On extraspecial left conjugacy closed loops

A loop Q is said to be left conjugacy closed (LCC) if is a left translation for all x,y Q. We describe all LCC loops Q such that Q/Z is an elementary abelian p-group, where Z Q is a central subloop of order p. We single out those that are right conjugacy closed as well, and show their connection to trilinear mappings and quadratic forms. Isomorphism classes are determined for the case Z=Z(Q), i.e. for the extraspecial loops.