  Symmetry plays a fundamental role in design of experiments. In particular,
symmetries of factorial designs that preserve their statistical properties are
exploited to find designs with the best statistical properties. By using a
result proved by Rosenberg [6], the concept of the LP relaxation orthogonal
array polytope is developed and studied. A complete characterization of the
permutation symmetry group of this polytope is made. Also, this
characterization is verified computationally for many cases. Finally, a proof
is provided.
