The Sorority and the Mystery Man. Those are the major players who have emerged in four days of hearings about the hiring scandals hobbling D.C. Mayor Vincent C. Gray.

The Sorority is the nickname coined by D.C. Council member Mary M. Cheh (D-Ward 3) to describe three close friends who were also top advisers to the Democratic mayor’s transition. They are former campaign chair Lorraine Green, former chief of staff Gerri Mason Hall and former interim human resources director Judy Banks.

The Mystery Man is former campaign consultant Howard Brooks, who is keeping a low profile and has refused to testify. He appears to be at the center of the big, remaining question in the scandal: whether criminal charges will be brought against members of Gray’s campaign or even the mayor himself.

The main thing learned in the hearings so far is that Gray showed bad judgment in allowing the Sorority to guide so much of the hiring for patronage jobs just below the cabinet rank. Although all three advisers were longtime personnel executives, they blundered repeatedly by overpaying people, doing inadequate vetting and hiring children of officials (including those of Green and Hall).

With Green’s testimony Friday, all three have now appeared before Cheh’s committee investigating the scandal. The results have been distasteful for anyone who’d like public servants to be straight­forward and transparent, especially when speaking under oath.

In particular, despite 20 hours of testimony in sessions that began March 28, the public still lacks a coherent, credible explanation for why there was a rush to hire Sulaimon Brown, a former minor mayoral candidate, for a $110,000-a-year job.

Brown has alleged in media interviews that the job was a reward for a secret deal he made last summer with the Gray campaign in which he would lambaste then-Mayor Adrian M. Fenty (D) at debates. Gray and Green have said they promised Brown only a job interview, not an actual job.

The problem with that defense is that Brown did get a job early in the administration. He got it although, Green said Friday, she’d already decided he was “delusional” because of an erratic statement and other odd behavior.

Green’s cautious and often unconvincing testimony was pronounced “implausible” by Cheh. For instance, Green was vague about why an early background check was ordered for Brown, even before a job had been identified for him.

The other two Sorority members did no better at earlier hearings. Hall tried to shoulder all the blame and only succeeded in proving she was a loyal soldier willing to be sacrificed for others’ sake. So many people have contradicted Banks’s testimony that Cheh publicly accused her of perjury.

As for Mystery Man Brooks, he started in Gray’s campaign as a volunteer. But after the mayor’s primary victory, a decision was made to award Brooks $44,000 in bonuses for his work. In declining to testify, he cited his Fifth Amendment right to avoid self-incrimination.

Brooks is crucial because he’s the one most implicated in Brown’s other allegation — that the Gray campaign gave Brown thousands of dollars of cash in envelopes during the campaign so he’d continue the nasty attacks on Fenty.

Brown originally made the charge in an explosive interview with my colleague Nikita Stewart published March 6. Brown said he was paid initially by Green but later by Brooks.

If such a deal was made, it could be a basis for charges against the Gray campaign for violating campaign finance regulations or the District’s corrupt-practices act. Green and Brooks have denied the allegation, and The Post has not independently corroborated that cash changed hands.

Both the U.S. attorney and a congressional committee are investigating. In a sign that Brooks could be central to a possible case, Green abruptly stopped answering questions at Friday’s hearing when she was asked about conversations she’d had with Brooks about Brown. Describing such talks could intrude on the federal prosecutor’s inquiry, Green’s attorney said.

Where does all this leave the mayor and the city? As I’ve written before, the scandal has spoiled Gray’s debut and will always be a stain on his legacy. Whether the U.S. attorney brings charges will probably depend on whether there’s physical evidence to support Brown’s allegations and on what prosecutors learn from Brooks or others about his dealings with Brown.

The mayor could help his own cause by testifying voluntarily under oath before Cheh’s committee and by publicly pressuring Green, Brooks and others to be more forthcoming with the public.

Gray has avoided doing that, saying it could interfere with the investigation. He also might be reluctant because of loyalty to longtime friends, especially Green, or because he has something to hide.

Assuming he isn’t indicted, however, I still believe Gray can put this behind him by forcefully pushing ahead more with a positive agenda for the city, especially on education and jobs. There’s still time to climb out of the hole that the Sorority and the Mystery Man have helped dig for him.