A single-wall carbon nanotube can be imagined as a rolled up graphene along the chiral vector. Those symmetry operations that preserved when the graphene sheet is rolled into a cylinder form the nanotube symmetry group. We study a mathematical model and using this model we compute the symmetry groups of nanotubes. The set is the mathematical model for the nanotube with chiral vector c . Transformations which and are symmetry transformations for all translation vector w . , we can give the irreducible representations of the symmetry groups of nanotubes.