The Hochschild cohomology of the group G²₃

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.