A telecommunications network (10) comprises a group call service server (18) which facilitates a group call over a radio interface (32) between different user equipment units (30) in a defined group within the telecommunications network. The group call service server (18) receives a floor request from a requesting user equipment unit (32j) included in the group, and handles the floor request based on a media type associated with the floor request. In conjunction with such handling, in one aspect of its operation the group call service server prioritizes the floor request from the user equipment unit based on the media type (e.g., based on delay sensitivity of the media type associated with the floor request). In one example implementation, the group call service server comprises a queue (42) and a floor request handler (40). The group call service server queues the floor request from the requesting user equipment in the queue (42); the floor request handler (40) prioritizes the floor request within the queue based on the media type. In a specific example implementation, the group call service is Push-to-Talk over Cellular (PoC) and the group call service server comprises PoC server situated in a service network. Also provided are a group call service which handles the floor request based on a media type, and a message format for the floor request itself.