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We use a rigidity argument to prove the existence of two related degreetwenty-eight covers of the projective plane with Galois group SU3(3).2 = G2(2).Constructing corresponding two-parameter polynomials directly from the defininggroup-theoretic data seems beyond feasablity. Instead we provide twoindependent constructions of these polynomials, one from 3-division points oncovers of the projective line studied by Deligne and Mostow, and one from2-division points of genus three curves studied by Shioda. We explain how oneof the covers also arises as a 2-division polynomial for a family of G2 motivesin the classification of Dettweiler and Reiter. We conclude by specializing ourtwo covers to get interesting three-point covers and number fields which wouldbe hard to construct directly.

Division polynomials with Galois group SU3(3).2 = G2(2)