Computation of modular cohomology rings of finite groups

The p_group_cohomology package for SageMath is able to compute the mod-2 cohomology rings of all groups of order 128
and the mod-p cohomology of the Third Conway group and some other sporadic groups. We will explain the underlying
algorithm (non-commutative F5 algorithm for modules over path algebras) and demonstrate its usage.

This program led to the classification of the cohomology rings of all p-groups of order up to 81 (order 64
being the most interesting) in terms of graded ring isomorphisms.