In our paper [A. B. M. Basheer and J. Moori, On a group of the form $2^{10}{:}(U_{5}(2){:}2)$] we calculated the inertia factors, Fischer matrices and the ordinary character table of the split extension $ 2^{10}{:}(U_{5}(2){:}2)$ by means of Clifford-Fischer Theory. The second inertia factor group of $2^{10}{:}(U_{5}(2){:}2)$ is a group of the form $2_{-}^{1+6}{:}((3^{1+2}{:}8){:}2).$ The purpose of this paper is the determination of the conjugacy classes of $\overline{G}$ using the coset analysis method, the determination of the inertia factors, the computations of the Fischer matrices and the ordinary character table of the split extension $\overline{G}=2_{-}^{1+6}{:}((3^{1+2}{:}8){:}2)$ by means of Clifford-Fischer Theory. Through various theoretical and computational aspects we were able to determine the structures of the inertia factor groups. These are the groups $H_{1} = H_{2} = (3^{1+2}{:}8){:}2,\ $ $H_{3} =QD_{16}$ and $H_{4} = D_{12}.$ The Fischer matrices $\mathcal{F}_{i}$ of $\overline{G},$ which are complex valued matrices, are all listed in this paper and their sizes range between 2 and 5. The full character table of $\overline{G},$ which is $41 \times 41$ complex valued matrix, is available in the PhD thesis of the first author, which could be accessed online.