Number of selected skew morphism classes of C729 is 0
Total number of skew morphisms of C729 is 59050
Total number of skew morphism classes of C729 is 37
Total number of automorphisms of C729 is 486

1. Skew morphsim class of size 1
     
     of order 1
     with kernel of order 729
     and smallest kernel generator 1
     and power function values [ 1 ]
     and with periodicity 1
     and with complexity 0
     and with auto-order 729
     φ | √φ | φ' | φ|<729>
   
   

2. Skew morphsim class of size 1
     
     of order 2
     with kernel of order 729
     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 3
     with kernel of order 729
     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
   
   

4. Skew morphsim class of size 2
     
     of order 6
     with kernel of order 729
     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
   
   

5. Skew morphsim class of size 6
     
     of order 9
     with kernel of order 729
     and smallest kernel generator 1
     and power function values [ 1 ]
     and with periodicity 1
     and with complexity 1
     and with auto-order 9
     φ | √φ | φ' | φ9
   
   

6. Skew morphsim class of size 6
     
     of order 18
     with kernel of order 729
     and smallest kernel generator 1
     and power function values [ 1 ]
     and with periodicity 1
     and with complexity 1
     and with auto-order 18
     φ | √φ | φ' | φ18
   
   

7. Skew morphsim class of size 18
     
     of order 27
     with kernel of order 729
     and smallest kernel generator 1
     and power function values [ 1 ]
     and with periodicity 1
     and with complexity 1
     and with auto-order 27
     φ | √φ | φ' | φ27
   
   

8. Skew morphsim class of size 18
     
     of order 54
     with kernel of order 729
     and smallest kernel generator 1
     and power function values [ 1 ]
     and with periodicity 1
     and with complexity 1
     and with auto-order 54
     φ | √φ | φ' | φ54
   
   

9. Skew morphsim class of size 54
     
     of order 81
     with kernel of order 729
     and smallest kernel generator 1
     and power function values [ 1 ]
     and with periodicity 1
     and with complexity 1
     and with auto-order 81
     φ | √φ | φ' | φ81
   
   

10. Skew morphsim class of size 54
      
      of order 162
      with kernel of order 729
      and smallest kernel generator 1
      and power function values [ 1 ]
      and with periodicity 1
      and with complexity 1
      and with auto-order 162
      φ | √φ | φ' | φ162
    
    

11. Skew morphsim class of size 162
      
      of order 243
      with kernel of order 729
      and smallest kernel generator 1
      and power function values [ 1 ]
      and with periodicity 1
      and with complexity 1
      and with auto-order 243
      φ | √φ | φ' | φ243
    
    

12. Skew morphsim class of size 162
      
      of order 486
      with kernel of order 729
      and smallest kernel generator 1
      and power function values [ 1 ]
      and with periodicity 1
      and with complexity 1
      and with auto-order 486
      φ | √φ | φ' | φ486
    
    

13. Skew morphsim class of size 12
      
      of order 9
      with kernel of order 243
      and smallest kernel generator 3
      and power function values [ 1, 4, 7 ]
      and with periodicity 1
      and with complexity 2
      and with auto-order 3
      φ | √φ | φ' | φ|<3>
    
    

14. Skew morphsim class of size 36
      
      of order 27
      with kernel of order 243
      and smallest kernel generator 3
      and power function values [ 1, 10, 19 ]
      and with periodicity 1
      and with complexity 2
      and with auto-order 3
      φ | √φ | φ' | φ|<3>
    
    

15. Skew morphsim class of size 108
      
      of order 81
      with kernel of order 243
      and smallest kernel generator 3
      and power function values [ 1, 28, 55 ]
      and with periodicity 1
      and with complexity 2
      and with auto-order 3
      φ | √φ | φ' | φ|<3>
    
    

16. Skew morphsim class of size 324
      
      of order 243
      with kernel of order 243
      and smallest kernel generator 3
      and power function values [ 1, 82, 163 ]
      and with periodicity 1
      and with complexity 2
      and with auto-order 3
      φ | √φ | φ' | φ|<3>
    
    

17. Skew morphsim class of size 108
      
      of order 27
      with kernel of order 81
      and smallest kernel generator 9
      and power function values [ 1, 4, 16, 10, 13, 25, 19, 22, 7 ]
      and with periodicity 1
      and with complexity 2
      and with auto-order 9
      φ | √φ | φ' | φ|<9>
    
    

18. Skew morphsim class of size 324
      
      of order 81
      with kernel of order 81
      and smallest kernel generator 9
      and power function values [ 1, 10, 19, 28, 37, 46, 55, 64, 73 ]
      and with periodicity 1
      and with complexity 2
      and with auto-order 9
      φ | √φ | φ' | φ|<9>
    
    

19. Skew morphsim class of size 4
      
      of order 6
      with kernel of order 243
      and smallest kernel generator 3
      and power function values [ 1, 3, 5 ]
      and with periodicity 2
      and with complexity 3
      and with auto-order 2
      φ | √φ | φ' | φ2
    
