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We characterize the finite projective planes П of order  n  with a collineation group  G  acting 2-transitively on a point orbit of length  n  – 3. Aside from the trivial cases, the plane П must have order 9 or 16 and  G  is isomorphic to  PSL (2,5) or  AGL (1,13), respectively.

Finite projective planes of order n with a 2-transitive orbit of length n – 3