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The structural, electronic as well as the magnetic properties of the Co2CrX (XAl, Ga and In) full-Heusler alloy have been studied using first-principles calculations performed in the framework of density functional theory (DFT) within the generalized gradient approximation (GGA). It was taken into account both possible L21 structures (i.e. Hg2CuTi- and Cu2MnAl-type). Basically, for all compounds, the Cu2MnAl-type structure is energetically more stable than Hg2CuTi-type structure at the equilibrium volume. The electronic structure calculations for Co2CrAl reveal that half-metallic (HM) character in Cu2MnAl-type structure, Co2CrGa show nearly HM behavior and Co2CrIn has a metallic character. The predicted total magnetic moment is for Co2CrX (XAl, Ga) which is in good convergence with the Slater-Pauling (SP) rule. [ABSTRACT FROM AUTHOR]