A 13-year-old Melbourne girl has been charged with 52 offences including allegedly shouting antisemitic remarks, throwing eggs and swerving a stolen car towards members of the Jewish community.

Victorian police said in a statement on Tuesday that the girl and two other girls were alleged to have been seen driving the stolen black Hyundai sedan in the south-eastern suburbs of Hampton, Ripponlea and Caulfield over multiple days last week.

Police alleged that on 25 March, the girls shouted “offensive, antisemitic remarks” and threw eggs at pedestrians.

Three days later, the car, allegedly driven by the 13-year-old, swerved towards Jewish families in Ripponlea about 7pm, police said, as the group crossed the road at the intersection of Hotham Street and Glen Eira Road.

They “narrowly escaped being struck by the car”, police said.

“There were no physical injuries and the car, which was allegedly stolen from a gym in Caulfield, fled the scene.

“Police will allege the driver, a 13-year-old girl from the Bayside area, was also involved in several other incidents involving erratic driving in stolen cars.”

On Monday night, police responded to an alleged hit-and-run in Brighton.

It is alleged a male cyclist was travelling along St Kilda Street when an occupant of a stolen silver SUV attempted to hit the bike with the passenger door about 6.50pm.

The driver of the SUV then allegedly crashed into the rear of the bike.

The cyclist, a 45-year-old Brighton man, was taken to hospital with non-life-threatening injuries, police said, and the driver fled the scene.

Just after midnight on Tuesday morning, police said teenagers travelling in a stolen white Volkswagen Golf rammed an e-scooter with two people on board in Elwood.

“Both riders fell from the e-scooter as it crashed into a parked vehicle. They did not require medical attention,” police said.

“One of the victims and a passerby began filming the offending vehicle, before one of the teenagers allegedly threatened them.”

Police spotted the van that was allegedly involved in the crash a short time later.

Police said the driver allegedly travelled across a footpath and “took off at speed” on the Nepean Highway, before travelling on the Dingley Bypass, the EastLink, Princes Highway and the Monash Freeway.

“Police successfully deployed stop sticks on Dandenong Road in East Malvern, before the car came to a stop on Waverley Road,” police said.

“The three female occupants were arrested at the scene and taken into custody.”

The 13-year-old girl from the Bayside area was charged with 52 offences including reckless conduct endangering serious injury, multiple counts of theft, multiple counts of theft of motor vehicle, burglary, handling stolen goods and “threatening physical harm or property damage on ground of a protected attribute”.

She was remanded to appear at a children’s court.

Another 13-year-old girl and a 16-year-old girl, both from the Cardinia area, were also arrested.

They were charged with theft of motor vehicle and handling stolen goods and were bailed to appear at a children’s court at a later date.

“Investigations into the series of incidents remains ongoing,” police said.

“There is absolutely no place at all in our society for hate-based behaviour and such activity will not be tolerated.”