Number of selected skew morphism classes of C689 is 0
Total number of skew morphisms of C689 is 1248
Total number of skew morphism classes of C689 is 41
Total number of automorphisms of C689 is 624

1. Skew morphsim class of size 1
     
     of order 1
     with kernel of order 689
     and smallest kernel generator 1
     and power function values [ 1 ]
     and with periodicity 1
     and with complexity 0
     and with auto-order 689
     φ | √φ | φ' | φ|<689>
   
   

2. Skew morphsim class of size 12
     
     of order 13
     with kernel of order 689
     and smallest kernel generator 1
     and power function values [ 1 ]
     and with periodicity 1
     and with complexity 1
     and with auto-order 13
     φ | √φ | φ' | φ13
   
   

3. Skew morphsim class of size 1
     
     of order 2
     with kernel of order 689
     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
   
   

4. Skew morphsim class of size 2
     
     of order 4
     with kernel of order 689
     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
   
   

5. Skew morphsim class of size 12
     
     of order 26
     with kernel of order 689
     and smallest kernel generator 1
     and power function values [ 1 ]
     and with periodicity 1
     and with complexity 1
     and with auto-order 26
     φ | √φ | φ' | φ26
   
   

6. Skew morphsim class of size 24
     
     of order 52
     with kernel of order 689
     and smallest kernel generator 1
     and power function values [ 1 ]
     and with periodicity 1
     and with complexity 1
     and with auto-order 52
     φ | √φ | φ' | φ52
   
   

7. Skew morphsim class of size 1
     
     of order 2
     with kernel of order 689
     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
   
   

8. Skew morphsim class of size 2
     
     of order 3
     with kernel of order 689
     and smallest kernel generator 1
     and power function values [ 1 ]
     and with periodicity 1
     and with complexity 1
     and with auto-order 3
     φ | √φ | φ' | φ3
   
   

9. Skew morphsim class of size 2
     
     of order 4
     with kernel of order 689
     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
   
   

10. Skew morphsim class of size 2
      
      of order 6
      with kernel of order 689
      and smallest kernel generator 1
      and power function values [ 1 ]
      and with periodicity 1
      and with complexity 1
      and with auto-order 6
      φ | √φ | φ' | φ6
    
    

11. Skew morphsim class of size 4
      
      of order 12
      with kernel of order 689
      and smallest kernel generator 1
      and power function values [ 1 ]
      and with periodicity 1
      and with complexity 1
      and with auto-order 12
      φ | √φ | φ' | φ12
    
    

12. Skew morphsim class of size 12
      
      of order 26
      with kernel of order 689
      and smallest kernel generator 1
      and power function values [ 1 ]
      and with periodicity 1
      and with complexity 1
      and with auto-order 26
      φ | √φ | φ' | φ26
    
    

13. Skew morphsim class of size 24
      
      of order 39
      with kernel of order 689
      and smallest kernel generator 1
      and power function values [ 1 ]
      and with periodicity 1
      and with complexity 1
      and with auto-order 39
      φ | √φ | φ' | φ39
    
    

14. Skew morphsim class of size 24
      
      of order 52
      with kernel of order 689
      and smallest kernel generator 1
      and power function values [ 1 ]
      and with periodicity 1
      and with complexity 1
      and with auto-order 52
      φ | √φ | φ' | φ52
    
    

15. Skew morphsim class of size 24
      
      of order 78
      with kernel of order 689
      and smallest kernel generator 1
      and power function values [ 1 ]
      and with periodicity 1
      and with complexity 1
      and with auto-order 78
      φ | √φ | φ' | φ78
    
    

16. Skew morphsim class of size 48
      
      of order 156
      with kernel of order 689
      and smallest kernel generator 1
      and power function values [ 1 ]
      and with periodicity 1
      and with complexity 1
      and with auto-order 156
      φ | √φ | φ' | φ156
    
    

17. Skew morphsim class of size 1
      
      of order 2
      with kernel of order 689
      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
    
    

18. Skew morphsim class of size 2
      
      of order 4
      with kernel of order 689
      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
    
    

19. Skew morphsim class of size 2
      
      of order 6
      with kernel of order 689
      and smallest kernel generator 1
      and power function values [ 1 ]
      and with periodicity 1
      and with complexity 1
      and with auto-order 6
      φ | √φ | φ' | φ6
    
    

20. Skew morphsim class of size 4
      
      of order 12
      with kernel of order 689
      and smallest kernel generator 1
      and power function values [ 1 ]
      and with periodicity 1
      and with complexity 1
      and with auto-order 12
      φ | √φ | φ' | φ12
    
    

21. Skew morphsim class of size 12
      
      of order 26
      with kernel of order 689
      and smallest kernel generator 1
      and power function values [ 1 ]
      and with periodicity 1
      and with complexity 1
      and with auto-order 26
      φ | √φ | φ' | φ26
    
    

