What do J. Edgar Hoover, William Loeb, Rep. James C. Cleveland (R-N.H.) and Dean Whitlock have in common? The answer: they all dealt in some way with Jessie L. Gill, the former Cambridge woman whom The Crimson revealed last week was working for the FBI while she was active in Harvard SDS.

Gill, who was active in SDS between 1967 and 1970, was secretly feeding information to the FBI, and she claims, the CIA. She said she was in constant contact with both intelligence organizations, and that she gave the FBI the names of "thousands" of radicals.

Dean Whitlock knew her then, and he said he never suspected she was anything more than a vocal and at times bizarre advocate for the tenants in her Harvard-owned apartment building. He never connected her with a phone call he received from the FBI in the summer of 1969 warning him that a secretary he had hired for the summer was actually an SDS member.

"I always wondered how the FBI found out," Whitlock said. From her New Hampshire retreat, Gill acknowledged that she had provided the Bureau with the information.

Gill, however, has thus far declined to elaborate about the nature of the information she passed, who her contacts were or what methods of operation she used, or how much she was paid, other than to say her salary was "under the minimum wage."

In fact, money in a sense proved her undoing. The Crimson broke the story after obtaining two letters indicating that Gill was having difficulty getting her back pay, and linking Cleveland, Loeb and Hoover with her efforts to balance her financial accounts with the FBI.

The Crimson published a February 1972 letter from the late Hoover to Cleveland acknowledging that Gill had worked for the FBI and informing him that "no money is owed her by this Bureau."

Vincent H. Rueul, an assistant special agent in the FBI's Boston office, Monday confirmed that Gill was on the Bureau payroll, but he and other national FBI officials have refused further comment.

Gill, however, said last week that Cleveland had contacted the wrong intelligence chief. She said the FBI had paid her all along, and that it was the CIA that was in arrears.

She said the CIA owed her the money for telephone calls, and that two Agency agents--one of whom she said was Herman A. "Rocky" Mountain, chief of the Agency's Cambridge Bureau--traveled to North Conway, N.H. to pay her $350 on March 3, 1972.

What happened between early February, when the Hoover-Cleveland-Loeb correspondence took place, and March 3, when Gill says the CIA paid her, remains a secret. Gill would not elaborate how the "mix-up" was rectified.

Loeb for his part acknowledged last week he had helped expedite payments to Gill, but he would only explain that he "took the appropriate steps in Washington." He said he never met Gill and had no knowledge of any CIA connections.

The CIA connection is one of the biggest missing pieces in a still largely uncompleted puzzle. Mountain and his national superiors in Langley, Va. have refused comment on any aspect of the case.