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existence of this splitting and a formula (in terms of adifferent set of coordinates) was proved by S.D. Miller in an unpublished note;the formula in terms of Pl\"{u}cker coordinates is advantageous to thecomputation of the Fourier coefficients of an Eisenstein series on the doublecover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

A Splitting into the Double Cover of SL(3,$\mathbb{R}$)