What is the GROTG?
The Great Races of the Galaxy is just shorthand for “The Supreme Interstellar Senate of the Great Races of the Galaxy.” It’s sort of like the United Nations of pre-hyperspace Earth, but as orders of magnitude increase for scope, so do those for bureaucratic inefficiency and political infighting. Still, the institution manages to keep conflicts from escalating to full alliance-activation by keeping problems in as wide a public forum as possible. This is fortunate because MAD is orders of magnitude greater as well. While conventional wars (as between APA and the Silicon Lords) are fought for prestige and minor territorial rights between well-shielded ships fielding relatively weak weapons, the strategic weapons in reserve are “the good toys.” These include your Stellar Imploders, your Atmospheric Deprivation Weapons, and your Ultracavitating Chronosphere Drivers.
Another similarity to the UN of pre-hyperdrive Earth is the distribution of wealth, power, and influence into a handful of superpowers and their economic allies. There are many relatively dominant empires and federations which either started early or made a big impact as fierce competitors when they got the hyperdrive. There are also innumerable “developing” races which have reserved / allotted fallow territory near their homeworld.