  Suppose $G$ is a connected complex Lie group and $\Gamma$ is a discrete
subgroup such that $X := G/\Gamma$ is K\"ahler and the codimension of the top
non--vanishing homology group of $X$ with coefficients in $\mathbb Z_2$ is less
than or equal to two. We show that $G$ is solvable and a finite covering of $X$
is biholomorphic to a product $C\times A$, where $C$ is a Cousin group and $A$
is $\{e \}$, $\mathbb C$, $\mathbb C^*$, or $\mathbb C^*\times\mathbb C^*$.
