We present a systematic investigation of the gain properties of a gas electron multiplier (GEM) foil in pure dimethyl ether (DME) at low pressures. The GEM is made from copper- clad liquid crystal polymer insulator (LCP-GEM) designed for space use, a
nd is applied to a time projection chamber filled with low-pressure DME gas to observe the linear polarization of cosmic X-rays. We have measured gains of a 100 um-thick LCP-GEM as a function of the voltage between GEM electrodes at various gas pressures ranging from 10 to 190 Torr with 6.4 keV X-rays. The highest gain at 190 Torr is about 2x10^4, while that at 20 Torr is about 500. We find that the pressure and electric-field dependence of the GEM gain is described by the first Townsend coefficient. The energy scale from 4.5 to 8.0 keV is linear with non-linearity of less than 1.4% above 30 Torr.
