Let @ be the automorphism group of a finitely generated free group F of rank n. The action of @ on the quotient of F by its commutator subgroup gives a homomorphism p from @ onto G&(Z), whose kernel we denote by K. For n = 2, this representation gives much information since Nielsen [6] proved that K is the subgroup of inner automorphisms. For n > 3, however, K is much larger and its structure unknown, so that this representation alone is no longer satisfactory. We therefore attempt to find integral representations of @ whose kernels are smaller than K. In Section 2 we consider integral representations, pc , constructed from the action of Cp on C/C’, where C is a characteristic subgroup of finite index in F. w e prove that such representations “exhaust” @, in the sense that nc kernel (pc) = 1. In fact, we construct in this way an infinite sequence of representations pi , with kernels Ki , such that K = K,, 2 Kl 3 ... r) Ki 3 K.i+l 3 ..., and ni Ki = 1. Each pi contains piPI as a constituent and this leads to a faithful representation of @ in terms of infinite matrices. Since the degrees of the representations pi become quite large, one would like to know their irreducible constituents. This is a difficult problem to solve in general. In Section 3, we limit ourselves to the free group of rank 3 and obtain the reduction for pr . We prove that when pa = p is “split off” from p1 , the remaining constituent is irreducible. This provides an example of an irreducible representation of @ which doesn’t factor through p. Irreducibility is established by a highly computational method. The representation in question is first viewed as a representation of a finite subgroup G of @, G being generated by three of the four known generators for @. Using our knowledge ‘of the irreducible representations of G, we find all proper Ginvariant submodules of our representation space and prove that none of