  There are different notions of homology and cohomology that can be defined
for a group with an action of another group by group automorphisms. In this
paper we address three natural questions that arise in this context. Namely,
the relation of these notions with the usual (co)homology of a semidirect
product, the interpretation of the first homology group as some kind of
abelianization and the classification of (invariant) group extensions.
