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So I want to start by saying that removing the agitator is going to be very difficult for you. The agitator itself is just held on by a lot of friction onto a plastic hub below the agitator. The agitators from GE don't have bolts or screws holding them down, they are just held down by friction. You have to grab underneath the agitator and pull up (usually helps with 2 people) really really hard and it will pop off and you can remove it. GE makes a special tool for the job which is basically a bicycle inner tube that slides under the agitator and inflates to pop the agitator off. Once you have the agitator off, check the plastic hub and make sure the center bolt is completely tightened down. If it is and the hub doesn't move, then try to re-install the agitator and if it still has a lot of play, the agitator itself would need to be replaced.
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