  Aluminum monochloride (AlCl) has been proposed as an excellent candidate for
laser cooling. Here we present absorption spectroscopy measurements on the
$A^1\Pi \leftarrow X^1\Sigma^+$ 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
$A^1\Pi$ state, we estimate a Franck-Condon factor of the $A^1\Pi \leftarrow
X^1\Sigma^+$ of 99.88%, which confirms that AlCl is amenable to laser cooling.
