Irreducible collineation groups with two orbits forming an oval

Let G be a collineation group of a finite projective plane P of odd order fixing an oval \u3a9. We investigate the case in which G has even order, has two orbits \u3a9_0 and \u3a9_1 on \u3a9, and the action of G on \u3a9_0 is primitive.We show that if G is irreducible, then P has a G-invariant desarguesian subplane P_0 and \u3a9_0 is a conic of P_0