  We present a new class of extended affine Weyl groups
$\widetilde{W}^{(k,k+1)}(A_l)$ for $1\leq k <l$ and obtain an analogue of
Chevalley-type theorem for their invariants. We further show the existence of
Frobenius manifold structures on the orbit spaces of
$\widetilde{W}^{(k,k+1)}(A_l)$ and also construct Landau--Ginzburg
superpotentials for these Frobenius manifold structures.
