Based on a presentation of Cnβ and the help of [GAP], we
construct the character table of the Clifford group Cnβ for
n=1,2,3. As an application, we can efficiently decompose the (higher power
of) tensor product of the matrix representation in those cases. Our results
recover some known results in [HWW, WF] and reveal some new phenomena. We prove
that the trivial character is the only linear character for Cnβ and
hence Cnβ equals to its commutator subgroup when nβ₯3. A few
conjectures about Cnβ for general n are proposed.Comment: 13 pages; comments and suggestions are welcom