The Milky Way is 2.5 million light years from Andromeda and the size of the Local Group has a diameter of approxmiately 10 million light years across.
What is the distance from this Local Group to the next closest galaxy?
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Your question can be interpreted in many ways.
Wikipedia has a list of nearby galaxies to reference, so I'll pick the first one.
One problem with answering this question is it's not entirely clear which galaxies are part of the Local Group. Another is many of our distance calculations to nearby galaxies have high error bars. Candidates include...
|Galaxy||Distance from Milky Way||Notes|
|NGC 300||6.07 ± 0.23 Mly||Bound to NGC 55. Probably neither part of the Local Group nor Sculptor Group.|
|NGC 55||6.5 ± 0.65 Mly||Bound to NGC 300. Probably neither part of the Local Group nor Sculptor Group.|
|IC 5152||5.87 ± 1.22 Mly||Might be part of the Local Group|
|KKR 25||6.37 ± 0.35 Mly||Closest to, but probably not part of, the Local Group|
The answer is about 6 million light years.