Magnetic groups include antilinear operators as well as linear operators. They need to be dealt with using Wigner's theory of corepresentations of unitary and antiunitary groups. A significant departure from standard representation theory is that the multiplicity of the irreducible corepresentation j 3 ∗ ∗ in the direct product of the irreducible corepresentations j 1 ⊗ ⊗ j 2 is generally smaller than the multiplicity of the trivial corepresentation in the triple product j 1 ⊗ ⊗ j 2 ⊗ ⊗ j 3 , leading to significant differences between the Clebsch-Gordon coefficients and the 3 j symbol.