On conjugacy classes in groups

Let G be a group. Write G^⁎=G﹨{1}. An element x of G^⁎ will be called deficient if 〈x〉<C_G(x) and it will be called non-deficient if 〈x〉=C_G(x). If x∈G is deficient (non-deficient), then the conjugacy class xG of x in G will be also called deficient (non-deficient). Let j be a non-negative integer. We shall say that the group G has defect j, denoted by G∈D(j) or by the phrase “G is a D(j)-group”, if exactly j non-trivial conjugacy classes of G are deficient.