The quantity that is set by the dominant firm in an oligopolistic industry:

 is at the level where its marginal revenue and marginal cost are equal.

Explanation

The dominant firm is the one that accounts for a significant share of the oligopolistic market than its rivals. The dominant firm faces a downward sloping demand curve. After the dominant firm calculates the residual demand curve, it produces the quantity of output at which the marginal revenue is equal to marginal cost.  The dominant firm acts based on the information it has on the other firms in the industry, forcing them to act as price takers.

Reference

Microeconomics. By Roger A. Arnold P. 246