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The space-time symmetry group of a model of a relativistic spin 1/2elementary particle, which satisfies Dirac's equation when quantized, isanalyzed. It is shown that this group, larger than the Poincare group, alsocontains space-time dilations and local rotations. It has two Casimiroperators, one is the spin and the other is the spin projection on the bodyframe. Its similarities with the standard model are discussed. If we considerthis last spin observable as describing isospin, then, this Dirac particlerepresents a massive system of spin 1/2 and isospin 1/2. There are two possibleirreducible representations of this kind of particles, a colourless or acoloured one, where the colour observable is also another spin contributionrelated to the zitterbewegung. It is the spin, with its twofold structure, theonly intrinsic property of this Dirac elementary particle.Comment: Contribution to the JINR(Dubna) SPIN05 workshop, 18 pages, 1 figure.  Abstract and minor changes of sections 2 to

The spacetime symmetry group of a spin 1/2 elementary particle