It's four days before All Hallow's Day, so I guess that makes today Hallowe'en-e'en-e'en-e'en? Here's another pumpkin spice flavored Advanced Knowledge Problem of the Week to celebrate it.
Keep reading to see my formulation of the solution!
Did you come up with another Cayley table for the quotient groups, and what representative elements did you use? Do you want to see more chalkboard drawings in the Problems of the Week? Let us know in the comments section, and have a happy Halloween!