How many central symmetries does the pyramid have?

The pyramid has no central symmetry. If we take any point taken outside the base of the pyramid as the center of the symmetry, then we will be forced to construct a reflection of the base in a plane parallel to the base. That is, the result will look like a prism, not a pyramid. If you take a point on the base as the center, then the vertex that is above the base will be translated to a point that is outside the pyramid.
Answer: The pyramid does not and cannot have central symmetry.