ON THE FINITE-DIMENSIONAL QUANTUM-GROUP M-3-CIRCLE-PLUS-(M-2 1(LAMBDA(2)))(0)/

We describe a few properties of the nonsemisimple associative algebra H = M-3 + (M-2/1(Lambda(2)))(0), where Lambda(2) is the Grassmann alge bra with two generators. We show that H is not only a finite-dimension al algebra but also a (noncommutative) Hopf algebra, hence a finite-di mensional quantum group. By selecting a system of explicit generators, we show how it is related with the quantum enveloping of SLq(2) when the parameter q is a cubic root of unity. We describe its indecomposab le projective representations as well as the irreducible ones. We also comment about the relation between this object and the theory of modu lar representation of the group St(2, F-3), i.e. the binary tetrahedra l group. Finally, we briefly discuss its relation with the Lorentz gro up and, as already suggested by A. Connes, make a few comments about t he possible use of this algebra in a modification of the Standard Mode l of particle physics (the unitary group of the semisimple algebra ass ociated with H is U(3) x U(2) x U(1)).