As the basis for derivation of the $(P,l)$-symmetry groups and reduction of the theory of multiple antisymmetry to the theory of simple antisymmetry, a generalization of antisymmetric characteristic $(AC)$ is used. A catalogue of non-isomorphic $AC$ formed by $1\le l\le4$ generators is given. The algebraic properties of $AC$ are discussed and the direct product of $AC$ is defined.