I think I posted something about this long ago "Over There". The GP discussion reminded me we haven't discussed it here. (That I recall....)
FH in GEoD wrote: Idaho lifted his right hand in acknowledgment. He was emerging into the open space now and the dimensions of this enclosed place awed him. He set his trained eyes the task of estimating the dimensions as he mounted to the ledge and guessed the hall to be at least eleven hundred meters on a side-a square with rounded corners. It was packed with women, and Idaho reminded himself that these were only the chosen representatives of the far scattered Fish Speaker regiments—three women from each planet. They stood now, their bodies pressed so closely together that Idaho doubted one of them could fall. They had left only a space about fifty meters wide along the ledge where Idaho now stopped and surveyed the scene. The faces looked up at him-faces, faces.
Ignoring the "rounded corners" and open space mentioned towards the end, that's 1,210,000 square meters. If you assume six people (hunky women?) can stand in one square meter (that happens to be the figure they're using for crowd estimates at the Inauguration today), that gives 7,260,000 women. Assuming every planet in the Empire had a Fish Speaker regiment, three per planet gives at least 2,420,000 planets.
Or nearly 2.5 million.