We present first principle calculations of the structural, electronic, magnetic, vibrational and elastic properties of the k-Fe3AlC perovskite, within the ab initio formalisms of the Density Functional Theory (DFT) and the linear response theory of the DFT. These properties are compared with those of the intermetallic Fe3Al-L12 isostructural phase of k, permitting to interpret the role of the carbon element. We also discuss the influence of the spin effects (GGA and SGGA approaches) on the vibrational properties of some FeeAl intermetallics.