My current understanding of the Little group is that it is the symmetry of a given state in the Fock space. This means that given a massive or massless particle in n dimensions, I can tell the number of degrees of freedom by looking at its little group. Or given the little group of a particle, I can classify it as a massive or massless particle.
Now, my question is: I don’t understand why the little group is necessary for any of the above. Anything I can do with the Little group, I can also do with the Poincaré group. So, why study the little group? Or is there some other way that it’s useful that I’m missing?