The two-dimensional material MXene has recently attracted interest for its excellent performance in diverse perspectives. Etched from the parental MAX phase with hydrofluoric acid, the synthesized MXene surface is normally functionalized by oxygen (-O), fluorine (-F) or hydroxyl (-OH) groups. Herein, using first-principles density functional calculations, we investigate the structural, mechanical and electronic properties of the carbide MXene M2CT2 (M=Sc, Ti, V, Cr, Zr, Nb, Mo, Hf, Ta, W; T=-O, -F, -OH). Both the M atom and the surface group T have a significant effect on the MXenes properties. Generally, oxygen functionalized MXenes present smaller lattice parameters and stronger mechanical strength compared to those functionalized by fluorine and hydroxyl groups. exhibits the smallest interlayer thickness and shows the strongest mechanical strength. In regard to electronic properties, five oxygen functionalized members M2CO2 (M=Sc, Ti, Zr, Hf, W), two fluorine functionalized members M2CF2 (M=Sc, Mo), and hydroxyl functionalized Sc2C(OH)2 present semiconducting characteristics, but only Sc2C(OH)2 exhibits a direct band gap.