Even though everybody lights at home, the Hanukkah lights are also kindled in the Synagogue between Minha and 'Arbith because of Pirsumei Nisa (publicizing the miracle). However, in the Synagogue the Hanukkah (Menorah) is always lit on the Southern wall.
Even though the lights in the Synagogue are lit with a Beracha (blessing), a person does not fulfil his obligation with this lighting, but must light again at home. If there aren't ten people present in the Synagogue at the time of lighting, then they are lit without a Beracha.
When the first night of Hanukkah falls on a Friday, and everyone present in the Synagogue has already lit at home prior to coming to there, the Berakha of Sheheheyanu must be omitted since everyone has already said it at home.
(Sh. 'A. 671: 7, Rama ibid. Kaf Hahayim ibid, Oth 65 and 72. Ben Ish Hai, Wayyesheb, Hanukkah, Oth 11.)
