Group cohomology of groups of prime-cube order

This article describes the group cohomology of groups of prime-cube order. The two cases $$p = 2$$ (see group cohomology of groups of order 8) and $$p = 3$$ (see group cohomology of groups of order 27) are somewhat special.

Schur multipliers and Schur covering groups
The Schur multiplier is defined as second cohomology group for trivial group action, $$H^2(G;\mathbb{C}^\ast)$$, and also as the second homology group $$H_2(G;\mathbb{Z})$$. A corresponding Schur covering group of $$G$$ is a group that arises as a stem extension with base normal subgroup the Schur multiplier and the quotient group is $$G$$.