  We introduce a notion of c-group, which is a group up to congruence relation
and consider the corresponding category. Extensions, actions and crossed
modules (c-crossed modules) are defined in this category and the semi-direct
product is constructed. We prove that each categorical group gives rise to
c-groups and to a c-crossed module, which is a connected, special and strict
c-crossed module in the sense defined by us. The results obtained here will be
applied in the proof of an equivalence of the categories of categorical groups
and connected, special and strict c-crossed modules.
