This is a preowned Fedora hat labeled New York Hat Co. on the inside.  It did not have a size but the circumference inside is 22" so guessing size 7.  The hat is stiff but covered as felt or wool but not sure which it is but soft to the touch.  It is an off white/Ivory color with a 1-3/4" black band with black eyelets on two sides.  The brim is 2" and the inside height is 3" at the front and 4" at the back.  So it sits high on the head.

It is a nice looking hat.  Looks like it would be for male or female.

If you have questions please ask and I will try to get it answered.