  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.
