On the finite spaces of irreduciblecharacters of finite groups

Let [Formula: see text] be a nontrivial finite group and denote by [Formula: see text] the set of all pairs [Formula: see text] with nontrivial subgroups [Formula: see text] and the irreducible complex character [Formula: see text] of [Formula: see text]. We say that [Formula: see text] in [Formula: see text] if [Formula: see text] and [Formula: see text] is a constituent of [Formula: see text]. The connectivity of the poset [Formula: see text] is studied in this paper. In fact, we prove that [Formula: see text] is disconnected if and only if [Formula: see text] is a cyclic group of prime power order or a quaternion group.