Lattice and complex extensions of point groups. I

Abstract

The formulae enabling in a simple way to determine the explicit form of factors of non-equivalent extensions of the point groups by lattice groups and multiplicative group of complex numbers are derived. It is shown that the number of all non-equivalent extensions of the groups C 2 h , D 2 h , D 4 h by lattice groups Γ m , Γ o , Γ q is equal 88, an and the explicit form of the factors of these extensions is determined. Also the explicit form of the factors of all non-equivalent extensions of the groups C nh , D n , D nh by the multiplicative group of complex numbers is derived.