Context. Photometric variability is an essential feature that sheds light on the intrinsic properties of celestial variable sources, the more so when photometry is available in various bands. In this respect, the all-sky Gaia mission is particularly attractive as it collects, among other quantities, epoch photometry measured quasi-simultaneously in three optical bands for sources ranging from a few magnitudes to fainter than magnitude 20. Aims. The second data release (DR2) of the mission provides mean G, G_BP, and G_RP photometry for ∼1.4 billion sources, but light curves and variability properties are available for only ∼0.5 million of them. Here, we provide a census of large-amplitude variables (LAVs) with amplitudes larger than ∼0.2 mag in the G band for objects with mean brightnesses between 5.5 and 19 mag. Methods. To achieve this, we rely on variability amplitude proxies in G, G_BP, and G_RP computed from the uncertainties on the magnitudes published in DR2. We then apply successive filters to identify two subsets containing sources with reliable mean G_BP and G_RP (for studies using colours) and sources having compatible amplitude proxies in G, G_BP, and G_RP (for multi-band variability studies). Results. The full catalogue gathers 23 315 874 LAV candidates, and the two subsets with increased levels of purity contain, respectively, 1 148 861 and 618 966 sources. A multi-band variability analysis of the catalogue shows that different types of variable stars can be categorized according to their colours and blue-to-red amplitude ratios as determined from the G, G_BP, and G_RP amplitude proxies. More specifically, four groups are globally identified. They include: long-period variables in a first group with amplitudes more than twice larger in the blue than in the red; hot compact variables in a second group with amplitudes smaller in the blue than in the red; classical instability strip pulsators in a third group with amplitudes larger in the blue than in the red by 50% to 80%; and other non-pulsating variables in a fourth group, mainly achromatic, but 10% of them still having 20% to 50% larger amplitudes in the blue than in the red. Conclusions. The catalogue constitutes the first census of Gaia LAV candidates extracted from the public DR2 archive. The overview presented here illustrates the added value of the mission for multi-band variability studies, even at this stage when epoch photometry is not yet available for all sources.