Stock of the Washington Post Co. was most active on the American Stock Exchange yesterday, following a purchase by the company itself of 560,000 shares in one block.

According to an announcement by the communications company, directors authorized the purchase of a million shares of class B common stock -- bringing to about 1.35 million the number of shares authorized for purchase at this time.

Under this expanded authorization, the Post Co. bought the huge block -- about 3 1/2 percent of outstanding shares -- at $20.375 a share just before noon yesterday. Post stock subsequently closed up 50 cents for the day at $21 a share on a total volume of 576,600.

After the purchase yesterday, the Post Co. has outstanding about 11.7 million class B, publicly traded shares. In addition there are about 3 million class A shares. The company did not announce a ceiling price or a time limit for the continued stock purchases, to be accomplished mostly through block transactions.

Vice president for finance Martin Cohen said last night that no director or officer of the company was involved in yesterday's transaction. He said the purchase was made from an institutional investor, who could not be identified.

At a meeting with analysts in New York on Tuesday, Post Co. Chairman Katharine Graham noted that the firm ahd bought up some 4.7 million shares -- 25 percent of the outstanding shares -- in recent years through stock purchases for $59 million. "We will continue to buy stock as long as the market provides the opportunity," she said of Post Co. acquisition of it's own stock.

Separately, the firm said that regular publication of a new magazine, Inside Sports, is expected to reduce pretax profits by about $8 million in 1980 and by lesser amounts in future years.