We consider the construction of group block codes, i.e., subgroups of Gn, the n-fold direct product of a group G. Two concepts are introduced that make this construction similar to that of codes over gf(2). The first concept is that of an indecomposable code. The second is that of a parity-check matrix. As a result, group block codes over a decomposable Abelian group of exponent dm can be seen as block codes over the ring of residues modulo dm, and their minimum Hamming distance can be easily determined. We also prove that, under certain technical conditions, (n, k) systematic group block codes over non-Abelian groups are asymptotically bad, in the sense that their minimum Hamming distance cannot exceed [n/k].