Prudential Insurance Co., in a move that surprised Wall Street late yesterday, tapped George Ball, president of the E.F. Hutton Group Inc., to be chief executive of The Bache Group Inc. and chairman of a new financial services subsidiary.

In hiring Ball, 43, away from the third largest securities firm on Wall Street, Prudential moved aside Bache Chief Executive Harry Jacobs and President H. Virgil Sherrill.

"I'm stunned," said the chief executive at a competing brokerage firm. "But it's a brilliant move on Prudential's part."

Prudential paid $385 million last year to buy Bache, the nation's sixth biggest brokerage firm, but one beset by what most industry observers considered stodgy management.

Prudential's purchase of Bache was the first of a series of consolidations in the so-called financial services industry in which American Express bought Shearson Loeb Rhoades, the second biggest broker; the big trading firm Phibro Corp. purchased Salomon Brothers, the fourth biggest; and Sears, Roebuck & Co. bought Dean Witter Reynolds, Wall Street's fifth biggest firm.

Wall Street sources said Hutton has turned down many merger offers from financial services firms. "Ball sees the need for this type of amalgamation. Since he couldn't get it at Hutton, he moved to Prudential, where he'll get to play in a bigger sandbox."

Prudential organized a new subsidiary, Prudential Capital and Investment Services Inc., that includes Bache and another Prudential subsidiary, Pru Capital Inc., that specializes in lending to utilities and medium-sized companies as well as investment banking. The backbone of the new subsidiary, at least for the short term, is Bache, which has more than $300 million in capital and about 200 offices across the country.

Jacobs and Sherrill will remain in figurehead roles at Bache. Jacobs will retain the title chairman without the chief executive rank, and Sherrill will become vice chairman.

"It was a move that was waiting to happen," according to the head of another large brokerage firm.

Prudential announced it would buy Bache in March 1980 for $32 a share, a move that thwarted a takeover try by the Belzberg Brothers of Vancouver.