  Eick & Leedham-Green sketched a construction for infinite sequences of finite
$p$-groups with fixed coclass. These infinite sequences have turned out to be
very useful in the theory of finite $p$-groups. We exhibit a detailed
description for the construction of the finite sequences and we determine
presentations for the infinite sequences for the primes and coclasses $(2,1)$,
$(2,2)$ and $(3,1)$.
