  In this paper, we give a systolic inequality for a quotient space of a Carnot
group $\Gamma\backslash G$ with Popp's volume. Namely we show the existence of
a positive constant $C$ such that the systole of $\Gamma\backslash G$ is less
than ${\rm Cvol}(\Gamma\backslash G)^{\frac{1}{Q}}$, where $Q$ is the Hausdorff
dimension. Moreover, the constant depends only on the dimension of the grading
of the Lie algebra $\mathfrak{g}=\bigoplus V_i$. To prove this fact, the scalar
product on $G$ introduced in the definition of Popp's volume plays a key role.
