Group cohomology of semidihedral groups

We describe here the homology and cohomology groups of the semidihedral group of order $$2^n$$, which is obtained as the external semidirect product of a cyclic group of order $$2^{n-1}$$ and cyclic group:Z2 where the non-identity element acts via multiplication by $$2^{n-2} - 1$$.

Over the integers
The homology groups with coefficients in the ring of integers are given as follows:

$$H_q(SD_{2^n};\mathbb{Z}) = \left \lbrace \begin{array}{rl} \mathbb{Z}, & q = 0 \\ (\mathbb{Z}/2\mathbb{Z})^{(q + 7)/4}, & q \equiv 1 \pmod 4 \\ (\mathbb{Z}/2\mathbb{Z})^{(q - 2)/4}, & q \equiv 2 \pmod 4 \\ \mathbb{Z}/2^{n-1}\mathbb{Z} \oplus (\mathbb{Z}/2\mathbb{Z})^{(q + 1)/4}, & q \equiv 3 \pmod 4 \\ (\mathbb{Z}/2\mathbb{Z})^{q/4}, & q \equiv 0 \pmod 4, q > 0 \\\end{array}\right.$$