it's definitly a "chalice" of some type (echinophyllia, etc). Med - med/high lighting (I'd keep yours on the lower side for now). Med flow. When it's happy, it can send out sweeper tentecles several inches long (6" isn't uncommon). They tend to be a fairly aggressive coral, in the sense that they can sweep all around their space and have a potent sting.
The flesh of it should expand to cover he skeleton more, and it's a bit browned out, but it should turn right around for yah