  The majority of graphs whose sandpile groups are known are either regular or
simple. We give an explicit formula for a family of non-regular multi-graphs
called thick cycles. A thick cycle graph is a cycle where multi-edges are
permitted. Its sandpile group is the direct sum of cyclic groups of orders
given by quotients of greatest common divisors of minors of its Laplacian
matrix. We show these greatest common divisors can be expressed in terms of
monomials in the graph's edge multiplicities.
