[I'm impressed by the amount of algebra that Dickson had to do by hand in the 1890's.] The only perm polys over GF(5) are: x*{1, x^2, x^2-2x-2, x^2+2x-2, x^2-x+2, x^2+x+2} and linear (a*x+b) functions of these. This makes sense, as there are 5 choices for b, 4 choices for a, and 6=3*2 choices for the non-x factor. There are 120 monic perm polys over GF(7) with an "x" factor; once again, this makes sense, as there are 7 choices for b and 6 choices for a when you do linear (a*x+b) functions of these. Many of these 120 factors are irreducible quartics, many have an irreducible cubic times another factor of "x", etc. There are also six factors which are squares of irreducible quadratics: (x^2-3x-1)^2, (x^2+3x-1)^2, (x^2-2x-2)^2, (x^2+2x-2)^2, (x^2-x+3)^2, (x^2+x+3)^2 None of these 120 factors seems to be a perm poly by itself.