  To apply lattice QCD in the calculation of glueball spectrum it is needed
firstly to know associated operators acting on vacuum. We show how to find all
the independent representations and operators, of group $SO(3)^{PC}$ at
different dimension, since the work is not trivial. Then, we decompose these
representation into irreducible representation of $O^{PC}$ group, which are
listed in the note. At last we argue that $f_J(2220)$ and $g_T$ states can not
be tensor glueball simultaneously.
