The Hochschild cohomology of the group \(G^2_3\)

We apply discrete algebraic Morse theory to calculate the Anick resolution of the group algebra of the group \(G_3^2\). As a corollary, we evaluate Hochschild cohomologies of \(G_3^2\) with coefficients in all 1-dimensional bimodules. Almost all these groups are trivial, the only exceptions are 1-dimensional \(H^2\) for two particular 1-dimensional bimodules.