Groups of prime-power order with a small second derived quotient

For odd primes we prove some structure theorems for finite p-groups G, such that G″≠1 and G′/G″=p3. Building on results of Blackburn and Hall, it is shown that γ3(G) is a maximal subgroup of G′, the group G has a central decomposition into two simpler subgroups, and, moreover, G′ has one of two isomorphism types.