 Alternately, one could use the Sylow theorems, which state generally that all Sylow p-subgroups are conjugate.The projective linear group of dimension two over the finite field with five elements, PGL(2, 5), acts on the projective line over the field with five elements, P1(F5), which has six elements.Further, this action is faithful and 3-transitive, as is always the case for the action of the projective linear group on the projective line.