I think that the catalyst GPU is AMD. According to the output of lspci -nnk | grep -iA2 VGA
you have no AMD GPU, and so your computer is already using the right graphics driver, the graphics driver that is built-in in Ubuntu.
Some models of the HP Pavilion g6 laptop have an additional discrete graphics processor and other models of the HP Pavilion g6 don't have one. For example, according to HP Pavilion g6-1304tx Notebook PC Product Specifications, that model of HP Pavilion g6 laptop, which has a 2nd Generation Intel Core i5 processor, does indeed also have an AMD Radeon HD 7450M graphics processor. If so, the correct graphics driver for that graphics processor would surely show up in the Additional Drivers utility. Search the Dash for Additional Drivers and click the Additional Drivers icon to open Additional Drivers to check if there is a proprietary graphics driver available for your laptop.
lspci -nnk | grep -iA2 VGA
say? – JoKeR Jun 15 '14 at 15:27lspci | grep -i ati
oramd
etc and nothing is found it can be disabled by default in bios, you need to look for it and enable it in bios. – JoKeR Jun 15 '14 at 15:33