Codes that are concatenations of group codes are considered. It is shown that whenGandHare finite groups and the inner and outer codes areG-andH-codes, respectively, then under certain conditions the concatenated code is aG times Hcode. A necessary and sufficient condition is given for aG times Hcode to have a structure as a concatenated code. Further, under the assumption that all group algebras involved are semisimple, it is shown how the character of a concatenated code can be expressed in terms of the characters of the inner and outer codes. This leads to an application of a result by Ward  which enables one to find (or lower bound) the exponent of the concatenated code by a computation on characters ofGandH. In an example this result enables the improvement of the usual minimum distance bound on concatenated codes. A general upper bound on the exponent of concatenated group codes is proved, and it is shown to be tight by an example.