  A class of infinite dimensional Galilean conformal algebra in (2+1)
dimensional spacetime is studied. Each member of the class, denoted by
\alg_{\ell}, is labelled by the parameter \ell. The parameter \ell takes a spin
value, i.e., 1/2, 1, 3/2, .... We give a classification of all possible central
extensions of \alg_{\ell}. Then we consider the highest weight Verma modules
over \alg_{\ell} with the central extensions. For integer \ell we give an
explicit formula of Kac determinant. It results immediately that the Verma
modules are irreducible for nonvanishing highest weights. It is also shown that
the Verma modules are reducible for vanishing highest weights. For half-integer
\ell it is shown that all the Verma module is reducible. These results are
independent of the central charges.
