wasd	navigate cursor
space	right-multiply element under cursor
shift-space	select coset generated by element under cursor
escape	clear coset selection
c	create/remove generator from element under cursor
q	take quotient with subgroup of selected coset
r	center on face defined by selected coset
f	stage current group as operand for product
g	take direct product of staged group with current group
z	undo quotient or product