Lycurgus set the number of Senators at 28. In discussing the reasoning behind the number Plutarch writes:
As for the determinate number of twenty-eight, Aristotle states, that it so fell out because two of the original associates, for want of courage, fell off from the enterprise; but Sphaerus assures us that there were but twenty-eight of the confederates at first; perhaps there is some mystery in the number, which consists of seven multiplied by four, and is the first of perfect numbers after six, being, as that is, equal to all its parts.
I have asked Kate what 6, 28 and 496 have in common. This will serve as her clue if she takes me up on my suggestion to read my blog. (Anything to drive up traffic.)