Number of selected skew morphism classes of C686 is 0
Total number of skew morphisms of C686 is 25512
Total number of skew morphism classes of C686 is 28
Total number of automorphisms of C686 is 294

1. Skew morphsim class of size 1
     
     of order 1
     with kernel of order 686
     and smallest kernel generator 1
     and power function values [ 1 ]
     and with periodicity 1
     and with complexity 0
     and with auto-order 686
     φ | √φ | φ' | φ|<686>
   
   

2. Skew morphsim class of size 2
     
     of order 3
     with kernel of order 686
     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
   
   

3. Skew morphsim class of size 6
     
     of order 7
     with kernel of order 686
     and smallest kernel generator 1
     and power function values [ 1 ]
     and with periodicity 1
     and with complexity 1
     and with auto-order 7
     φ | √φ | φ' | φ7
   
   

4. Skew morphsim class of size 12
     
     of order 21
     with kernel of order 686
     and smallest kernel generator 1
     and power function values [ 1 ]
     and with periodicity 1
     and with complexity 1
     and with auto-order 21
     φ | √φ | φ' | φ21
   
   

5. Skew morphsim class of size 42
     
     of order 49
     with kernel of order 686
     and smallest kernel generator 1
     and power function values [ 1 ]
     and with periodicity 1
     and with complexity 1
     and with auto-order 49
     φ | √φ | φ' | φ49
   
   

6. Skew morphsim class of size 84
     
     of order 147
     with kernel of order 686
     and smallest kernel generator 1
     and power function values [ 1 ]
     and with periodicity 1
     and with complexity 1
     and with auto-order 147
     φ | √φ | φ' | φ147
   
   

7. Skew morphsim class of size 1
     
     of order 2
     with kernel of order 686
     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 6
     
     of order 14
     with kernel of order 686
     and smallest kernel generator 1
     and power function values [ 1 ]
     and with periodicity 1
     and with complexity 1
     and with auto-order 14
     φ | √φ | φ' | φ14
   
   

9. Skew morphsim class of size 42
     
     of order 98
     with kernel of order 686
     and smallest kernel generator 1
     and power function values [ 1 ]
     and with periodicity 1
     and with complexity 1
     and with auto-order 98
     φ | √φ | φ' | φ98
   
   

10. Skew morphsim class of size 2
      
      of order 6
      with kernel of order 686
      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 12
      
      of order 42
      with kernel of order 686
      and smallest kernel generator 1
      and power function values [ 1 ]
      and with periodicity 1
      and with complexity 1
      and with auto-order 42
      φ | √φ | φ' | φ42
    
    

12. Skew morphsim class of size 84
      
      of order 294
      with kernel of order 686
      and smallest kernel generator 1
      and power function values [ 1 ]
      and with periodicity 1
      and with complexity 1
      and with auto-order 294
      φ | √φ | φ' | φ294
    
    

13. Skew morphsim class of size 6
      
      of order 7
      with kernel of order 343
      and smallest kernel generator 2
      and power function values [ 1, 6 ]
      and with periodicity 1
      and with complexity 2
      and with auto-order 2
      φ | √φ | φ' | φ|<2>
    
    

14. Skew morphsim class of size 42
      
      of order 49
      with kernel of order 343
      and smallest kernel generator 2
      and power function values [ 1, 48 ]
      and with periodicity 1
      and with complexity 2
      and with auto-order 2
      φ | √φ | φ' | φ|<2>
    
    

15. Skew morphsim class of size 294
      
      of order 343
      with kernel of order 343
      and smallest kernel generator 2
      and power function values [ 1, 342 ]
      and with periodicity 1
      and with complexity 2
      and with auto-order 2
      φ | √φ | φ' | φ|<2>
    
    

16. Skew morphsim class of size 252
      
      of order 49
      with kernel of order 98
      and smallest kernel generator 7
      and power function values [ 1, 8, 15, 22, 29, 36, 43 ]
      and with periodicity 1
      and with complexity 2
      and with auto-order 7
      φ | √φ | φ' | φ|<7>
    
    

17. Skew morphsim class of size 252
      
      of order 49
      with kernel of order 49
      and smallest kernel generator 14
      and power function values [ 1, 6, 36, 20, 22, 34, 8, 48, 43, 13, 29, 27, 15, 41 ]
      and with periodicity 1
      and with complexity 2
      and with auto-order 14
      φ | √φ | φ' | φ|<14>
    
    

18. Skew morphsim class of size 36
      
      of order 14
      with kernel of order 98
      and smallest kernel generator 7
      and power function values [ 1, 3, 5, 7, 9, 11, 13 ]
      and with periodicity 2
      and with complexity 3
      and with auto-order 2
      φ | √φ | φ' | φ2
    
    

