The police union has already taken several actions in response, including a plan to expel any officer involved.
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"I say this to anyone who participated. The union will provide you no shelter, no protection," Paul Kelly, SJPOA president, said.
"There is no place in our police department or union for racists or bigots," he said.
The union and department have not provided many specifics on the Facebook group or the posts.
In a statement, San Jose Police Chief Eddie Garcia says he has no control over retired employees, but added, "Any current employee involved with bigoted activity online will promptly be investigated and held accountable to the fullest extent in my power. We have no place for this."
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The department has a complicated history with incidents like this.
In 2016, a San Jose officer made "menacing" tweets about the Black Lives Matter movement.
An arbitrator reversed the chief's decision to fire the officer.
Mayor Sam Liccardo is currently pushing to change this system.
"It is too hard for chiefs in this city or any other city to fire bad cops," he said.
As for this new case, Mayor Liccardo is calling for a full investigation.