Let \(k\) be a field of finite characteristic and \(G\) a finite group. The purpose of the paper is to study the cohomology ring \(H^*(G,k)\) via certain spectral sequences determined by what is called systems of homogeneous parameters for \(H^*(G,k)\). This notion arises from abstracting certain formal properties of a free \(G\)-action on a product of spheres. The idea of using it to define filtrations on projective resolutions was developed in earlier work of the authors. The paper revolves around the investigation of a certain finite complex of projective \(G\)-modules associated to a system of parameters. This complex is equivalent to a Poincaré duality complex and gives rise to a hypercohomology spectral sequence which passes information from the finite complex to minimal resolutions and cohomology. Some of its differentials are described as multiplications by the parameters and metric Massey products. When the cohomology is Cohen-Macaulay its Poincaré series satisfies a certain functional equation, and a result, too technical to be reproduced here, entails that the minimal projective resolution for the trivial module can be constructed by splicing together copies of the finite complex. In general the cohomology is not Cohen- Macaulay, and another result says that at least some part of the finite complex is visible in the cohomology of the group. It is also shown that the structure of the complex implies the existence of certain large degree cohomology classes which are not in the ideal generated by the parameters.