Aluminum monochloride (AlCl) has been proposed as an excellent candidate for laser cooling. Here we present absorption spectroscopy measurements on the X1Σ+ ← A1Π transition in AlCl inside a cryogenic Helium buffer-gas beam cell. The high resolution absorption data enables a rigorous, quantitative comparison with our high-level ab initio calculations of the electronic and rovibronic energies, providing a comprehensive picture of the AlCl quantum structure. The combination of high resolution spectral data and theory permits the evaluation of spectroscopic constants and associated properties, like equilibrium bond length, with an order of magnitude higher precision. Based on the measured molecular equilibrium constants of the A1Π state, we estimate a Franck-Condon factor of the X1Σ+ ← A1Π of 99.88%, which confirms that AlCl is amenable to laser cooling.