Fundamental group schemes of Hilbert scheme of n points on a smooth projective surface

Let k be an algebraically closed field of characteristic p>3. Let X be an irreducible smooth projective surface over k. Fix an integer n≥2 and let HilbXn be the Hilbert scheme parameterizing effective 0-cycles of length n on X. The aim of the present article is to find the S-fundamental group scheme and Nori's fundamental group scheme of the Hilbert scheme HilbXn.