Number of selected skew morphism classes of C128 is 0
Total number of skew morphisms of C128 is 1196
Total number of skew morphism classes of C128 is 43
Total number of automorphisms of C128 is 64

1. Skew morphsim class of size 1
     
     of order 1
     with kernel of order 128
     and smallest kernel generator 1
     and power function values [ 1 ]
     and with periodicity 1
     and with complexity 0
     and with auto-order 128
     φ | √φ | φ' | φ|<128>
   
   

2. Skew morphsim class of size 1
     
     of order 2
     with kernel of order 128
     and smallest kernel generator 1
     and power function values [ 1 ]
     and with periodicity 1
     and with complexity 1
     and with auto-order 2
     φ | √φ | φ' | φ2
   
   

3. Skew morphsim class of size 2
     
     of order 4
     with kernel of order 128
     and smallest kernel generator 1
     and power function values [ 1 ]
     and with periodicity 1
     and with complexity 1
     and with auto-order 4
     φ | √φ | φ' | φ4
   
   

4. Skew morphsim class of size 4
     
     of order 8
     with kernel of order 128
     and smallest kernel generator 1
     and power function values [ 1 ]
     and with periodicity 1
     and with complexity 1
     and with auto-order 8
     φ | √φ | φ' | φ8
   
   

5. Skew morphsim class of size 8
     
     of order 16
     with kernel of order 128
     and smallest kernel generator 1
     and power function values [ 1 ]
     and with periodicity 1
     and with complexity 1
     and with auto-order 16
     φ | √φ | φ' | φ16
   
   

6. Skew morphsim class of size 16
     
     of order 32
     with kernel of order 128
     and smallest kernel generator 1
     and power function values [ 1 ]
     and with periodicity 1
     and with complexity 1
     and with auto-order 32
     φ | √φ | φ' | φ32
   
   

7. Skew morphsim class of size 16
     
     of order 32
     with kernel of order 128
     and smallest kernel generator 1
     and power function values [ 1 ]
     and with periodicity 1
     and with complexity 1
     and with auto-order 32
     φ | √φ | φ' | φ32
   
   

8. Skew morphsim class of size 8
     
     of order 16
     with kernel of order 128
     and smallest kernel generator 1
     and power function values [ 1 ]
     and with periodicity 1
     and with complexity 1
     and with auto-order 16
     φ | √φ | φ' | φ16
   
   

9. Skew morphsim class of size 4
     
     of order 8
     with kernel of order 128
     and smallest kernel generator 1
     and power function values [ 1 ]
     and with periodicity 1
     and with complexity 1
     and with auto-order 8
     φ | √φ | φ' | φ8
   
   

10. Skew morphsim class of size 2
      
      of order 4
      with kernel of order 128
      and smallest kernel generator 1
      and power function values [ 1 ]
      and with periodicity 1
      and with complexity 1
      and with auto-order 4
      φ | √φ | φ' | φ4
    
    

11. Skew morphsim class of size 1
      
      of order 2
      with kernel of order 128
      and smallest kernel generator 1
      and power function values [ 1 ]
      and with periodicity 1
      and with complexity 1
      and with auto-order 2
      φ | √φ | φ' | φ2
    
    

12. Skew morphsim class of size 1
      
      of order 2
      with kernel of order 128
      and smallest kernel generator 1
      and power function values [ 1 ]
      and with periodicity 1
      and with complexity 1
      and with auto-order 2
      φ | √φ | φ' | φ2
    
    

13. Skew morphsim class of size 2
      
      of order 4
      with kernel of order 64
      and smallest kernel generator 2
      and power function values [ 1, 3 ]
      and with periodicity 1
      and with complexity 2
      and with auto-order 2
      φ | √φ | φ' | φ|<2>
    
    

14. Skew morphsim class of size 4
      
      of order 8
      with kernel of order 64
      and smallest kernel generator 2
      and power function values [ 1, 7 ]
      and with periodicity 1
      and with complexity 2
      and with auto-order 2
      φ | √φ | φ' | φ|<2>
    
    

15. Skew morphsim class of size 8
      
      of order 16
      with kernel of order 64
      and smallest kernel generator 2
      and power function values [ 1, 15 ]
      and with periodicity 1
      and with complexity 2
      and with auto-order 2
      φ | √φ | φ' | φ|<2>
    
