  Dowling and Rhodes defined different lattices on the set of triples (Subset,
Partition, Cross Section) over a fixed finite group G. Although the Rhodes
lattice is not a geometric lattice, it defines a matroid in the sense of the
theory of Boolean representable simplicial complexes. This turns out to be the
direct sum of a complete matroid with a lift matroid of the complete biased
graph over G. As is well known, the Dowling lattice defines the frame matroid
over a similar biased graph. This gives a new perspective on both matroids and
also an application of matroid theory to the theory of finite semigroups. We
also make progress on an important question for these classical matroids: what
are the minimal Boolean representations and the minimum degree of a Boolean
matrix representation?
