I am currently going through Galois Theory by Ian Stewart. I am on Chapter 22 of the third edition and trying to solve exercise 22.6 at the end of the chapter which is the following:

Show that any transitive group of S4 is one of the following S4, A4, D8, V or Z4, defined as follows:

A4 = alternating group of degree 4.

V= {1,(12)(34),(13)(24),(14)(23)}.

D8= group generated by V and (12).

Z4 = group generated by (1234).

Amy ideas?

Thanks