We present an explicit method to perform similarity reduction of a n-Hilbert factorization problem for a homogeneous loop group and use our results to find solutions to the Painlevé VI equation for N = 3. The tau function of the reduced hierarchy is shown to satisfy the σ-form of the Painlevé VI equation. A class of tau functions of the reduced integrable hierarchy is constructed by means of a Grassmannian formulation. These solutions provide rational solutions of the Painlevé VI equation.