  Mayall II = G1 is one of the most luminous globular clusters (GCs) in M31.
Here, we determine its age and mass by comparing multicolor photometry with
theoretical stellar population synthesis models. Based on far- and
near-ultraviolet GALEX photometry, broad-band UBVRI, and infrared JHK_s 2MASS
data, we construct the most extensive spectral energy distribution of G1 to
date, spanning the wavelength range from 1538 to 20,000 A. A quantitative
comparison with a variety of simple stellar population (SSP) models yields a
mean age that is consistent with G1 being among the oldest building blocks of
M31 and having formed within ~1.7 Gyr after the Big Bang. Irrespective of the
SSP model or stellar initial mass function adopted, the resulting mass
estimates (of order $10^7 M_\odot$) indicate that G1 is one of the most massive
GCs in the Local Group. However, we speculate that the cluster's exceptionally
high mass suggests that it may not be a genuine GC. We also derive that G1 may
contain, on average, $(1.65\pm0.63)\times10^2 L_\odot$ far-ultraviolet-bright,
hot, extreme horizontal-branch stars, depending on the SSP model adopted. On a
generic level, we demonstrate that extensive multi-passband photometry coupled
with SSP analysis enables one to obtain age estimates for old SSPs to a similar
accuracy as from integrated spectroscopy or resolved stellar photometry,
provided that some of the free parameters can be constrained independently.
