Sym (K_{m, n} ) when m = n

Let G = Sym (K_{3, 3})

1. Show that G is vertex-transitive.

2. Show that G is flag transitive.

3. Show that G is 2-transitive. That is, elements of G (ghee) can take any embedded arc of combinatorial length 2 to any other such arc.

4. Show that G is also 3-transitive.

5. Is G 4- transitive?