  This paper provides some properties of Brauer symmetry classes of tensors. We
derive a dimension formula for the orbital subspaces in the Brauer symmetry
classes of tensors corresponding to the irreducible Brauer characters of the
groups having cyclic groups support on non-linear Brauer characters. Using the
derived formula, we investigate the necessary and sufficient condition for the
existence of the o-basis of Dicyclic groups, Semi-dihedral groups and also
reinvestigate those things on Dihedral groups. Some criteria for the
non-vanishing elements in the Brauer symmetry classes of tensors associated to
those groups are also included.
