Homology of dihedral groups of even degree I'm looking for a reference or an idea about how to calculate the homology groups of dihedral groups $D_{2n}$ with integer coefficients or any abelian group when the degree $n$ is even. Here https://groupprops.subwiki.org/wiki/Group_cohomology_of_dihedral_groups is the result that I need but there is no reference nor idea of how to calculate the homology groups.
In the case when $n$  is odd I have made the computations via spectral sequences and the fact that $n$ is odd helps to have $E^2=E^\infty$ what doesn't happen when $n$ is even.
 A: There is a nice explicit free resolution of $D_{2n}$ constructed by Suguru Hamada and C. T. C. Wall in the early 1960's.  See the following paper for a simplified description of the Hamada-Wall resolution:
Handel, David. "On products in the cohomology of the dihedral groups." Tohoku Mathematical Journal, Second Series 45, no. 1 (1993): 13-42.
Handel uses this free resolution to compute the integral cohomology of $D_{2m}$ (Theorems 5.2 and 5.3 of his paper).  See this answer for a summary of Handel's result. Once we know the cohomology we can compute the homology using the universal coefficient theorem.
For the record, when $m\geq 3$ is odd and $n\geq 1$, the integral homology of $D_{2m}$ is
$$
H_n(D_{2m};\mathbb{Z}) \;=\; \begin{cases}
0 & \text{if }n\text{ is even,} \\
\mathbb{Z}/2 & \text{if }n\equiv 1\pmod 4, \\
\mathbb{Z}/2m & \text{if }n\equiv 3\pmod 4.
\end{cases}
$$
When $m\geq 2$ is even and $n\geq 1$, the integral homology of $D_{2m}$ is
$$
H_n(D_{2m};\mathbb{Z}) \;=\; \begin{cases}
(\mathbb{Z}/2)^{n/2} & \text{if }n\text{ is even}, \\
(\mathbb{Z}/2)^{(n+3)/2} & \text{if }n\equiv 1\pmod 4, \\
(\mathbb{Z}/2)^{(n+1)/2} \oplus (\mathbb{Z}/m) & \text{if }n\equiv 3\pmod 4.
\end{cases}
$$
(Of course $H_0(D_{2m};\mathbb{Z})\cong\mathbb{Z}$ in both cases.)
Note that we can now compute the homology with respect to any abelian group by using the universal coefficient theorem again.
