Thallium gallium sulphur selenite is a quaternary layered semiconductor compound. Single crystals of TlGaSSe were prepared using a modified Bridgman technique. The thermoelectric power of a TlGaSSe crystal was measured with the temperature gradient perpendicular to the cleavage plane. Our studies covered a wide range of temperatures. The sample under test was found to have p-type conductivity throughout the entire range of temperatures. Investigation into the values of the thermoelectric power, in conjunction with the previously obtained data, reveals the main physical parameters of this compound. The effective masses of holes and electrons were determined to be m(p)* = 8.82 x 10(-30) kg and m(n)* = 6.64 x 10(-36) kg, respectively. The charge carrier mobilities of the holes and electrons were found to be 1.502 x 10(4) cm(2)/Vs and 3.210 x 10(4) cm(2)/Vs, respectively. The diffusion coefficient, relaxation time and diffusion length for holes were calculated to be 385.92 cm(2)/s, 8.22 x 10(-14) s and 5.63 x 10(-6) cm, respectively. For electrons, these values, abbreviated D-n, tau(n), and L-n were calculated to be 8.25 cm(2)/s, 1.32 x 10(-19) s and 10 x 10(-7) cm, respectively. In addition to these pronounced parameters, the efficiency of the thermoelectric element (figure of merit) was calculated, which leads to better applications in many fields. (C) 2013 Elsevier B.V. All rights reserved.