Repeat Exercise 18 for the group S 3 . List the elements of S 3 in the order , (1, 2, 3), (1, 3, 2),

Repeat Exercise 18 for the group S₃. List the elements of S₃ in the order ι, (1, 2, 3), (1, 3, 2), (2, 3), (1, 3), (1, 2).

Data from Exercise 18

Up to isomorphism, how many transitive Z₄ sets X are there? (Use the preceding exercises.) Give an example of each isomorphism type, listing an action table of each as in Table 16.10. Take lowercase names a, b, c, and so on for the elements in the set X.