It Does not resemble any agate I've ever seen or heard described. It may not help but if you tell us where you are from it could help narrow the possibilities some. if it was bought from a dealer then he might have more information.
Lake Superior greenstone is usually smaller than a dime. More accurately, most never half as big as a dime. Usually smaller than a half a peanut..
Some things to help us would be dimensions roughly, where the stone comes from and a relative hardness Is the rock easy to scratch? Some rocks you can scratch with your thumbnail and some won't scratch with a pocketknife.