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We describe the explicit computation of a family of 4-branch-point rationalfunctions of degree 63 with monodromy group PSL(6,2). This, in particular,negatively answers a question by J. K\"onig whether there exists a such afunction with rational coefficients. The computed family also gives rise tonon-regular degree-126 realizations of Aut(PSL(6,2)) over Q(t).

A family of 4-branch-point covers with monodromy group PSL(6,2)