  A matrix group is said to be permutation-like if any matrix of the group is
similar to a permutation matrix. G. Cigler proved that, if a permutation-like
matrix group contains a normal cyclic subgroup which is generated by a maximal
cycle and the matrix dimension is a prime, then the group is similar to a
permutation matrix group. This paper extends the result to the case where the
matrix dimension is a square of a prime.
