What does 'Elk' mean in this context?

Watching Columbo, S02E04 Dagger of the Mind and this exchange takes place between Columbo and a Detective. They are in a gentleman's club, leather furniture, bookcases of old books, butler, etc.

Detective: Would you, uh, care to sit here?
Columbo: When you said "club," I thought you meant a country club or a health club.
Detective: Mm. Bit stuffy, I'm afraid. Hasn't changed since Father's day.
Columbo: My father was an Elk once, till my mother stopped him.
Detective: Ah.

It is quite hard to hear what Columbo is saying but it sounds like he's saying "My father was an Elk once".

I don't know what this might mean though, in the context.

The Benevolent and Protective Order of Elks of the U.S.A. is a fraternal organization with nearly a million members and a 141-year history, according to their website.