On the Fischer-Clifford matrices of a maximal subgroup of the Lyons group Ly

‎The non-split extension group $\overline{G} = 5^3{^.}L(3,5)$ is a‎ ‎subgroup of order $46500000$ and of index $1113229656$ in $Ly$‎. ‎The‎ ‎group $\overline{G}$ in turn has $L(3,5)$ and $5^2{:}2.A_5$ as‎ ‎inertia factors‎. ‎The group $5^2{:}2.A_5$ is of order $3 000$ and is‎ ‎of index $124$ in $L(3,5)$‎. ‎The aim of this paper is to compute the‎ ‎Fischer-Clifford matrices of $\overline{G}$‎, ‎which together with‎ ‎associated partial character tables of the inertia factor groups‎, ‎are used to compute a full character table of $\overline{G}$‎. ‎A‎ ‎partial projective character table corresponding to $5^2{:}2A_5$ is‎ ‎required‎, ‎hence we have to compute the Schur multiplier and‎ ‎projective character table of $5^2{:}2A_5$‎.