The group-theoretical classification of trion states (charged excitons X ± ) is presented. It is based on considerations of products of irreducible projective representations of the 2D translation group. For a given BvK period N degeneracy of obtained states is N 2 . Trions X ± consist of two identical particles (holes or electrons), so the symmetrization of states with respect to particles transposition is considered. There are N (N + 1)/2 symmetric and N (N − 1) antisymmetric states. Completely antisymmetric states can be constructed by introducing antisymmetric and symmetric spin functions, respectively. Two symmetry adapted bases are considered: the first is obtained from a direct conjugation of three representations, whereas in the second approach the states of a electrically neutral pair hole-electron are determined in the first step. The third possibility, a conjugation of representations corresponding to identical particles in the first step, is postponed for the further investigations.