The class of (1,3)-groups with homocyclic regulator quotient of exponent p4 has bounded representation type

The class of almost completely decomposable groups with a critical typeset of type (1,3) and a homocyclic regulator quotient of exponent p4 is shown to be of bounded representation type. There are only nine near-isomorphism types of indecomposables, all of rank ⩽6.