  Landau-Ginzburg mirror symmetry studies isomorphisms between graded Frobenius
algebras, known as A- and B-models. Fundamental to constructing these models is
the computation of the finite, Abelian $\textit{maximal symmetry group}$
$G_{W}^{\max}$ of a given polynomial $W$. For $\textit{invertible}$
polynomials, which have the same number of monomials as variables, a generating
set for this group can be computed efficiently by inverting the
$\textit{polynomial exponent matrix}$. However, this method does not work for
$\textit{noninvertible}$ polynomials with more monomials than variables since
the resulting exponent matrix is no longer square.
  A previously conjectured algorithm to address this problem relies on
intersecting groups generated from $\textit{submatrices}$ of the exponent
matrix. We prove that this method is correct, but intractable in general. We
overcome intractability by presenting a group isomorphism based on the Smith
normal form of the exponent matrix. We demonstrate an algorithm to compute
$G_{W}^{\max}$ via this isomorphism, and show its efficiency in all cases.
