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Abstract. We use a rigidity argument to prove the existence of two re-lated degree twenty-eight covers of the projective plane with Galois group SU3(3).2 ∼ = G2(2). Constructing corresponding two-parameter polynomials directly from the defining group-theoretic data seems beyond feasablity. In-stead we provide two independent constructions of these polynomials, one from 3-division points on covers of the projective line studied by Deligne and Mostow, and one from 2-division points of genus three curves studied by Sh-ioda. We explain how one of the covers also arises as a 2-division polynomial for a family of G2 motives in the classification of Dettweiler and Reiter. We conclude by specializing our two covers to get interesting three-point cover