(My answer on Quora).
Earth exists in the Milky Way galaxy whose galactic center is about 0.0265 million light years from us here on the Third Rock. Ironically the Canis Major Dwarf satellite galaxy is 0.0250 million light years from Earth although its classification as a galaxy is disputed.
There are a myriad of satellite galaxies that are very close to the Milky Way (including the Small and Large Magellanic Clouds) but the closest Major galaxy to the Milky Way is Andromeda (M31) which is about 2.5 million light years from Earth. It is a barred spiral galaxy with about twice as many stars as the Milky Way.
Source: D. Karachentsev et al.(2004) A Catalog of Neighboring Galaxies.
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