The group homology 
of a group 
with coefficients in a right 
-module 
is the left derived functor
of coinvariants. It may be computed by tensoring a projective resolution of the trivial
module with 
and taking homology.
Group Homology
See also
Derived Functor, Group, Homology Group, ModuleExplore with Wolfram|Alpha
References
Brown, K. S. Cohomology of Groups. New York: Springer-Verlag, 1982.Cite this as:
Weisstein, Eric W. "Group Homology." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/GroupHomology.html