  When an universal untruncated star cluster initial mass function (CIMF)
described by a power-law distribution is assumed, the mass of the most massive
star cluster in a galaxy (M_max) is the result of the size-of-sample (SoS)
effect. This implies a dependence of M_max on the total number of star clusters
(N). The SoS effect also implies that M_max within a cluster population
increases with equal logarithmic intervals of age. This is because the number
of clusters formed in logarithmic age intervals increases (assuming a constant
cluster formation rate). This effect has been observed in the SMC and LMC.
Based on the maximum pressure (P_int) inside molecular clouds, it has been
suggested that a physical maximum mass (M_max[phys]) should exist. The theory
predicts that M_max[phys] should be observable, i.e. lower than M_max that
follows from statistical arguments, in big galaxies with a high star formation
rate. We compare the SoS relations in the SMC and LMC with the ones in M51 and
model the integrated cluster luminosity function (CLF) for two cases: 1) M_max
is determined by the SoS effect and 2) M_max=M_max[phys]=constant. The observed
CLF of M51 and the comparison of the SoS relations with the SMC and LMC both
suggest that there exists a M_max[phys] of 5*10^5 M_sun in M51. The CLF of M51
looks very similar to the one observed in the ``Antennae'' galaxies. A direct
comparison with our model suggests that there M_max[phys]=2*10^6 M_sun.
