  The full symmetry groups for all single- and multi-wall carbon nanotubes are
found. As for the single-wall tubes, the symmetries form nonabelian
nonsymorphic line groups, enlarging the groups reported in literature. In the
multi-wall case, any type of the line and the axial point groups can be
obtained, depending on single-wall constituents and their relative position.
Several other consequences are discussed: quantum numbers and related selection
rules, electronic and phonon bands, and their degeneracy, application to tensor
properties.
