  We provide a formula for the splitting of a congruence subgroup of
SL$(3,\mathbb{R})$ into the double cover of SL$(3,\mathbb{R})$ in terms of
Pl\"{u}cker coordinates and prove that the splitting satisfies a twisted
multiplicativity. The existence of this splitting and a formula (in terms of a
different set of coordinates) was proved by S.D. Miller in an unpublished note;
the formula in terms of Pl\"{u}cker coordinates is advantageous to the
computation of the Fourier coefficients of an Eisenstein series on the double
cover of SL$(3)$ over $\mathbb{Q}$. The computation of these Fourier
coefficients will be addressed in a forthcoming work.
