  This article focuses on those aspects about partial actions of groups which
are related to Schur's theory on projective representations. It provides an
exhaustive description of the partial Schur multiplier, and this result is
achieved by introducing the concept of a second partial cohomology group
relative to an ideal, together with an appropriate analogue of a central
extension. In addition, the new framework is proved to be consistent with the
earlier notion of cohomology over partial modules.
