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 $5^2{:}2a_5$.