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In this paper we prove that $2^{20+1}.U_6(2)$, known as the centralizer of aninvolution in the group $2E_6(2)$ is a quotient of a Coxeter group. We obtain apresentation of $2^{20+1}.U_6(2)$ as a $Q_{222}$-group, which now resolve along pending question.

Sur le centralisateur d'une involution de 2E6(2)