Kernel 1)
 
Number of actions with isolated fixed points: 486 
 
Number of good cohomology classes: 6

Number of biholomorphism classes: 1 
 
Actions [G,H]: 
 [
[
[             0              0              1 1/3*(2*ze + 1)]
[             1              0              0              0]
[             0              1              0 1/3*(2*ze + 1)]
[             0              0              0              1],

[       1        0        0 1/3*ze]
[       0  -ze - 1        0 1/3*ze]
[       0        0       ze 1/3*ze]
[       0        0        0        1]
]
] 
 
 
 
Kernel 2)
 
Number of actions with isolated fixed points: 1458 
 
Number of good cohomology classes: 6

Number of biholomorphism classes: 1 
 
Actions [G,H]: 
 [
[
[           0            0            1            0]
[           1            0            0 1/3*(ze + 2)]
[           0            1            0            0]
[           0            0            0            1],

[         1          0          0 2/3*ze]
[         0    -ze - 1          0    2/3]
[         0          0         ze    2/3]
[         0          0          0          1]
]
]