    

20. Skew morphsim class of size 12
      
      of order 18
      with kernel of order 243
      and smallest kernel generator 3
      and power function values [ 1, 7, 13 ]
      and with periodicity 2
      and with complexity 3
      and with auto-order 2
      φ | √φ | φ' | φ2
    
    

21. Skew morphsim class of size 36
      
      of order 18
      with kernel of order 81
      and smallest kernel generator 9
      and power function values [ 1, 3, 5, 7, 9, 11, 13, 15, 17 ]
      and with periodicity 2
      and with complexity 3
      and with auto-order 2
      φ | √φ | φ' | φ2
    
    

22. Skew morphsim class of size 36
      
      of order 54
      with kernel of order 243
      and smallest kernel generator 3
      and power function values [ 1, 19, 37 ]
      and with periodicity 2
      and with complexity 3
      and with auto-order 2
      φ | √φ | φ' | φ2
    
    

23. Skew morphsim class of size 108
      
      of order 54
      with kernel of order 81
      and smallest kernel generator 9
      and power function values [ 1, 7, 13, 19, 25, 31, 37, 43, 49 ]
      and with periodicity 2
      and with complexity 3
      and with auto-order 2
      φ | √φ | φ' | φ2
    
    

24. Skew morphsim class of size 324
      
      of order 54
      with kernel of order 27
      and smallest kernel generator 27
      and power function values [ 1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39, 41, 43, 45, 47, 49, 51, 53 ]
      and with periodicity 2
      and with complexity 3
      and with auto-order 2
      φ | √φ | φ' | φ2
    
    

25. Skew morphsim class of size 972
      
      of order 81
      with kernel of order 27
      and smallest kernel generator 27
      and power function values [ 1, 4, 16, 64, 13, 52, 46, 22, 7, 28, 31, 43, 10, 40, 79, 73, 49, 34, 55, 58, 70, 37, 67, 25, 19, 76, 61 ]
      and with periodicity 3
      and with complexity 3
      and with auto-order 3
      φ | √φ | φ' | φ3
    
    

26. Skew morphsim class of size 108
      
      of order 162
      with kernel of order 243
      and smallest kernel generator 3
      and power function values [ 1, 55, 109 ]
      and with periodicity 2
      and with complexity 3
      and with auto-order 2
      φ | √φ | φ' | φ2
    
    

27. Skew morphsim class of size 324
      
      of order 162
      with kernel of order 81
      and smallest kernel generator 9
      and power function values [ 1, 19, 37, 55, 73, 91, 109, 127, 145 ]
      and with periodicity 2
      and with complexity 3
      and with auto-order 2
      φ | √φ | φ' | φ2
    
    

28. Skew morphsim class of size 972
      
      of order 162
      with kernel of order 27
      and smallest kernel generator 27
      and power function values [ 1, 7, 13, 19, 25, 31, 37, 43, 49, 55, 61, 67, 73, 79, 85, 91, 97, 103, 109, 115, 121, 127, 133, 139, 145, 151, 157 ]
      and with periodicity 6
      and with complexity 3
      and with auto-order 6
      φ | √φ | φ' | φ6
    
    

29. Skew morphsim class of size 972
      
      of order 243
      with kernel of order 81
      and smallest kernel generator 9
      and power function values [ 1, 28, 55, 82, 109, 136, 163, 190, 217 ]
      and with periodicity 3
      and with complexity 3
      and with auto-order 3
      φ | √φ | φ' | φ3
    
    

30. Skew morphsim class of size 2916
      
      of order 243
      with kernel of order 27
      and smallest kernel generator 27
      and power function values [ 1, 10, 100, 28, 37, 127, 55, 64, 154, 82, 91, 181, 109, 118, 208, 136, 145, 235, 163, 172, 19, 190, 199, 46, 217, 226, 73 ]
      and with periodicity 9
      and with complexity 3
      and with auto-order 9
      φ | √φ | φ' | φ9
    
    

31. Skew morphsim class of size 324
      
      of order 486
      with kernel of order 243
      and smallest kernel generator 3
      and power function values [ 1, 163, 325 ]
      and with periodicity 2
      and with complexity 3
      and with auto-order 2
      φ | √φ | φ' | φ2
    
    

32. Skew morphsim class of size 972
      
      of order 486
      with kernel of order 81
      and smallest kernel generator 9
      and power function values [ 1, 55, 109, 163, 217, 271, 325, 379, 433 ]
      and with periodicity 6
      and with complexity 3
      and with auto-order 6
      φ | √φ | φ' | φ6
    
    

33. Skew morphsim class of size 2916
      
      of order 486
      with kernel of order 27
      and smallest kernel generator 27
      and power function values [ 1, 19, 37, 55, 73, 91, 109, 127, 145, 163, 181, 199, 217, 235, 253, 271, 289, 307, 325, 343, 361, 379, 397, 415, 433, 451, 469 ]
      and with periodicity 18
      and with complexity 3
      and with auto-order 18
      φ | √φ | φ' | φ18
    
