Groups with maximal central quotient

Abstract : A well known result of I. Schur asserts that the commutator subgroup of a group is finite whenever the central quotient is finite.Moreover the size of the central quotient is bounded in terms of the size of the commutator subgroup and size of the minimal generating set of the central quotient. In this talk I'll present a classification (upto isoclinism) of all groups whose central quotient is finite in size and attains the bound.