Magnetic topological semimetals have interesting anomalous behavior and can be manipulated by tuning the symmetry-protected nodal crossings. ${\mathrm{Co}}_{2}$-based full Heusler compounds serve as a fertile playground where various novel topological properties can be investigated. In this paper, we present a systematic investigation of the anomalous Hall effect (AHE) in the ferromagnetic Heusler compound ${\mathrm{Co}}_{2}\mathrm{CrGa}$ using combined experimental and theoretical studies. The anomalous Hall resistivity ${\ensuremath{\rho}}_{yx}^{A}$ is observed to scale nearly quadratically with the longitudinal resistivity ${\ensuremath{\rho}}_{xx}$, and further experimental analysis suggests that the AHE in ${\mathrm{Co}}_{2}\mathrm{CrGa}$ should be dominated by the intrinsic Karplus-Luttinger Berry phase mechanism. Experimental results also reveal that the anomalous Hall conductivity (AHC) is as large as $\ensuremath{\sim}569$ S/cm at 10 K with an intrinsic contribution of $\ensuremath{\sim}526$ S/cm and the observed AHC is nearly temperature independent. In addition to the large AHC, we also found an exceptionally large anomalous Hall angle of $\ensuremath{\sim}8.5$% and a large anomalous Hall factor of $\ensuremath{\sim}0.23 {\mathrm{V}}^{\ensuremath{-}1}$ simultaneously at room temperature. First-principles calculations suggest that the Berry curvature originates from a gapped nodal line and that Weyl nodes which are generated from the triple point near the Fermi level ${E}_{F}$ in the presence of spin-orbit coupling are responsible for the observed large AHC in this compound.