The board was custom-made for HP who do not publish compatibility information. You only get that info for retail desktop motherboards as purchased by home DIY computer builders.
HP may be able to tell you but even that may just be "We don't know".
It could be upgraded to an Intel® Core™ i7-2620M but only if it's valid for all Pavilion G6-xxxx series.
Check your original processor and see if it appear in the list.