To make my question more clear, I want to ask two questions:
Is it possible for molecule to be achiral even though molecule has chirality center?
Is it possible for molecule to be chiral even though molecule doesn't have chirality center?
I thought of these questions because the definitions of chiral center and chiral do not have a one to one correspondence.
A chiral center is defined by carbon having four different ligands around it and chiral is defined by a compound being non-superimposable with its mirror image. They are quite related, but I think there will be counterexamples that satisfy one condition but not satisfy the other one.