On the classification of groups of prime-power order

This talk gives a survey on the state of the art in the classification of the finite groups of prime-power order. Given a prime p and a natural number n, one can consider the function f(p,n) of groups of order p^n (up to isomorphism). The function f(p,n) can be considered as a function in p or as a function in n and then has different interesting asymptotic properties. However, using the order is not the only way to approach the classification of groups of prime-power order. An alternative approach is to classify the groups of prime-power order using their coclass as primary invariant. The talk will explain this in more detail and also exhibit some of the results of this approach.