Add extra field to group contact - relation
If i understand correctly, in your example, you have 2 organizations contact called "Group 1" and "Group 2" and one individual contact called "User 1".

In that case, I can think of several way of doing what you want :


create different relationship type "Chairman", "Secretary", ... and use the proper relationship between the contacts. This way, you will see in the tab Relationship all the information you need
Have one type of relationship (e.g. Employee) and add the function in the description. The description is visible in the Relationship tab so it will give you a quick way to see the function but it is less obvious in a user experience point of view that description = function
Create a custom field "Function" on the Relationship type that you want. The drawback is that your custom field won't be visible from the Relationship tab without clicking on the "View" link for a particuliar relationship.