Kernel 1)
 
Number of actions with isolated fixed points: 8 
 
Number of good cohomology classes: 8

Size of the normalizer: 1296 
 
Number of biholomorphism classes: 1 
 
Actions [H]: 
 [
[             1              0              0 1/3*(2*ze + 1)]
[             0        -ze - 1              0   1/3*(ze + 2)]
[             0              0             ze 1/3*(2*ze + 1)]
[             0              0              0              1]
] 
 
 
 
Kernel 2)
 
Number of actions with isolated fixed points: 36 
 
Number of good cohomology classes: 4

Size of the normalizer: 216 
 
Number of biholomorphism classes: 1 
 
Actions [H]: 
 [
[             1              0              0       1/3*ze]
[             0        -ze - 1              0       1/3*ze]
[             0              0             ze 1/3*(2*ze + 1)]
[             0              0              0              1]
] 
 
 
 
Kernel 3)
 
Number of actions with isolated fixed points: 54 
 
Number of good cohomology classes: 6

Size of the normalizer: 324 
 
Number of biholomorphism classes: 1 
 
Actions [H]: 
 [
[         1          0          0    2/3]
[         0    -ze - 1          0 2/3*ze]
[         0          0         ze    2/3]
[         0          0          0          1]
] 
 
 
 
Kernel 4)
 
Number of actions with isolated fixed points: 54 
 
Number of good cohomology classes: 2

Size of the normalizer: 324 
 
Number of biholomorphism classes: 1 
 
Actions [H]: 
 [
[       1        0        0 1/3*ze]
[       0  -ze - 1        0  1/3]
[       0        0       ze  2/3]
[       0        0        0        1]
]