Group Objects

try this,

var doc = app.activeDocument;
var links = doc.links;
for(var i=0;i<links.length;i++)
{
        if(links.name == "test.eps")

        {
                var grp = links.parent.parent.parent;

            }
    }

Regards,

Chinna

This would be the general approach in AppleScript - get a reference to the link via the file name, then navigate up the link's parental hierarchy to find the group.

tell application "Adobe InDesign CC 2015"

  tell document 1

  set theLinks to links whose name = "tick_icon.eps"

  set theLink to item 1 of theLinks

  set theParent to parent of theLink --parent should be PDF

  set theGrandparent to parent of theParent --parent should be rectangle

  set theGreatGrandparent to parent of theGrandparent --parent should be group

  if class of theGreatGrandparent is group then

  select theGreatGrandparent

  end if

  end tell

end tell

try using a Script Label to identify each element that will be sought by the script.