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A central organization is the main body of a group of organizations.
Also, "central organization" refers to something with an aesthetic center, such as a flower. The aesthetic make-up draws the viewer's eye towards the center.
According to the IRS Publication 557 (Rev. July 2001), Tax-Exempt Status for Your Organization Chapter 1 Page 6, a central organization is an organization that has one or more subordinate organizations under its general supervision or control. For example, the American Red Cross is considered a central organization. Its local chapters are subordinate organizations, since they are independent, but also fall under the control of the main chapter