    

16. Skew morphsim class of size 16
      
      of order 32
      with kernel of order 64
      and smallest kernel generator 2
      and power function values [ 1, 31 ]
      and with periodicity 1
      and with complexity 2
      and with auto-order 2
      φ | √φ | φ' | φ|<2>
    
    

17. Skew morphsim class of size 32
      
      of order 64
      with kernel of order 64
      and smallest kernel generator 2
      and power function values [ 1, 63 ]
      and with periodicity 1
      and with complexity 2
      and with auto-order 2
      φ | √φ | φ' | φ|<2>
    
    

18. Skew morphsim class of size 4
      
      of order 8
      with kernel of order 64
      and smallest kernel generator 2
      and power function values [ 1, 3 ]
      and with periodicity 1
      and with complexity 2
      and with auto-order 2
      φ | √φ | φ' | φ|<2>
    
    

19. Skew morphsim class of size 8
      
      of order 16
      with kernel of order 64
      and smallest kernel generator 2
      and power function values [ 1, 7 ]
      and with periodicity 1
      and with complexity 2
      and with auto-order 2
      φ | √φ | φ' | φ|<2>
    
    

20. Skew morphsim class of size 16
      
      of order 32
      with kernel of order 64
      and smallest kernel generator 2
      and power function values [ 1, 15 ]
      and with periodicity 1
      and with complexity 2
      and with auto-order 2
      φ | √φ | φ' | φ|<2>
    
    

21. Skew morphsim class of size 32
      
      of order 64
      with kernel of order 64
      and smallest kernel generator 2
      and power function values [ 1, 63 ]
      and with periodicity 1
      and with complexity 2
      and with auto-order 2
      φ | √φ | φ' | φ|<2>
    
    

22. Skew morphsim class of size 4
      
      of order 8
      with kernel of order 64
      and smallest kernel generator 2
      and power function values [ 1, 5 ]
      and with periodicity 1
      and with complexity 2
      and with auto-order 2
      φ | √φ | φ' | φ|<2>
    
    

23. Skew morphsim class of size 8
      
      of order 16
      with kernel of order 64
      and smallest kernel generator 2
      and power function values [ 1, 9 ]
      and with periodicity 1
      and with complexity 2
      and with auto-order 2
      φ | √φ | φ' | φ|<2>
    
    

24. Skew morphsim class of size 16
      
      of order 32
      with kernel of order 64
      and smallest kernel generator 2
      and power function values [ 1, 17 ]
      and with periodicity 1
      and with complexity 2
      and with auto-order 2
      φ | √φ | φ' | φ|<2>
    
    

25. Skew morphsim class of size 16
      
      of order 32
      with kernel of order 64
      and smallest kernel generator 2
      and power function values [ 1, 17 ]
      and with periodicity 1
      and with complexity 2
      and with auto-order 2
      φ | √φ | φ' | φ|<2>
    
    

26. Skew morphsim class of size 8
      
      of order 16
      with kernel of order 64
      and smallest kernel generator 2
      and power function values [ 1, 9 ]
      and with periodicity 1
      and with complexity 2
      and with auto-order 2
      φ | √φ | φ' | φ|<2>
    
    

27. Skew morphsim class of size 4
      
      of order 8
      with kernel of order 64
      and smallest kernel generator 2
      and power function values [ 1, 5 ]
      and with periodicity 1
      and with complexity 2
      and with auto-order 2
      φ | √φ | φ' | φ|<2>
    
    

28. Skew morphsim class of size 2
      
      of order 4
      with kernel of order 64
      and smallest kernel generator 2
      and power function values [ 1, 3 ]
      and with periodicity 1
      and with complexity 2
      and with auto-order 2
      φ | √φ | φ' | φ|<2>
    
    

29. Skew morphsim class of size 16
      
      of order 16
      with kernel of order 32
      and smallest kernel generator 4
      and power function values [ 1, 3, 9, 11 ]
      and with periodicity 1
      and with complexity 2
      and with auto-order 4
      φ | √φ | φ' | φ|<4>
    
    

30. Skew morphsim class of size 32
      
      of order 32
      with kernel of order 32
      and smallest kernel generator 4
      and power function values [ 1, 7, 17, 23 ]
      and with periodicity 1
      and with complexity 2
      and with auto-order 4
      φ | √φ | φ' | φ|<4>
    
