How to compute the stabilizer of any polynomial of degree $n$ with distinct roots? I was told in case of polynomials of degree 3 in 2 variables this is related to the fact that there is a unique automorphism of $\mathbb P^1$ that fixes three points.
Any helful hints of calculating the stabilizer say of p(x) = $x^2y^5 + xy$? I am using the $n^{th}$ inverse of the determinant as a character, where $n$ is the degree of the polynomial.