The GGMFO&CP has been such since before J* came about. The 'group' refers to internal Qantas mainline. It's been confused with the subsequent branding of the 'Qantas Group' to also include J*, QFLink, etc.
Whilst 'QF Group Flight Training' is a marketing name and a cost center code. I don't think there is any aspect of it being truly a 'group flight training' organisation- at least in the context you mean HF3000- occurring for quite some time. There are some examples of this if you talk to the right people but not for this forum.