Cohen-Lenstra heuristics at the bad primes

The goal of this project is to understand the statistical behaviour of p-Sylows of class groups of Galois number fields in cases where p divides the degree of the extension, and also the statistics of the Galois module structure of integral unit groups in Galois numberfields. The first case to look at could be, for example, 3-class groups and unit groups of S3-extensions.