One of the recent generalizations of classical symmetry is Wp-symmetry [1]. In a family with the same generating group G there are 8 different types groups of Wp-symmetry: the generating group, one major group and usually several middle, semi-major, semi-middle, semi-minor, pseudo-middle and pseudo-minor groups. Any group of Wp-symmetry is a subgroup of the major group of the same family. Any major group of Wp-symmetry with the finite groups G and P is constructed as a left standard direct wreath product of G with initial group P, accompanied by the fixed isomorphism  formula  Any group G(Wp) of Wp-symmetry with the finite group W can be derived from its finite generating group G and the group W = Q gi2G Pgi of multicomponent permutations by making the following steps:formula1) we find in W all subgroups V and subsets W0, which can be decomposed into left cosets of V , and in G we find all the subgroups H of index equal to the power of the set of all left cosets of W0 of V and for which there is an isomorphism ¸, which apply the quotient group G1=H into W1=V1 by the rule ¸(Hg) = wV , where G1 · G, W1 · DiagW and V1 = V \ DiagW · W1; 2) we construct a generalized exact natural left quasi-homomorphism ~¹ of the group G onto the set of all left cosets of W0 with respect to V by the rule ~¹(Hg) = wV and which preserves the correspondence between the elements of quotient groups G1=H and W1=V1 received as a result of isomorphism ¸; 3) we combine pairwise each g0 of Hg with each w0 of wV = ~¹(g0); 4) we introduce on the set of all these pairs the rule of the compositionformulaIf V = w0, where w0 is the unit of the group W, then the mapping ~¹ is an ordinary exact natural left quasi-homomorphism. In this case, the universal deduction method of the groups ofWp-symmetry becomes more simple and takes the form of the deduction method of semi-minor groups (w0 < W0 < W) or of the pseudo-minor groups, respectively, depending on W0, where w0 ½ W0 ½ W, but W0 is not a subgroup of W (see [2,3]).