Number of selected skew morphism classes of C_689 is 0
Total number of skew morphisms of C_689 is 1248
Total number of skew morphism classes of C_689 is 41
Total number of automorphisms of C_689 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
   
   

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
   
   

3. 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
   
   

4. 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
   
   

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
   
   

6. 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
   
   

7. 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
   
   

8. 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
   
   

9. 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
   
   

10. 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
    
    

11. 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
    
    

12. 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
    
    

13. 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
    
    

14. 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
    
    

15. 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
    
    

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
    
    

17. 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
    
    

18. 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
    
    

19. 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
    
    

20. 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
    
    

21. 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
    
    

22. 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
    
    

23. 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
    
    

24. 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
    
    

25. 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
    
    

26. 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
    
    

27. 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
    
    

28. 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
    
    

29. 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
    
    

30. 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
    
    

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
    
    

32. 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
    
    

33. 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
    
    

34. 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
    
    

35. 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
    
    

36. 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
    
    

37. 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
    
    

38. 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
    
    

39. 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
    
    

40. 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
    
    

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, 16, 44, 15, 28, 24, 13, 49, 42, 36, 46, 47, 10 ] #
      and with periodicity 1