  We show that the Clifford group - the normaliser of the Weyl-Heisenberg group
- can be represented by monomial phase-permutation matrices if and only if the
dimension is a square number. This simplifies expressions for SIC vectors, and
has other applications to SICs and to Mutually Unbiased Bases. Exact solutions
for SICs in dimension 16 are presented for the first time.
