The eight inequivalent spinorial double covers of the full Lorentz group (L) are described explicitly. Two among them include the antilinear representations of space and time reflections on two-component spinors, discovered in 1976 by Staruszkiewicz. The group of all inequivalent central extensions of (L) by (Z₂) has 16 elements and contains an eight-element subgroup of `vectorial' double covers, characterized by the property of being trivial when restricted to the proper Lorentz group.

PACS numbers: 02.20.--a, 03.65.Fd, 04.20.Gz