The Los Angeles Times, citing sources within the department it did not name, said the group is known as the Jump Out Boys.
Investigators say they have discovered a code of conduct for the group that appears to regard officer-involved shootings as a mark of distinction.
The investigation is targeting the Gang Enforcement Unit, the Times said.
Other cliques or factions in the department have been uncovered, some of them operating like street gangs. Several deputies who had allegedly formed a "3000" faction on the third floor of the Men's Central Jail were fired last year for fighting other deputies at a Christmas party.
Investigators told the Times the "3000" group had an initiation requirement -- breaking an inmate's bones.