You're right, it's a fake. Date is bad, denticals are bad, I don't like the area where the drapery on the arm meets the leg, I don't like the pole etc.
I've bought one of these that was fake before. They get MUCH more convincing than this. Nowadays they're making these and all sorts of coins out of "white metal" - a non magnetic material. It makes the coins feel different in-hand. I picked up one 1896-S Barber Quarter made out of it. It failed the "ping" test, but it was a truly masterful fake... truly. I knew it was fake when I bought it for $25 (eBay seller admitted it), but I had to see it in person to believe it. These are SO convincing. Scary stuff. Simple advice: 1. If it ships from China, avoid. 2. If the seller doesn't have a return policy, avoid. 3. Get a scale, not just a magnet. 4. If it's too good to be true, (key date, absurdly low price, "seller requires instant payment", etc.) it isn't.