Representation zeta function of a family of maximal class groups: various exceptional cases

This paper continues Representation zeta function of a family of maximal class groups: non-exceptional primes [Citation7]. Using the explicit methods from the prequel, we compute exceptional cases of p-local representation zeta functions for finitely generated nilpotent groups Mn of maximal class. Specifically, we construct all irreducible representations of dimension pN for Mp+1 and dimension 2N for M4. Combined with previous results, this completes the classification of irreducible representations for M3 and M4 and their global representation zeta functions.