  We extend our previous work [J. Chem. Phys, \textbf{136}, 124121], which
described a spin-adapted (SU(2) symmetry) density matrix renormalization group
(DMRG) algorithm, to additionally utilize general non-Abelian point group
symmetries. A key strength of the present formulation is that the requisite
tensor operators are not hard-coded for each symmetry group, but are instead
generated on the fly using the appropriate Clebsch-Gordan coefficients. This
allows our single implementation to easily enable (or disable) any non-Abelian
point group symmetry (including SU(2) spin symmetry). We use our implementation
to compute the ground state potential energy curve of the C$_2$ dimer in the
cc-pVQZ basis set (with a frozen-core), corresponding to a Hilbert space
dimension of 10$^{12}$ many-body states. While our calculated energy lies
within the 0.3 mE$_h$ error bound of previous initiator full configuration
interaction quantum Monte Carlo (i-FCIQMC) and correlation energy extrapolation
by intrinsic scaling (CEEIS) calculations, our estimated residual error is only
0.01 mE$_h$, much more accurate than these previous estimates. Further, due to
the additional efficiency afforded by the algorithm, we compute the potential
energy curves of twelve states: the three lowest levels for each of the
irreducible representations $^1\Sigma^+_g$, $^1\Sigma^+_u$, $^1\Sigma^-_g$ and
$^1\Sigma^-_u$, to an estimated accuracy within 0.1 mE$_h$ of the exact result
in this basis.
