# Group cohomology of groups of prime-cube order

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This article gives specific information, namely, group cohomology, about a family of groups, namely: groups of prime-cube order.

View group cohomology of group families | View other specific information about groups of prime-cube order

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

## Second cohomology groups and extensions

### Schur multipliers and Schur covering groups

The Schur multiplier is defined as second cohomology group for trivial group action, , and also as the second homology group . A corresponding Schur covering group of is a group that arises as a stem extension with base normal subgroup the Schur multiplier and the quotient group is .