q=17 (l=17 f=1) OK  [0.1s]
   L21                          ok  |C(U)|=17 (q=17) 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: 9}
   P4 (two classes fused)       ok  involutions=153, V4 total=204, |S-class of V|=102, |N_S(V)|=24, |PGL-class|=204
q=19 (l=19 f=1) OK  [0.2s]
   L21                          ok  |C(U)|=19 (q=19) 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: 9, 5: 10}
   L24b P4                      ok  involutions=171, V4 total=285, |S-class of V|=285, |N_S(V)|=12, |PGL-class|=285; beta in delta normalizing V: 12, trivial on N_S(V)/V: 0
q=23 (l=23 f=1) OK  [0.2s]
   L21                          ok  |C(U)|=23 (q=23) 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: 12, 11: 11}
   P4 (two classes fused)       ok  involutions=253, V4 total=506, |S-class of V|=253, |N_S(V)|=24, |PGL-class|=506
q=25 (l=5 f=2) OK  [0.4s]
   L21                          ok  |C(U)|=25 (q=25) non-translations=0
   L22 eps=0,j=1,r=2            ok  beta in c normalizing U: 300 (expect 300); trivial on B/U: 0
   L23 eps=0,j=1,r=2            ok  claim t=13; (b1)-primes t' (odd, not l, not r) with no beta in c centralizing Q_t': [13]
   L24a                         ok  beta in delta centralizing U: 0
   delta-cent-Sylow             ok  beta in delta centralizing Sylow t (odd t != l): {3: 12, 13: 13}
   L22 eps=1,j=1,r=2            ok  beta in c normalizing U: 300 (expect 300); trivial on B/U: 0
   L23 eps=1,j=1,r=2            ok  claim t=13; (b1)-primes t' (odd, not l, not r) with no beta in c centralizing Q_t': [13]
   P5 j=1                       ok  j=1 r=2: |C_PGL(sigma^j)|=120 (|PGL(2,5)|=120); #order-r in coset=130 (|PGL|/|C|=130); involutions in delta*phi_0: 0
   P4 (two classes fused)       ok  involutions=325, V4 total=650, |S-class of V|=325, |N_S(V)|=24, |PGL-class|=650
q=27 (l=3 f=3) OK  [0.9s]
   L21                          ok  |C(U)|=27 (q=27) non-translations=0
   L22 eps=0,j=1,r=3            ok  beta in c normalizing U: 351 (expect 351); 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, 13]
   L22 eps=0,j=2,r=3            ok  beta in c normalizing U: 351 (expect 351); 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, 13]
   L24a                         ok  beta in delta centralizing U: 0
   delta-cent-Sylow             ok  beta in delta centralizing Sylow t (odd t != l): {7: 14, 13: 13}
   P5 j=1                       ok  j=1 r=3: |C_PGL(sigma^j)|=24 (|PGL(2,3)|=24); #order-r in coset=819 (|PGL|/|C|=819)
   P5 j=2                       ok  j=2 r=3: |C_PGL(sigma^j)|=24 (|PGL(2,3)|=24); #order-r in coset=819 (|PGL|/|C|=819)
   L24b P4                      ok  involutions=351, V4 total=819, |S-class of V|=819, |N_S(V)|=12, |PGL-class|=819; beta in delta normalizing V: 12, trivial on N_S(V)/V: 0
q=29 (l=29 f=1) OK  [0.6s]
   L21                          ok  |C(U)|=29 (q=29) 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: 15, 5: 15, 7: 14}
   L24b P4                      ok  involutions=435, V4 total=1015, |S-class of V|=1015, |N_S(V)|=12, |PGL-class|=1015; beta in delta normalizing V: 12, trivial on N_S(V)/V: 0
q=31 (l=31 f=1) OK  [0.4s]
   L21                          ok  |C(U)|=31 (q=31) 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: 15, 5: 15}
   P4 (two classes fused)       ok  involutions=465, V4 total=1240, |S-class of V|=620, |N_S(V)|=24, |PGL-class|=1240
q=32 (l=2 f=5) OK  [2.7s]
   L21                          ok  |C(U)|=32 (q=32) non-translations=0
   L22 eps=0,j=1,r=5            ok  beta in c normalizing U: 992 (expect 992); trivial on B/U: 0
   L23 eps=0,j=1,r=5            ok  claim t=11; (b1)-primes t' (odd, not l, not r) with no beta in c centralizing Q_t': [11, 31]
   L22 eps=0,j=2,r=5            ok  beta in c normalizing U: 992 (expect 992); trivial on B/U: 0
   L23 eps=0,j=2,r=5            ok  claim t=11; (b1)-primes t' (odd, not l, not r) with no beta in c centralizing Q_t': [11, 31]
   L22 eps=0,j=3,r=5            ok  beta in c normalizing U: 992 (expect 992); trivial on B/U: 0
   L23 eps=0,j=3,r=5            ok  claim t=11; (b1)-primes t' (odd, not l, not r) with no beta in c centralizing Q_t': [11, 31]
   L22 eps=0,j=4,r=5            ok  beta in c normalizing U: 992 (expect 992); trivial on B/U: 0
   L23 eps=0,j=4,r=5            ok  claim t=11; (b1)-primes t' (odd, not l, not r) with no beta in c centralizing Q_t': [11, 31]
   P5 j=1                       ok  j=1 r=5: |C_PGL(sigma^j)|=6 (|PGL(2,2)|=6); #order-r in coset=5456 (|PGL|/|C|=5456)
   P5 j=2                       ok  j=2 r=5: |C_PGL(sigma^j)|=6 (|PGL(2,2)|=6); #order-r in coset=5456 (|PGL|/|C|=5456)
   P5 j=3                       ok  j=3 r=5: |C_PGL(sigma^j)|=6 (|PGL(2,2)|=6); #order-r in coset=5456 (|PGL|/|C|=5456)
   P5 j=4                       ok  j=4 r=5: |C_PGL(sigma^j)|=6 (|PGL(2,2)|=6); #order-r in coset=5456 (|PGL|/|C|=5456)
ALL OK
nice -n 10 python3 -I witness_psl2.py  5.47s user 0.01s system 99% cpu 5.491 total
