Solution
= Solution
For the trivial action, crossed homomorphisms $G\to\mathbb Q$ are ordinary <group homomorphisms>, while principal crossed homomorphisms vanish. The image of a finite group in the torsion-free additive group $\mathbb Q$ must be trivial, so
$$
\boxed{H^1(G,\mathbb Q)=0}.
$$
Degree-zero cohomology is the <invariant submodule>; the action is trivial, so
$$
\boxed{H^0(G,\mathbb Q)=\mathbb Q}.
$$