The third homotopy module of a 2-complex

Given a connected 2-complex X with fundamental group G, we show how pi_3(X) may be computed as a module over Z[G]. Further we show that if X is a finite connected 2-complex with G (the fundamental group) finite of odd order, then the stable class of pi_3(X) is determined by G.
Comment: Paper published in peer reviewed journal in 2008. arXiv admin note: text overlap with arXiv:2308.11844