== A5: |S| = 60, |A| = 120, 59 subgroups in 9 S-classes
  coset odd        r=2 p=2  : WITNESS EXISTS; 1 classes, e.g. |X|=5 b1(q=5) |N_S(X)|=10 |F*|=5
  coset odd        r=2 p=3  : WITNESS EXISTS; 3 classes, e.g. |X|=4 b2 |N_S(X)|=12 |F*|=4; |X|=5 b1(q=5) |N_S(X)|=10 |F*|=5; |X|=12 b2 |N_S(X)|=12 |F*|=4
  coset odd        r=2 p=5  : 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 odd        r=2 p=7  : WITNESS EXISTS; 3 classes, e.g. |X|=4 b2 |N_S(X)|=12 |F*|=4; |X|=5 b1(q=5) |N_S(X)|=10 |F*|=5; |X|=12 b2 |N_S(X)|=12 |F*|=4
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== A5_wrong_inner: |S| = 60, |A| = 120, 59 subgroups in 9 S-classes
  coset INNER      r=2 p=2  : NO WITNESS among all 7 Aut-invariant classes
  coset INNER      r=2 p=3  : NO WITNESS among all 7 Aut-invariant classes
  coset INNER      r=2 p=5  : NO WITNESS among all 7 Aut-invariant classes
  coset INNER      r=2 p=7  : NO WITNESS among all 7 Aut-invariant classes
  (time 0.0s)