22. Skew morphsim class of size 24
      
      of order 52
      with kernel of order 689
      and smallest kernel generator 1
      and power function values [ 1 ]
      and with periodicity 1
      and with complexity 1
      and with auto-order 52
      φ | √φ | φ' | φ52
    
    

23. Skew morphsim class of size 24
      
      of order 78
      with kernel of order 689
      and smallest kernel generator 1
      and power function values [ 1 ]
      and with periodicity 1
      and with complexity 1
      and with auto-order 78
      φ | √φ | φ' | φ78
    
    

24. Skew morphsim class of size 48
      
      of order 156
      with kernel of order 689
      and smallest kernel generator 1
      and power function values [ 1 ]
      and with periodicity 1
      and with complexity 1
      and with auto-order 156
      φ | √φ | φ' | φ156
    
    

25. Skew morphsim class of size 2
      
      of order 4
      with kernel of order 689
      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
    
    

26. Skew morphsim class of size 4
      
      of order 12
      with kernel of order 689
      and smallest kernel generator 1
      and power function values [ 1 ]
      and with periodicity 1
      and with complexity 1
      and with auto-order 12
      φ | √φ | φ' | φ12
    
    

27. Skew morphsim class of size 2
      
      of order 4
      with kernel of order 689
      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
    
    

28. Skew morphsim class of size 4
      
      of order 12
      with kernel of order 689
      and smallest kernel generator 1
      and power function values [ 1 ]
      and with periodicity 1
      and with complexity 1
      and with auto-order 12
      φ | √φ | φ' | φ12
    
    

29. Skew morphsim class of size 24
      
      of order 52
      with kernel of order 689
      and smallest kernel generator 1
      and power function values [ 1 ]
      and with periodicity 1
      and with complexity 1
      and with auto-order 52
      φ | √φ | φ' | φ52
    
    

30. Skew morphsim class of size 48
      
      of order 156
      with kernel of order 689
      and smallest kernel generator 1
      and power function values [ 1 ]
      and with periodicity 1
      and with complexity 1
      and with auto-order 156
      φ | √φ | φ' | φ156
    
    

31. Skew morphsim class of size 24
      
      of order 52
      with kernel of order 689
      and smallest kernel generator 1
      and power function values [ 1 ]
      and with periodicity 1
      and with complexity 1
      and with auto-order 52
      φ | √φ | φ' | φ52
    
    

32. Skew morphsim class of size 48
      
      of order 156
      with kernel of order 689
      and smallest kernel generator 1
      and power function values [ 1 ]
      and with periodicity 1
      and with complexity 1
      and with auto-order 156
      φ | √φ | φ' | φ156
    
    

33. Skew morphsim class of size 2
      
      of order 6
      with kernel of order 689
      and smallest kernel generator 1
      and power function values [ 1 ]
      and with periodicity 1
      and with complexity 1
      and with auto-order 6
      φ | √φ | φ' | φ6
    
    

34. Skew morphsim class of size 4
      
      of order 12
      with kernel of order 689
      and smallest kernel generator 1
      and power function values [ 1 ]
      and with periodicity 1
      and with complexity 1
      and with auto-order 12
      φ | √φ | φ' | φ12
    
    

35. Skew morphsim class of size 24
      
      of order 78
      with kernel of order 689
      and smallest kernel generator 1
      and power function values [ 1 ]
      and with periodicity 1
      and with complexity 1
      and with auto-order 78
      φ | √φ | φ' | φ78
    
    

36. Skew morphsim class of size 48
      
      of order 156
      with kernel of order 689
      and smallest kernel generator 1
      and power function values [ 1 ]
      and with periodicity 1
      and with complexity 1
      and with auto-order 156
      φ | √φ | φ' | φ156
    
    

37. Skew morphsim class of size 2
      
      of order 4
      with kernel of order 689
      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
    
    

38. Skew morphsim class of size 4
      
      of order 12
      with kernel of order 689
      and smallest kernel generator 1
      and power function values [ 1 ]
      and with periodicity 1
      and with complexity 1
      and with auto-order 12
      φ | √φ | φ' | φ12
    
    

39. Skew morphsim class of size 24
      
      of order 52
      with kernel of order 689
      and smallest kernel generator 1
      and power function values [ 1 ]
      and with periodicity 1
      and with complexity 1
      and with auto-order 52
      φ | √φ | φ' | φ52
    
    

40. Skew morphsim class of size 48
      
      of order 156
      with kernel of order 689
      and smallest kernel generator 1
      and power function values [ 1 ]
      and with periodicity 1
      and with complexity 1
      and with auto-order 156
      φ | √φ | φ' | φ156
    
    

41. Skew morphsim class of size 624
      
      of order 53
      with kernel of order 53
      and smallest kernel generator 13
      and power function values [ 1, 10, 47, 46, 36, 42, 49, 13, 24, 28, 15, 44, 16 ]
      and with periodicity 1
      and with complexity 2
      and with auto-order 13
      φ | √φ | φ' | φ|<13>