All fundamental fermions fit inside one su(1|5) irreducible representation

The Lie superalgebra su(1|5) has irreducible representations of dimension 32, in which the 32 fundamental fermions of one generation (leptons and quarks, of left and right chirality, and their antiparticles) can be accommodated. The branching of these su(1|5) representations with respect to its subalgebra su(3)× su(2)×u(1) reproduces precisely the classification of these fundamental fermions according to the gauge group su(3) × su(2) × u(1) of the Standard Model. Furthermore, a simple construction of the relevant representations is given, and some consequences are discussed. PACS: 02.20.+b, 11.30.-j, 12.10.-g.