  We describe a few properties of the non semi-simple associative algebra H =
M_3 + (M_{2|1}(Lambda2))_0, where Lambda2 is the Grassmann algebra with two
generators. We show that H is not only a finite dimensional algebra but also a
(non co-commutative) Hopf algebra, hence a finite dimensional quantum group. By
selecting a system of explicit generators, we show how it is related with the
quantum enveloping algebra of SLq(2) when the parameter q is a cubic root of
unity. We describe its indecomposable projective representations as well as the
irreducible ones. We also comment about the relation between this object and
the theory of modular representations of the group SL(2,F3), i.e. the binary
tetrahedral group. Finally, we briefly discuss its relation with the Lorentz
group and, as already suggested by A.Connes, make a few comments about the
possible use of this algebra in a modification of the Standard Model of
particle physics (the unitary group of the semi-simple algebra associated with
H is U(3) x U(2) x U(1)).
