Again, use the same cyclic subgroup of order 4 in the group of symmetries of an 8-gon. Check that the subgroup is normal by using part (2) of Theorem 10.1.3. Construct a one-line command that does the complete check and returns True. Maybe sort the elements of the subgroup S first, then slowly build up the necessary lists, commands, and conditions in steps. Notice that this check does not require ever building the cosets.