i wonna to produce a page with listing of all groups, for my template.
However i aren't able to find the way in which the way i can perform this.
Maybe I must give a new file during my template folder?
Have a look at Template Tags/wp list categories Β« WordPress Codex for that function and code good examples. You will want to create a page template to make use of that function by itself page: Page Templates Β« WordPress Codex.