Each alliance can designate a single system as their Alliance Capital if they have an active Territorial Claim Unit in that system. The capital can be changed whenever it is desired or needed, but it requires 7 days to take effect. This grants a +2 bonus to the system's Activity Defense Multiplier, but it still cannot exceed the value of 6.
If an alliance capital is lost, then a new one can be designated normally. If an alliance only holds sovereignty over one system or is reduced to one system, that system will automatically become their alliance capital. This is an exception to the 7 day wait requirement.