Its not a GT. Gt did make a California cruiser, that is not one of them. A few diff. Companies used a knock off of the GT sprocket. You might have some luck Jeff if you clean some of the paint off the head tube. Its most likely a sticker instead of a head badge. You might be able to read something. I know Savage Bicycles used that sprocket and had a painted frame and chrome forks. Its a toss up though until you can check the head tube, down tube or chain guard for some painted over info.
-Kreep-