- I tried to find a reference for the computation of the Schur multiplier of groups of order $p^4$. The case in which $p=2$ is well known, see e.g. Table 1 at http://pages.bangor.ac.uk/~mas010/pdffiles/non-abel-tensor.pdf. However, I didn't find any reference for the odd case. Since there is a well known (not too big) classification of such groups, it seems reasonable that this work was already done. Is there a paper or a book in which I can find such computation?
- I am particularly interested in special elements of the Schur multiplier. These elements of $M(G)$ correspond to projective representation of $G$ of dimension $\sqrt{|G|}$. Groups admitting such elements are called of central type (non-classical). Is there a known classification of groups of central type of order $p^4$?

Thanks in advance.