  An extension of the Poincar\'e group with half-integer spin generators is
explicitly constructed. We start discussing the case of three spacetime
dimensions, and as an application, it is shown that hypergravity can be
formulated so as to incorporate this structure as its local gauge symmetry.
Since the algebra admits a nontrivial Casimir operator, the theory can be
described in terms of gauge fields associated to the extension of the
Poincar\'e group with a Chern-Simons action. The algebra is also shown to admit
an infinite-dimensional non-linear extension, that in the case of fermionic
spin-$3/2$ generators, corresponds to a subset of a contraction of two copies
of WB$_2$. Finally, we show how the Poincar\'e group can be extended with
half-integer spin generators for $d\geq3$ dimensions.
