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.
D8= group generated by V and (12).
Z4 = group generated by (1234).