Schur multiplicators of finite p-groups with fixed coclass

We investigate the Schur multiplicators M(G) of p-groups G using coclass theory. For p > 2 we show that there are at most finitely many p-groups G of coclass r with vertical bar M(G)vertical bar <= s for every r and s. We observe that this is not true for p = 2 by constructing infinite series of 2-groups G with coclass r and vertical bar M(G)vertical bar = 1. We investigate the Schur multiplicators of the 2-groups of coclass r further.