  In this paper, we construct a seven-term exact sequence involving the
cohomology groups of a group extension. Although the existence of such a
sequence can be derived using spectral sequence arguments, there is little
knowledge about some of the maps occuring in the sequence, limiting its
usefulness. Here we present a construction using only very elementary tools,
always related to the notion of conjugation in a group. This results in a
complete and usable description of all the maps, which we describe both on
cocycle level as on the level of the interpretations of low dimensional
cohomology groups (e.g. group extensions).
