I know the teachers have a union. But are school administrators also entitled to organize and form a union?

Yes, so long as the persons who desire to form an employee organization (union) are “supervisory” employees and are not “management” or “confidential” employees.  Supervisory employees are those persons who, regardless of job description, have authority in the interest of the employer to hire, transfer, suspend, lay off, recall, promote, discharge, assign, reward, or discipline other employees, or the responsibility to assign work to and direct them, or to adjust their grievances, or effectively recommend that action, if, in connection with the foregoing functions, the exercise of that authority is not of a merely routine or clerical nature, but requires the use of independent judgment.  A person need only satisfy one of these criteria to qualify.

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