19. Skew morphsim class of size 72
      
      of order 21
      with kernel of order 98
      and smallest kernel generator 7
      and power function values [ 1, 4, 7, 10, 13, 16, 19 ]
      and with periodicity 3
      and with complexity 3
      and with auto-order 3
      φ | √φ | φ' | φ3
    
    

20. Skew morphsim class of size 72
      
      of order 42
      with kernel of order 98
      and smallest kernel generator 7
      and power function values [ 1, 7, 13, 19, 25, 31, 37 ]
      and with periodicity 6
      and with complexity 3
      and with auto-order 6
      φ | √φ | φ' | φ6
    
    

21. Skew morphsim class of size 252
      
      of order 98
      with kernel of order 98
      and smallest kernel generator 7
      and power function values [ 1, 15, 29, 43, 57, 71, 85 ]
      and with periodicity 2
      and with complexity 3
      and with auto-order 2
      φ | √φ | φ' | φ2
    
    

22. Skew morphsim class of size 504
      
      of order 147
      with kernel of order 98
      and smallest kernel generator 7
      and power function values [ 1, 22, 43, 64, 85, 106, 127 ]
      and with periodicity 3
      and with complexity 3
      and with auto-order 3
      φ | √φ | φ' | φ3
    
    

23. Skew morphsim class of size 504
      
      of order 294
      with kernel of order 98
      and smallest kernel generator 7
      and power function values [ 1, 43, 85, 127, 169, 211, 253 ]
      and with periodicity 6
      and with complexity 3
      and with auto-order 6
      φ | √φ | φ' | φ6
    
    

24. Skew morphsim class of size 1764
      
      of order 343
      with kernel of order 49
      and smallest kernel generator 14
      and power function values [ 1, 48, 295, 97, 246, 146, 197, 195, 148, 244, 99, 293, 50, 342 ]
      and with periodicity 7
      and with complexity 4
      and with auto-order 2
      φ | √φ | φ' | φ|<2>
    
    

25. Skew morphsim class of size 1764
      
      of order 98
      with kernel of order 14
      and smallest kernel generator 49
      and power function values [ 1, 3, 47, 35, 65, 39, 55, 15, 17, 61, 49, 79, 53, 69, 29, 31, 75, 63, 93, 67, 83, 43, 45, 89, 77, 9, 81, 97, 57, 59, 5, 91, 23, 95, 13, 71, 73, 19, 7, 37, 11, 27, 85, 87, 33, 21, 51, 25, 41 ]
      and with periodicity 14
      and with complexity 5
      and with auto-order 2
      φ | √φ | φ' | φ2
    
    

26. Skew morphsim class of size 3528
      
      of order 147
      with kernel of order 14
      and smallest kernel generator 49
      and power function values [ 1, 4, 112, 31, 55, 37, 124, 22, 25, 133, 52, 76, 58, 145, 43, 46, 7, 73, 97, 79, 19, 64, 67, 28, 94, 118, 100, 40, 85, 88, 49, 115, 139, 121, 61, 106, 109, 70, 136, 13, 142, 82, 127, 130, 91, 10, 34, 16, 103 ]
      and with periodicity 21
      and with complexity 5
      and with auto-order 3
      φ | √φ | φ' | φ3
    
    

27. Skew morphsim class of size 3528
      
      of order 294
      with kernel of order 14
      and smallest kernel generator 49
      and power function values [ 1, 7, 181, 229, 151, 241, 205, 43, 49, 223, 271, 193, 283, 247, 85, 91, 265, 19, 235, 31, 289, 127, 133, 13, 61, 277, 73, 37, 169, 175, 55, 103, 25, 115, 79, 211, 217, 97, 145, 67, 157, 121, 253, 259, 139, 187, 109, 199, 163 ]
      and with periodicity 42
      and with complexity 5
      and with auto-order 6
      φ | √φ | φ' | φ6
    
    

28. Skew morphsim class of size 12348
      
      of order 343
      with kernel of order 7
      and smallest kernel generator 98
      and power function values [ 1, 6, 239, 209, 183, 20, 176, 125, 218, 181, 309, 188, 106, 146, 295, 55, 190, 258, 134, 69, 127, 174, 169, 230, 260, 237, 57, 195, 246, 104, 141, 307, 85, 118, 78, 223, 120, 279, 211, 286, 8, 244, 197, 153, 92, 13, 36, 167, 29, 272, 71, 328, 162, 335, 302, 293, 148, 202, 43, 62, 330, 216, 323, 321, 22, 34, 113, 41, 253, 342, 99, 251, 337, 111, 281, 265, 274, 27, 316, 83, 64, 90, 204, 48, 50, 300, 288, 160, 232, 314, 225, 76, 267, 132, 15, 139, 155, 97 ]
      and with periodicity 49
      and with complexity 6
      and with auto-order 2
      φ | √φ | φ' | φ|<2>