  We study the internal radial gradients of the stellar populations in a sample
comprising 522 early-type galaxies (ETGs) from the SAMI (Sydney- AAO
Multi-object Integral field spectrograph) Galaxy Survey. We stack the spectra
of individual spaxels in radial bins, and derive basic stellar population
properties: total metallicity ([Z/H]), [Mg/Fe], [C/Fe] and age. The radial
gradient ($\nabla$) and central value of the fits (evaluated at R$_e$/4) are
compared against a set of six possible drivers of the trends. We find that
velocity dispersion ($\sigma$) - or, equivalently gravitational potential - is
the dominant driver of the chemical composition gradients. Surface mass density
is also correlated with the trends, especially with stellar age. The decrease
of $\nabla$[Mg/Fe] with increasing $\sigma$ is contrasted by a rather shallow
dependence of $\nabla$[Z/H] with $\sigma$ (although this radial gradient is
overall rather steep). This result, along with a shallow age slope at the
massive end, imposes stringent constraints on the progenitors of the
populations that contribute to the formation of the outer envelopes of ETGs.
The SAMI sample is split between a 'field' sample and a cluster sample. Only
weak environment-related differences are found, most notably a stronger
dependence of central total metallicity ([Z/H]$_{e4}$) with $\sigma$, along
with a marginal trend of $\nabla$[Z/H] to steepen in cluster galaxies, a result
that is not followed by [Mg/Fe]. The results presented here serve as
constraints on numerical models of the formation and evolution of ETGs.
