Under which of the following types of control is it permissible for the control operator to be at a location other than the control point?

The correct answer is automatic control. In amateur radio, automatic control allows for the operation of a station without the direct supervision of a control operator at the control point. This means that the control operator can be located elsewhere while still being able to maintain control over the station's operation through automated systems.

In automatic control, the equipment is capable of initiating and managing transmissions based on programmed settings or through an automated sequence, often involving modes such as packet radio or remote monitoring systems. This capability is valuable in situations where efficient and continuous operation is needed without the constant presence of a human operator.

Local control requires the control operator to be present at the station and actively manage its operations, while remote control allows an operator to control the station from a different location but still necessitates a dedicated operator at the control point. Indirect control might imply some form of non-direct interaction, but it still falls short of allowing an operator to be entirely away from the control point without real-time oversight. Thus, automatic control is the only type where an operator can be completely removed from the immediate control point while the station remains operational.