GE agitator problem

My GE washer will not agitate. It does spin, but appears the agitator is not engaged. If I push down on agitator it will engage. It seems like it is loose or a bad gear. I looked at the parts list and it appears it may be the agitator coupling. However, I can not figure out how to remove the agitator to see the coupling and the screw that holds the assembly together. Any help on how to remove the agitator would be appreciated.

I also have the GE Profile washer model WPSR3100WOWW. First, be aware that there is no nut, bolt, allen screw or similar that must be removed prior to tugging off the agitator. The agitator really does just pull off its splines all in one piece (that is, with fabric softener holder etc. still in place). I think the following hint was key for me: Put the water on "hot," set the washer to run for a medium load, and fill the tub. Let the hot water sit for 10 minutes. With the hot water still in the tub, use a loop of rope or strap slid underneath the agitator, close to its center at the bottom of the tub. Tie the ends tightly to form the loop. Make it long enough so that you can pull at a height of a few inches above the top of the agitator. Wobble the agitator using the rope or strap. Then try tugs. My washer’s agitator came free really easily only when I used the hot water soak. I drained the water through the bleach hose into several buckets. Before trying the hot water soak, I had spent an hour or so of pulling on the agitator, wobbling it, smacking its base a bit with a soft mallet, probing for some fastener that had to be released (wrong), and pondering with google. This youtube video gave me the hot water hint: Agitator coupler GE front serviceable washer - YouTube