Here are a couple of photos of Green Woodpeckers showing both male & female I took at Minsmere a few years ago. You should tell from this photo if it is the bird you saw.
Close ups of a scruffy female taken in my front garden last year.
If you look at the top photos of the pair you will note that the bird on the top of the mating pair has a red chin strap under the eye. That's the male.
John