The closest looking I know, Anemonia melanaster and Anemonia sargassensis, aren't from the right area and wouldn't be big enough to be this as described. That said, I'm inclined to believe it's an Actinia sp. (though I have no idea which one, and there are more species in the genus then I personally care to try and sort through at the moment), as a lot of these would be more appropriately sized, at least a few are from the right area, and I know at least a few have similar patterns around the mouth.
Regardless, it's a pretty specimen.