Counting the orbits on finite simple groups under the action of the automorphism group - Suzuki groups vs. linear groups

We determine the number omega(G) of orbits on the (finite) group G under the action of Aut(G) for G is an element of { PSL(2, q), SL(2, q), PSL(3,3),Sz(2(2m+1))}, covering all of the minimal simple groups as well as all of the simple Zassenhaus groups. This leads to recursive formulae on the one hand, and to the equation omega(Sz(q)) = omega(PSL(2, q)) + 2 on the other.