[By a theorem of L. Bieberbach](https://en.wikipedia.org/wiki/Flat_manifold) we know that that every closed flat Riemannian manifold is a quotient of a torus via action of a  finite group $\Gamma$. In this question we are interested in the particular case of $3$ dimensional flat riemannian manifolds. 
So we assume that $(M,g)$ is a flat Riemannian $3$-manifold. then by above theorem we know that $(M,g)\cong T^3/\Gamma$, where $\Gamma$ is a finite group. 

**Questions** 

-  Is there a  complete classification of  all  finite group actions on flat $3$-torus which resulting quotion space would be a an orientable manifold with vanishing first Betti number or first integral homology? 

- According to  Wikipedia  Wiki(https://en.wikipedia.org/wiki/Flat_manifold), there is a  complete list of all  6 orientable and 4 non-orientable  flat compact  manifolds. This list consists of  all Seifert fiber spaces. Does the link of wikipedia actually means that all  orientable Seifert Hyper spaces of dimension $4$ and $6$ have been classified?
 Any reference is welcome!