PGL(2,7) wr C3 [uncovered]: |A|=336 m=3 |G/N|=24 h(G/N)=2 -> h*(G)=3 ; best h_p over tested K: {2: (3, 'N(Syl3)'), 3: (4, 'S4 (pure perms)'), 5: (4, 'S4 (pure perms)'), 7: (4, 'S4 (pure perms)')} -> OK  [18s]
    K(N(Syl2)): |K|=12288  h_p(K): {2: 1, 3: 2, 5: 2, 7: 2}
    K(N(Syl3)): |K|=5184  h_p(K): {2: 3, 3: 2, 5: 3, 7: 3}
    K(N(Syl7)): |K|=222264  h_p(K): {2: 3, 3: 3, 5: 3, 7: 2}
    K(S4 (pure perms)): |K|=41472  h_p(K): {2: 3, 3: 4, 5: 4, 7: 4}
PGL(2,7) wr S3 [uncovered]: |A|=336 m=3 |G/N|=48 h(G/N)=3 -> h*(G)=4 ; best h_p over tested K: {2: (4, 'N(Syl3)'), 3: (5, 'S4 (pure perms)'), 5: (5, 'S4 (pure perms)'), 7: (5, 'S4 (pure perms)')} -> OK  [73s]
    K(N(Syl2)): |K|=24576  h_p(K): {2: 2, 3: 3, 5: 3, 7: 3}
    K(N(Syl3)): |K|=10368  h_p(K): {2: 4, 3: 3, 5: 4, 7: 4}
    K(N(Syl7)): |K|=444528  h_p(K): {2: 4, 3: 4, 5: 4, 7: 3}
    K(S4 (pure perms)): |K|=82944  h_p(K): {2: 4, 3: 5, 5: 5, 7: 5}
PGammaL(2,32) wr C2: |A|=163680 m=2 |G/N|=50 h(G/N)=2 -> h*(G)=3 ; best h_p over tested K: {2: (3, 'N(Syl3)'), 3: (3, 'N(Syl3)'), 5: (3, 'N(Syl3)'), 7: (3, 'N(Syl3)'), 11: (3, 'N(Syl31)'), 31: (3, 'N(Syl3)')} -> OK  [53s]
    K(N(Syl3)): |K|=217800  h_p(K): {2: 3, 3: 3, 5: 3, 7: 3, 11: 2, 31: 3}
    K(N(Syl11)): |K|=217800  h_p(K): {2: 3, 3: 3, 5: 3, 7: 3, 11: 2, 31: 3}
    K(N(Syl31)): |K|=192200  h_p(K): {2: 3, 3: 3, 5: 3, 7: 3, 11: 3, 31: 2}
ALL OK
