  The $n$-qubit Pauli group and its normalizer the $n$-qubit Clifford group
have applications in quantum error correction and device characterization.
Recent applications have made use of the representation theory of the Clifford
group. We apply the tools of (the coincidentally named) Clifford theory to
examine the representation theory of the Clifford group using the much simpler
representation theory of the Pauli group. We find an unexpected correspondence
between irreducible characters of the $n$-qubit Clifford group and those of the
$(n+1)$-qubit Clifford group.
