5 classes, e.g. |X|=11 b1(q=11) |N_S(X)|=66 |F*|=33; |X|=16 b1(q=2) |N_S(X)|=32 |F*|=32; |X|=31 b1(q=31) |N_S(X)|=62 |F*|=31; |X|=32 b1(q=2) |N_S(X)|=992 |F*|=32
  coset frob^3     r=5 p=11 : WITNESS EXISTS; 4 classes, e.g. |X|=16 b1(q=2) |N_S(X)|=32 |F*|=32; |X|=31 b1(q=31) |N_S(X)|=62 |F*|=31; |X|=32 b1(q=2) |N_S(X)|=992 |F*|=32; |X|=992 b2 |N_S(X)|=992 |F*|=32
  coset frob^3     r=5 p=31 : WITNESS EXISTS; 4 classes, e.g. |X|=11 b1(q=11) |N_S(X)|=66 |F*|=33; |X|=16 b1(q=2) |N_S(X)|=32 |F*|=32; |X|=32 b1(q=2) |N_S(X)|=992 |F*|=32; |X|=992 b2 |N_S(X)|=992 |F*|=32
  coset frob^3     r=5 p=7  : WITNESS EXISTS; 5 classes, e.g. |X|=11 b1(q=11) |N_S(X)|=66 |F*|=33; |X|=16 b1(q=2) |N_S(X)|=32 |F*|=32; |X|=31 b1(q=31) |N_S(X)|=62 |F*|=31; |X|=32 b1(q=2) |N_S(X)|=992 |F*|=32
  coset frob^4     r=5 p=2  : WITNESS EXISTS; 2 classes, e.g. |X|=11 b1(q=11) |N_S(X)|=66 |F*|=33; |X|=31 b1(q=31) |N_S(X)|=62 |F*|=31
  coset frob^4     r=5 p=3  : WITNESS EXISTS; 5 classes, e.g. |X|=11 b1(q=11) |N_S(X)|=66 |F*|=33; |X|=16 b1(q=2) |N_S(X)|=32 |F*|=32; |X|=31 b1(q=31) |N_S(X)|=62 |F*|=31; |X|=32 b1(q=2) |N_S(X)|=992 |F*|=32
  coset frob^4     r=5 p=11 : WITNESS EXISTS; 4 classes, e.g. |X|=16 b1(q=2) |N_S(X)|=32 |F*|=32; |X|=31 b1(q=31) |N_S(X)|=62 |F*|=31; |X|=32 b1(q=2) |N_S(X)|=992 |F*|=32; |X|=992 b2 |N_S(X)|=992 |F*|=32
  coset frob^4     r=5 p=31 : WITNESS EXISTS; 4 classes, e.g. |X|=11 b1(q=11) |N_S(X)|=66 |F*|=33; |X|=16 b1(q=2) |N_S(X)|=32 |F*|=32; |X|=32 b1(q=2) |N_S(X)|=992 |F*|=32; |X|=992 b2 |N_S(X)|=992 |F*|=32
  coset frob^4     r=5 p=7  : WITNESS EXISTS; 5 classes, e.g. |X|=11 b1(q=11) |N_S(X)|=66 |F*|=33; |X|=16 b1(q=2) |N_S(X)|=32 |F*|=32; |X|=31 b1(q=31) |N_S(X)|=62 |F*|=31; |X|=32 b1(q=2) |N_S(X)|=992 |F*|=32
  (time 4.4s)
