Birchat ha gomel is said in place of bringing a toda korban. Why is the birchat gomel said with a minyan? Why do we want to with a minyan to say birchat hagomel? Did a toda require a minyan?
The Rambam (MT Brachot 10:8) links the recitation of Birkat Hagomel in front of 10 people to a verse in Tehilim
These thanks must be rendered in the presence of ten people, of whom two are sages, as implied by Psalms 107:32: "They will exalt Him in the congregation of the people and they will praise Him in the seat of the elders."
For a much more involved discussion see here from R Yaakov Klass