Section 504 - Retirement board; members; terms of office; vacancies1. The general administration and responsibility for the proper operation of the retirement system and for making effective the provisions of this article shall continue to be vested in a retirement board. The retirement board shall from time to time establish rules and regulations for the administration and transaction of its business and for the control of the funds created herein and shall perform such other functions as are required for the execution of the provisions of this article.2. The retirement board shall consist of ten members as follows. a. One member, who is not an employee of the state, who shall be or shall have been an executive officer of a bank authorized to do business in this state, elected by the board of regents of The University of the State of New York to serve for a term of three years.b. Two members who are not employees of the state, each of whom shall be or shall have been a trustee or member of the board of education of a school district in this state, and at least one of whom shall be or shall have been an executive officer of an insurance company, elected by the board of regents of The University of the State of New York to serve for a term of three years, from a list of five or more persons having broad experience and ability in the fields of finance and investment to be presented to the regents by the board of directors of the New York State School Boards Association, Inc.c. Two administrative officers of the New York state school system, appointed by the commissioner of education, each to serve for a term of three years. Members of the present state teachers' retirement fund board shall be deemed to be administrative officers of the New York state school system within the meaning of this provision.d. The comptroller of the state of New York or one member appointed by him who shall serve until his successor is appointed.e. Three members elected from among the members of the retirement system, each to serve for a term of three years.f. One member, who must be a retired teacher, who shall be elected in accordance with the provisions of section five hundred five-a of this article to serve for a term of three years.3. A vacancy occurring during the term of a member elected by the board of regents or appointed by the commissioner of education shall be filled for the unexpired term by the election or appointment of a successor in the same manner as his predecessor. A vacancy occurring during a term in the case of a member elected from among the active members of the retirement system shall be filled, until the next annual convention of delegates, by the commissioner of education and shall be filled for the unexpired term by the delegates at the next annual convention in addition to the regular election. A vacancy occurring during the term of a retired teacher member shall be filled in accordance with the provisions of section five hundred five-a of this article.