Let be an automorphism.

Obviously, .

1)Now, has to be an element of order and so .

2)The same possibilities for however except for what was used in #1.

3)Once #1 and #2 are determined then and so is determined.

There are possibilities for #2 and possibilities #3, we therefore have at most automorphisms.

Check that all these six instead give a raise to a hextic automorphism group.