I have a problem in which it would be helpful to know about the integral representations of some groups of small order (probably of fairly low degree). From what I've gathered so far, cyclic groups of order p and order p^2 are understood, as are some special dihedral groups. But, often, Krull-Schmidt does not hold making a full classification difficult. Does anyone know of any papers where explicit examples are calculated? I can only find MCR Butler's example of the Klein group. I'd be happy to know about some cyclic cases that are not of order p or p^2.