    

31. Skew morphsim class of size 16
      
      of order 16
      with kernel of order 32
      and smallest kernel generator 4
      and power function values [ 1, 5, 9, 13 ]
      and with periodicity 1
      and with complexity 2
      and with auto-order 4
      φ | √φ | φ' | φ|<4>
    
    

32. Skew morphsim class of size 32
      
      of order 32
      with kernel of order 32
      and smallest kernel generator 4
      and power function values [ 1, 9, 17, 25 ]
      and with periodicity 1
      and with complexity 2
      and with auto-order 4
      φ | √φ | φ' | φ|<4>
    
    

33. Skew morphsim class of size 8
      
      of order 8
      with kernel of order 32
      and smallest kernel generator 4
      and power function values [ 1, 3, 5, 7 ]
      and with periodicity 2
      and with complexity 3
      and with auto-order 2
      φ | √φ | φ' | φ2
    
    

34. Skew morphsim class of size 16
      
      of order 16
      with kernel of order 32
      and smallest kernel generator 4
      and power function values [ 1, 5, 9, 13 ]
      and with periodicity 2
      and with complexity 3
      and with auto-order 2
      φ | √φ | φ' | φ2
    
    

35. Skew morphsim class of size 32
      
      of order 16
      with kernel of order 16
      and smallest kernel generator 8
      and power function values [ 1, 3, 5, 7, 9, 11, 13, 15 ]
      and with periodicity 2
      and with complexity 3
      and with auto-order 2
      φ | √φ | φ' | φ2
    
    

36. Skew morphsim class of size 32
      
      of order 32
      with kernel of order 32
      and smallest kernel generator 4
      and power function values [ 1, 9, 17, 25 ]
      and with periodicity 2
      and with complexity 3
      and with auto-order 2
      φ | √φ | φ' | φ2
    
    

37. Skew morphsim class of size 64
      
      of order 32
      with kernel of order 16
      and smallest kernel generator 8
      and power function values [ 1, 5, 9, 13, 17, 21, 25, 29 ]
      and with periodicity 2
      and with complexity 3
      and with auto-order 2
      φ | √φ | φ' | φ2
    
    

38. Skew morphsim class of size 64
      
      of order 32
      with kernel of order 16
      and smallest kernel generator 8
      and power function values [ 1, 3, 25, 11, 17, 19, 9, 27 ]
      and with periodicity 2
      and with complexity 3
      and with auto-order 2
      φ | √φ | φ' | φ2
    
    

39. Skew morphsim class of size 64
      
      of order 32
      with kernel of order 16
      and smallest kernel generator 8
      and power function values [ 1, 5, 25, 29, 17, 21, 9, 13 ]
      and with periodicity 2
      and with complexity 3
      and with auto-order 2
      φ | √φ | φ' | φ2
    
    

40. Skew morphsim class of size 64
      
      of order 64
      with kernel of order 32
      and smallest kernel generator 4
      and power function values [ 1, 31, 33, 63 ]
      and with periodicity 2
      and with complexity 3
      and with auto-order 2
      φ | √φ | φ' | φ2
    
    

41. Skew morphsim class of size 128
      
      of order 64
      with kernel of order 16
      and smallest kernel generator 8
      and power function values [ 1, 15, 17, 63, 33, 47, 49, 31 ]
      and with periodicity 4
      and with complexity 4
      and with auto-order 2
      φ | √φ | φ' | φ|<2>
    
    

42. Skew morphsim class of size 256
      
      of order 64
      with kernel of order 8
      and smallest kernel generator 16
      and power function values [ 1, 7, 9, 31, 17, 55, 25, 15, 33, 39, 41, 63, 49, 23, 57, 47 ]
      and with periodicity 8
      and with complexity 4
      and with auto-order 2
      φ | √φ | φ' | φ|<2>
    
    

43. Skew morphsim class of size 128
      
      of order 32
      with kernel of order 8
      and smallest kernel generator 16
      and power function values [ 1, 3, 13, 31, 25, 27, 5, 23, 17, 19, 29, 15, 9, 11, 21, 7 ]
      and with periodicity 4
      and with complexity 4
      and with auto-order 2
      φ | √φ | φ' | φ|<2>