2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/144006In 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.Group Theorytext