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