The groups of alternating colored permutations are the natural analogue of the alternating groups inside the wreath products \(\mathbb{Z}_{r}\wr S_{n}\). We present a ’Coxeter-like’ presentation for these groups and calculate the length function with respect to this presentation. Then we present these groups as coverings of \(\mathbb{Z}_{\frac{r}{2}}\wr S_{n}\) and use this point of view to give another expression for the length function. We also use this covering to lift known parameters of \(\mathbb{Z}_{\frac{r}{2}}\wr S_{n}\) to the group of alternating colored permutations.