PSL(2,16)            |G|=4080   h*=1 (layers [4080])  s=2  s_p: {2: 2, 3: 2, 5: 2, 17: 2}  O_p(G): all 1  soluble classes=19  -> OK (s_p >= h* for all p with O_p = 1)  [0s]
     orders of soluble K attaining the maxima: {'h': 6, 2: 6, 3: 12, 5: 6, 17: 6}; s_p for p not dividing |G| (p=7) equals s=2
PSL(2,16):2          |G|=8160   h*=2 (layers [4080, 8160])  s=3  s_p: {2: 2, 3: 3, 5: 3, 17: 3}  O_p(G): all 1  soluble classes=43  -> OK (s_p >= h* for all p with O_p = 1)  [1s]
     orders of soluble K attaining the maxima: {'h': 160, 3: 160, 5: 160, 17: 160, 2: 6}; s_p for p not dividing |G| (p=7) equals s=3
PGammaL(2,16)        |G|=16320  h*=2 (layers [4080, 16320])  s=3  s_p: {2: 2, 3: 3, 5: 3, 17: 3}  O_p(G): all 1  soluble classes=63  -> OK (s_p >= h* for all p with O_p = 1)  [2s]
     orders of soluble K attaining the maxima: {'h': 48, 3: 48, 5: 48, 17: 48, 2: 6}; s_p for p not dividing |G| (p=7) equals s=3
PGL(2,17)            |G|=4896   h*=2 (layers [2448, 4896])  s=3  s_p: {2: 2, 3: 3, 17: 3}  O_p(G): all 1  soluble classes=30  -> OK (s_p >= h* for all p with O_p = 1)  [0s]
     orders of soluble K attaining the maxima: {'h': 24, 2: 6, 3: 24, 17: 24}; s_p for p not dividing |G| (p=5) equals s=3
Sz(8)                |G|=29120  h*=1 (layers [29120])  s=2  s_p: {2: 2, 5: 2, 7: 2, 13: 2}  O_p(G): all 1  soluble classes=21  -> OK (s_p >= h* for all p with O_p = 1)  [2s]
     orders of soluble K attaining the maxima: {'h': 10, 5: 14, 7: 10, 13: 10, 2: 10}; s_p for p not dividing |G| (p=3) equals s=2
AGL(2,5)             |G|=12000  h*=3 (layers [25, 6000, 12000])  s=4  s_p: {2: 4, 3: 4, 5: 3}  O_p(G): {5: 25}  soluble classes=126  -> OK (s_p >= h* for all p with O_p = 1)  [3s]
     orders of soluble K attaining the maxima: {'h': 2400, 2: 2400, 3: 2400, 5: 96}; s_p for p not dividing |G| (p=7) equals s=4
2^6:PGL(2,7)         |G|=21504  h*=3 (layers [64, 10752, 21504])  s=3  s_p: {2: 2, 3: 3, 7: 3}  O_p(G): {2: 64}  soluble classes=1183  -> OK (s_p >= h* for all p with O_p = 1)  [29s]
     orders of soluble K attaining the maxima: {'h': 24, 3: 24, 7: 24, 2: 6}; s_p for p not dividing |G| (p=5) equals s=3
PSL(2,25):2=PSigmaL  |G|=15600  h*=2 (layers [7800, 15600])  s=3  s_p: {2: 3, 3: 3, 5: 3, 13: 3}  O_p(G): all 1  soluble classes=91  -> OK (s_p >= h* for all p with O_p = 1)  [2s]
     orders of soluble K attaining the maxima: {'h': 24, 3: 24, 5: 24, 13: 24, 2: 150}; s_p for p not dividing |G| (p=7) equals s=3
Sz(8):3              |G|=87360  h*=2 (layers [29120, 87360])  s=3  s_p: {2: 2, 3: 3, 5: 3, 7: 3, 13: 3}  O_p(G): all 1  soluble classes=37  -> OK (s_p >= h* for all p with O_p = 1)  [14s]
     orders of soluble K attaining the maxima: {'h': 168, 3: 168, 5: 168, 7: 168, 13: 168, 2: 10}; s_p for p not dividing |G| (p=11) equals s=3
PSL(2,27):3          |G|=29484  h*=2 (layers [9828, 29484])  s=3  s_p: {2: 3, 3: 2, 7: 3, 13: 3}  O_p(G): all 1  soluble classes=36  -> OK (s_p >= h* for all p with O_p = 1)  [2s]
     orders of soluble K attaining the maxima: {'h': 1053, 2: 1053, 3: 12, 13: 1053, 7: 1053}; s_p for p not dividing |G| (p=5) equals s=3
ALL OK
