Abstract
The Clifford group is a fundamental structure in quantum information with a wide variety of applications. We discuss the tensor representations of the q-qubit Clifford group, which is defined as the normalizer of the q-qubit Pauli group in U(2^q). In particular, we characterize all irreducible subrepresentations of the two-copy representation ϕ^⊗2 of the Clifford group on the matrix space C^d× d⊗ C^d× d with d=2^q. In an upcoming companion paper we applied this result to cut down the number of samples necessary to perform randomised benchmarking, a method for characterising quantum systems.