    

34. Skew morphsim class of size 2916
      
      of order 162
      with kernel of order 9
      and smallest kernel generator 81
      and power function values [ 1, 3, 77, 61, 117, 83, 121, 69, 89, 19, 21, 95, 79, 135, 101, 139, 87, 107, 37, 39, 113, 97, 153, 119, 157, 105, 125, 55, 57, 131, 115, 9, 137, 13, 123, 143, 73, 75, 149, 133, 27, 155, 31, 141, 161, 91, 93, 5, 151, 45, 11, 49, 159, 17, 109, 111, 23, 7, 63, 29, 67, 15, 35, 127, 129, 41, 25, 81, 47, 85, 33, 53, 145, 147, 59, 43, 99, 65, 103, 51, 71 ]
      and with periodicity 18
      and with complexity 5
      and with auto-order 2
      φ | √φ | φ' | φ2
    
    

35. Skew morphsim class of size 8748
      
      of order 243
      with kernel of order 9
      and smallest kernel generator 81
      and power function values [ 1, 4, 97, 145, 94, 214, 127, 22, 169, 190, 31, 205, 91, 121, 79, 73, 49, 34, 136, 58, 70, 37, 148, 187, 19, 76, 142, 82, 85, 178, 226, 175, 52, 208, 103, 7, 28, 112, 43, 172, 202, 160, 154, 130, 115, 217, 139, 151, 118, 229, 25, 100, 157, 223, 163, 166, 16, 64, 13, 133, 46, 184, 88, 109, 193, 124, 10, 40, 241, 235, 211, 196, 55, 220, 232, 199, 67, 106, 181, 238, 61 ]
      and with periodicity 27
      and with complexity 5
      and with auto-order 3
      φ | √φ | φ' | φ3
    
    

36. Skew morphsim class of size 8748
      
      of order 486
      with kernel of order 9
      and smallest kernel generator 81
      and power function values [ 1, 7, 445, 343, 187, 463, 199, 367, 481, 55, 61, 13, 397, 241, 31, 253, 421, 49, 109, 115, 67, 451, 295, 85, 307, 475, 103, 163, 169, 121, 19, 349, 139, 361, 43, 157, 217, 223, 175, 73, 403, 193, 415, 97, 211, 271, 277, 229, 127, 457, 247, 469, 151, 265, 325, 331, 283, 181, 25, 301, 37, 205, 319, 379, 385, 337, 235, 79, 355, 91, 259, 373, 433, 439, 391, 289, 133, 409, 145, 313, 427 ]
      and with periodicity 54
      and with complexity 5
      and with auto-order 6
      φ | √φ | φ' | φ6
    
    

37. Skew morphsim class of size 26244
      
      of order 486
      with kernel of order 3
      and smallest kernel generator 243
      and power function values [ 1, 3, 245, 241, 369, 413, 49, 303, 149, 397, 291, 425, 313, 333, 269, 283, 429, 167, 307, 93, 119, 385, 297, 125, 31, 69, 185, 217, 381, 299, 457, 261, 467, 265, 195, 203, 127, 183, 479, 43, 225, 323, 13, 321, 221, 37, 471, 173, 115, 189, 179, 247, 447, 239, 433, 273, 353, 187, 153, 35, 481, 87, 257, 343, 75, 47, 259, 117, 377, 229, 213, 275, 253, 363, 227, 331, 81, 233, 463, 339, 293, 163, 165, 407, 403, 45, 89, 211, 465, 311, 73, 453, 101, 475, 9, 431, 445, 105, 329, 469, 255, 281, 61, 459, 287, 193, 231, 347, 379, 57, 461, 133, 423, 143, 427, 357, 365, 289, 345, 155, 205, 387, 485, 175, 483, 383, 199, 147, 335, 277, 351, 341, 409, 123, 401, 109, 435, 29, 349, 315, 197, 157, 249, 419, 19, 237, 209, 421, 279, 53, 391, 375, 437, 415, 39, 389, 7, 243, 395, 139, 15, 455, 325, 327, 83, 79, 207, 251, 373, 141, 473, 235, 129, 263, 151, 171, 107, 121, 267, 5, 145, 417, 443, 223, 135, 449, 355, 393, 23, 55, 219, 137, 295, 99, 305, 103, 33, 41, 451, 21, 317, 367, 63, 161, 337, 159, 59, 361, 309, 11, 439, 27, 17, 85, 285, 77, 271, 111, 191, 25, 477, 359, 319, 411, 95, 181, 399, 371, 97, 441, 215, 67, 51, 113, 91, 201, 65, 169, 405, 71, 301, 177, 131 ]
      and with periodicity 162
      and with complexity 11
      and with auto-order 2
      φ | √φ | φ' | φ2