Let \(\overline{G}=p^{1+2n}{:}G\) be a finite split extension of an extra-special p-group \(P=p^{1+2n}\) by a group G. Since the center Z(P) is characteristic in P and hence normal in \(\overline{G}\) , we can construct the factor group \(\overline{F}=\frac{\overline{G}}{Z(P)}\cong p^{2n}{:}G\) , where \(P_1=p^{2n}\) is an elementary abelian p-group. In this paper, the Fischer–Clifford matrices M(g) of \(\overline{G}\) are constructed from the corresponding Fischer–Clifford matrices \(\widehat{M(g)}\) of \(\overline{F}\) by a method we called the lifting of Fischer–Clifford matrices. As an example, the ordinary character table of a 7-local maximal subgroup \(7_{+}^{1+4}{:}(3\times 2 S_7)\) of the Monster \(\mathbb {M}\) is re-constructed using the lifting method.
