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Granboulan computed an explicit polynomial whose Galois group over therational function field Q(t) is the Mathieu group M24. By a result of Malle andMatzat, it was known before that such a polynomial exists. Even more, theirproof showed that there is a 1-parameter family of such polynomials. In thisnote we compute this family.

A one--parameter family of polynomials with Galois group M24 over Q(t)