PGammaL(2,8) wr C2: |A|=1512 m=2 |G/N|=18 h(G/N)=2 -> h*(G)=3 ; best h_p over tested K: {2: (3, 'N(Syl2)'), 3: (4, 'N(Syl2)'), 5: (4, 'N(Syl2)'), 7: (4, 'N(Syl2)')} -> OK  [4s]
    K(N(Syl2)): |K|=56448  h_p(K): {2: 3, 3: 4, 5: 4, 7: 4}
    K(N(Syl3)): |K|=5832  h_p(K): {2: 2, 3: 1, 5: 2, 7: 2}
    K(N(Syl7)): |K|=3528  h_p(K): {2: 3, 3: 3, 5: 3, 7: 2}
PSL(2,7)^3.S3, S3 = twisted complement <(123),(d,d,d)(23)> [uncovered]: |A|=336 m=3 |G/N|=6 h(G/N)=2 -> h*(G)=3 ; best h_p over tested K: {2: (4, 'N(Syl3)'), 3: (4, 'S4 (pure perms)'), 5: (4, 'N(Syl3)'), 7: (4, 'N(Syl3)')} -> OK  [7s]
    K(N(Syl2)): |K|=3072  h_p(K): {2: 2, 3: 3, 5: 3, 7: 3}
    K(N(Syl3)): |K|=1296  h_p(K): {2: 4, 3: 3, 5: 4, 7: 4}
    K(N(Syl7)): |K|=55566  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}
PSL(2,7)^3.(2^2:S3), <(123),(d,1,1)(23)> [uncovered]: |A|=336 m=3 |G/N|=24 h(G/N)=3 -> h*(G)=4 ; best h_p over tested K: {2: (4, 'N(Syl3)'), 3: (4, 'N(Syl7)'), 5: (4, 'N(Syl3)'), 7: (4, 'N(Syl3)')} -> OK  [29s]
    K(N(Syl2)): |K|=12288  h_p(K): {2: 2, 3: 3, 5: 3, 7: 3}
    K(N(Syl3)): |K|=5184  h_p(K): {2: 4, 3: 3, 5: 4, 7: 4}
    K(N(Syl7)): |K|=222264  h_p(K): {2: 4, 3: 4, 5: 4, 7: 3}
Sz(8):3 wr C2: |A|=87360 m=2 |G/N|=18 h(G/N)=2 -> h*(G)=3 ; best h_p over tested K: {2: (3, 'N(Syl7)'), 3: (3, 'N(Syl7)'), 5: (3, 'N(Syl7)'), 7: (3, 'N(Syl13)'), 11: (3, 'N(Syl7)'), 13: (3, 'N(Syl7)')} -> OK  [6s]
    K(N(Syl5)): |K|=7200  h_p(K): {2: 2, 3: 2, 5: 2, 7: 2, 11: 2, 13: 2}
    K(N(Syl7)): |K|=3528  h_p(K): {2: 3, 3: 3, 5: 3, 7: 2, 11: 3, 13: 3}
    K(N(Syl13)): |K|=48672  h_p(K): {2: 3, 3: 3, 5: 3, 7: 3, 11: 3, 13: 2}
PGammaL(2,27) wr C2: |A|=58968 m=2 |G/N|=72 h(G/N)=2 -> h*(G)=3 ; best h_p over tested K: {2: (3, 'N(Syl7)'), 3: (3, 'N(Syl2)'), 5: (3, 'N(Syl2)'), 7: (3, 'N(Syl2)'), 13: (3, 'N(Syl2)')} -> OK  [10s]
    K(N(Syl2)): |K|=10368  h_p(K): {2: 2, 3: 3, 5: 3, 7: 3, 13: 3}
    K(N(Syl7)): |K|=56448  h_p(K): {2: 3, 3: 3, 5: 3, 7: 2, 13: 3}
    K(N(Syl13)): |K|=48672  h_p(K): {2: 3, 3: 3, 5: 3, 7: 3, 13: 2}
ALL OK
