The Information group Z_p is bad for non abelian group codes

We study non abelian time invariant group codes generated the extension of the additive group Zp = {0, 1, . . . , p − 1} by a finite group S, where p is a positive prime. When S is abelian the code has free distance limitations, and when S is non abelian we show that the code is non controllable. Therefore, the extension Zp by S is bad for non abelian group codes.