Anick complex, Hochschild cohomology, Hilbert and Poincare series of the Manturov (3,4)-group

The Manturov (3, 4)-group G(4)(3) is the group generated by four elements a, b, c, d with defining relations a(2) = b(2) = c(2) = d(2) = (abcd)(2) = (acdb)(2) = (adbc)(2) = 1. We apply the algebraic discrete Morse theory to calculate the Anick chain complex for G(4)(3), evaluate the Hochschild cohomology groups of the group algebra kG(4)(3) with coefficients in all 1-dimensional bimodules over a field k of characteristic zero, and derive its Hilbert and Poincare series.