  The orbits space of an irreducible linear representation of a finite group is
a variety whose coordinate ring is the ring of invariant polynomials. Boris
Dubrovin proved that the orbits space of the standard reflection representation
of an irreducible finite Coxeter group $\mathcal W$ acquires a natural
polynomial Frobenius manifold structure. We apply Dubrovin's method on various
orbits spaces of linear representations of finite groups. We find some of them
has non or several natural Frobenius manifold structures. On the other hand,
these Frobenius manifold structures include rational and trivial structures
which are not known to be related to the invariant theory of finite groups.
