The FC master role can only be changed by the FC master, regardless of what permissions you give to other FC members.
Even given the ability to promote/demote members, only the FC master can change the person in the FC master group (and can only have one member).
Promoting someone to the FC master group will demote the current FC master to the third group (I believe it is) the group that new members are inserted to when joining the FC.

Anyone in the FC can be granted every permission EXCEPT the permission to promote self or other person to FC master, this only the FC master can do.