Extended molecular symmetry groups

The group theoretical analysis of Longuet-Higgins molecular symmetry groupsG(m, n) andGB(m) and their torsional extensionsG^q(m, n) andGB²(m) of molecules consisting of two coaxially rotated parts is presented. The structure of the groups is described in terms of direct and semi-direct products. The groupsG^q(m, n) andGB²(m) are shown to be group extensions of the groupsG(m,n) andGB(m), respectively. All irreducible representations of the groupsG(m,n),GB(m), andGB²(m) are derived using standard techniques of the extension or induction. A restriction method is proposed for derivation of irreducible representations of the groupG^q(m,n). The class structure of the groups is determined and the character tables are given in the most general case.