Then all the Greeks took Sosthenes, the chief ruler of the synagogue, and beat [him] before the judgment seat. And Gallio cared for none of those things.
Note 13 at Ac 18:17: Sosthenes (Greek - "of safe strength"[Strong's Concordance]) became the chief ruler of the synagogue after Crispus converted to Christianity. It is also supposed that this Sosthenes became a Christian, because he was included in Paul's greeting to the Corinthians in 1Co 1:1. This is possibly why the Jews beat Sosthenes.
Since they couldn't take their wrath out on Paul, they turned on Sosthenes, who was sympathetic to Paul's teachings, or else had already embraced the Christian faith. If Sosthenes was not yet a believer when the Jews beat him, maybe that was the last straw that turned him from the hypocrisy of the Jews to the message of God's love that Paul taught.