How manage "file" template structure?

Hi all,

as usual, sorry for all my grammatical errors and for the stupidity of my questions

I'm trying to modify my template to make in sort to be able to display the icon of all groups.

Actually I'm stop here:

<li class='ipsResponsive_hidePhone'><img src='{file="$comment->author()->group['g_icon']" extension="core_Theme"}' alt='' class='cAuthorGroupIcon'></li>

I'm able to take out of author() the secondary groups id and split them but, here, I'm just frozen and, I admit, I didn't fully understand the red construction.

The question is:

how can I say: take the g_icon of the group with ID x?

Actually I didn't necessary need "the" answer, but some tips would be appreciate

Thank you for your kindness and your time.

Edit:

Ups... sorry, to many windows was open and I've started here instate of https://invisionpower.com/forums/forum/497-peer-to-peer-technical-support/