With a title like that you're probably expecting a lofty treatise on the dynamics of interpersonal relationships in the large group as expressed by its leaders. Relax. Nothing so lofty needs to be expressed here, just biblical principles worked out in the life of your chapter.

The executive committee (most usually known as "the exec") has the responsibility for setting the direction for the group and laying the foundation for plans. In large chapters it can be very helpful to have a member of the exec carry the responsibility for the chapter's large group meetings. This person need not lead the meetings but would instead be responsible for their plans and have a team of people who would be involved in carrying out the meetings.

If a member of your exec has the responsibility for large groups the exec can help by:

(a) reviewing the topics for meetings and helping this person put together interesting, timely topics.
(b) helping the large group coordinator identify people with talents which are needed at the large group meetings.
(c) praying for and with this person, particularly asking God to be present and working during large group meetings.
(d) attending large group meetings regularly.
(e) before, during, and after meetings, making an extra effort to welcome newcomers and build relationships with people throughout the chapter.
(f) offering appropriate feedback at appropriate times.

If your chapter is relatively small, and your executive committee small you should consider the role of large groups in your chapter life. It may be that as you consider large groups the only way you're going to get one started or improve yours is for someone to take on that responsibility who really cares and evidences some talents that can make a difference. You may need to review your job descriptions for each of your executive committee members and realign jobs so that one person can devote the majority of their leadership to leading and improving large group meetings.

Here are some suggestions for how a large group coordinator might fit as part of the executive committee: