The Capitol Hilton now ranks among Washington’s scandalicious hotels. (Bill O'Leary/WASHINGTON POST)

It’s a rarefied group, marked by fine room service, fluffy towels... and some (well-publicized) untoward doings.

Sharon Bialek said Cain upgraded her lodgings at the Capitol Hilton while she was on a trip to Washington. The two had a drink in the hotel bar, she said, after which they had dinner and he made unwelcome sexual advances.

That puts the Hilton in the elite pantheon of hotels of infamy.

The most famous might be the Watergate, the hotel within the complex where a burglary ultimately toppled President Nixon.

And then there was the Vista, the hotel where then-Mayor Marion Barry was caught on tape with a crack pipe. “B---- set me up” was Barry’s succinct assessment of the situation.

The Mayflower, of course, was where former New York governor Eliot Spitzer entertained a hooker. But that venerable establishment was no stranger to scandal: a rumored mistress of President Kennedy stayed there, and Monica Lewinsky, too, holed up at the tony lodgings while her dalliance with then-President Clinton made news.

Presidential aide Dick Morris’s escapades at the Jefferson Hotel reportedly included toe-sucking with a prostitute, who later said her former client had spilled White House secrets and took calls from the West Wing during their trysts.

But if it’s any consolation, the infamy might not be bad for the Capitol Hilton’s business: the Mayflower reportedly saw an uptick in business after the Spitzer headlines.

Maybe there really is no such thing as bad publicity.