q=4 (l=2 f=2) OK  [0.0s]
   L21                          ok  |C(U)|=4 (q=4) non-translations=0
   L22 eps=0,j=1,r=2            ok  beta in c normalizing U: 12 (expect 12); trivial on B/U: 0
   L23 eps=0,j=1,r=2            ok  claim t=5; (b1)-primes t' (odd, not l, not r) with no beta in c centralizing Q_t': [5]
   P5 j=1                       ok  j=1 r=2: |C_PGL(sigma^j)|=6 (|PGL(2,2)|=6); #order-r in coset=10 (|PGL|/|C|=10)
q=5 (l=5 f=1) OK  [0.0s]
   L21                          ok  |C(U)|=5 (q=5) non-translations=0
   L24a                         ok  beta in delta centralizing U: 0
   delta-cent-Sylow             ok  beta in delta centralizing Sylow t (odd t != l): {3: 3}
   L24b P4                      ok  involutions=15, V4 total=5, |S-class of V|=5, |N_S(V)|=12, |PGL-class|=5; beta in delta normalizing V: 12, trivial on N_S(V)/V: 0
q=7 (l=7 f=1) OK  [0.0s]
   L21                          ok  |C(U)|=7 (q=7) non-translations=0
   L24a                         ok  beta in delta centralizing U: 0
   delta-cent-Sylow             ok  beta in delta centralizing Sylow t (odd t != l): {3: 3}
   P4 (two classes fused)       ok  involutions=21, V4 total=14, |S-class of V|=7, |N_S(V)|=24, |PGL-class|=14
q=8 (l=2 f=3) OK  [0.0s]
   L21                          ok  |C(U)|=8 (q=8) non-translations=0
   L22 eps=0,j=1,r=3            ok  beta in c normalizing U: 56 (expect 56); trivial on B/U: 0
   L23 eps=0,j=1,r=3            ok  claim t=7; (b1)-primes t' (odd, not l, not r) with no beta in c centralizing Q_t': [7]
   L22 eps=0,j=2,r=3            ok  beta in c normalizing U: 56 (expect 56); trivial on B/U: 0
   L23 eps=0,j=2,r=3            ok  claim t=7; (b1)-primes t' (odd, not l, not r) with no beta in c centralizing Q_t': [7]
   P5 j=1                       ok  j=1 r=3: |C_PGL(sigma^j)|=6 (|PGL(2,2)|=6); #order-r in coset=84 (|PGL|/|C|=84)
   P5 j=2                       ok  j=2 r=3: |C_PGL(sigma^j)|=6 (|PGL(2,2)|=6); #order-r in coset=84 (|PGL|/|C|=84)
q=9 (l=3 f=2) OK  [0.0s]
   L21                          ok  |C(U)|=9 (q=9) non-translations=0
   L22 eps=0,j=1,r=2            ok  beta in c normalizing U: 36 (expect 36); trivial on B/U: 0
   L23 eps=0,j=1,r=2            ok  claim t=5; (b1)-primes t' (odd, not l, not r) with no beta in c centralizing Q_t': [5]
   L24a                         ok  beta in delta centralizing U: 0
   delta-cent-Sylow             ok  beta in delta centralizing Sylow t (odd t != l): {5: 5}
   L22 eps=1,j=1,r=2            ok  beta in c normalizing U: 36 (expect 36); trivial on B/U: 0
   L23 eps=1,j=1,r=2            ok  claim t=5; (b1)-primes t' (odd, not l, not r) with no beta in c centralizing Q_t': [5]
   P5 j=1                       ok  j=1 r=2: |C_PGL(sigma^j)|=24 (|PGL(2,3)|=24); #order-r in coset=30 (|PGL|/|C|=30); involutions in delta*phi_0: 0
   P4 (two classes fused)       ok  involutions=45, V4 total=30, |S-class of V|=15, |N_S(V)|=24, |PGL-class|=30
q=11 (l=11 f=1) OK  [0.0s]
   L21                          ok  |C(U)|=11 (q=11) non-translations=0
   L24a                         ok  beta in delta centralizing U: 0
   delta-cent-Sylow             ok  beta in delta centralizing Sylow t (odd t != l): {3: 6, 5: 5}
   L24b P4                      ok  involutions=55, V4 total=55, |S-class of V|=55, |N_S(V)|=12, |PGL-class|=55; beta in delta normalizing V: 12, trivial on N_S(V)/V: 0
q=13 (l=13 f=1) OK  [0.0s]
   L21                          ok  |C(U)|=13 (q=13) non-translations=0
   L24a                         ok  beta in delta centralizing U: 0
   delta-cent-Sylow             ok  beta in delta centralizing Sylow t (odd t != l): {3: 6, 7: 7}
   L24b P4                      ok  involutions=91, V4 total=91, |S-class of V|=91, |N_S(V)|=12, |PGL-class|=91; beta in delta normalizing V: 12, trivial on N_S(V)/V: 0
q=16 (l=2 f=4) OK  [0.1s]
   L21                          ok  |C(U)|=16 (q=16) non-translations=0
   L22 eps=0,j=2,r=2            ok  beta in c normalizing U: 240 (expect 240); trivial on B/U: 0
   L23 eps=0,j=2,r=2            ok  claim t=17; (b1)-primes t' (odd, not l, not r) with no beta in c centralizing Q_t': [17]
   P5 j=2                       ok  j=2 r=2: |C_PGL(sigma^j)|=60 (|PGL(2,4)|=60); #order-r in coset=68 (|PGL|/|C|=68)
ALL OK
nice -n 10 python3 -I witness_psl2.py  0.22s user 0.01s system 99% cpu 0.228 total
