A group of mathematical objects that is homomorphic to (i.e. has the same mathematical structure as) the original group. In particular, group representations made up of square matrices are of interest. The dimension of the representation is the number of rows or group representation columns of the matrix. The irreducible representations of a group, i.e. the representations that cannot be expressed in terms of lower-dimensional representations, are of great importance in quantum mechanics since the energy levels of a quantum mechanical system are labelled by the irreducible representations of the symmetry group of the system. This enables selection rules for the system to be derived.