If a = {ava2, ..., 0, is a partition of n then Xa denotes the associated irreducible character of Sn, the symmetric group on {1,2,...,«}, and, if ceCSn, the group algebra generated by C and Sn, then dc() denotes the generalized matrix function associated with c. If cvc2eCSn then we write Cj = 1 and as = 2, and a.' denotes {a^otj, . . . ,a8_j, 1'} then ^a ^ (K ® {2))* where f denotes character induction from Sn_2 x S2 to 5n . This in turn implies that if a = {«1,a2,...,as,l } with s> 1, as = 2, and /? denotes {a1 + 2,a2, ...,as_,, 1'} then Xa =< ip which, in conjunction with other known results, provides many new inequalities among immanants. In particular it implies that the permanent function dominates all normalized immanants whose associated partitions are of rank 2, a result which has proved elusive for some years. We also consider the non-relationship problem for immanants that is the problem of identifying pairs, (a,ff) such that Xa = A« and kg ^ Aa are both false.