This is a very unusual coat. Was it, perhaps, made for a play?
In my title, I've called the coat pink. It's an easy description. Some variety of fuchsia might be more precise, though fuchsias come in so many shades that the term doesn't seem terribly useful. Looking at Wikipedia's article on "Fuchsia (color)"Wayback, on my screen, the nearest variants would seem to be French Fuchsia and Fuchsia Purple.