Extraspecial groups, a subclass of p-groups, play an important role in the theory of this group family. They are also present in quantum information theory, in particular in quantum error correction, and in quantum computing in the context of the paradigmatic hidden subgroup problem. We give here an efficient algorithm for this problem in any extraspecial group. Our approach is quite different from the recent algorithms presented for the Heisenberg group, the extraspecial p- group of size p 3 and exponent p. Exploiting the automorphism structure of the groups we define specific group actions which are used to reduce the problem to hidden subgroup instances in abelian groups that can be dealtwith directly. This is joint work with Gbor Ivanyos and Luc Sanselme