# Integral representations of groups of small order

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.

Thanks!

• Try Curtis and Reiner's book, around 1981-1 – Geoff Robinson Jun 4 '14 at 14:56

As Geoff indicates, Methods of Representation Theory I by Curtis-Reiner has an extensive treatment of integral representations toward the end. In §34 there is a detailed discussion of examples, with the cautionary remark that a complete classification is essentially impossible for cyclic $p$-groups of higher order than $p^2$ due to infinite representation type.