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The central 0.1 parsecs of the Milky Way host a supermassive black hole identified with the position of the radio and infrared source Sagittarius A* (refs. 1,2 ), a cluster of young, massive stars (the S stars 3 ) and various gaseous features 4,5 . Recently, two unusual objects have been found to be closely orbiting Sagittarius A*: the so-called G sources, G1 and G2. These objects are unresolved (having a size of the order of 100 astronomical units, except at periapse, where the tidal interaction with the black hole stretches them along the orbit) and they show both thermal dust emission and line emission from ionized gas 6-10 . G1 and G2 have generated attention because they appear to be tidally interacting with the supermassive Galactic black hole, possibly enhancing its accretion activity. No broad consensus has yet been reached concerning their nature: the G objects show the characteristics of gas and dust clouds but display the dynamical properties of stellar-mass objects. Here we report observations of four additional G objects, all lying within 0.04 parsecs of the black hole and forming a class that is probably unique to this environment. The widely varying orbits derived for the six G objects demonstrate that they were commonly but separately formed.