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Codes that are concatenations of group codes are considered. It is shown that when and are finite groups and the inner and outer codes are and codes, respectively, then under certain conditions the concatenated code is a code. A necessary and sufficient condition is given for a code 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 of and . 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.