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Are there different classifications or just the one? How does our galaxy group compare with others?

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There is only one local group - the Local Group. This is the name of the galaxy group that the Milky Way resides in. Perhaps you are asking for a definition of a galaxy group? –  Moriarty Dec 31 '13 at 6:40
    
@Moriarty Yes, that's what I'm asking about. I edited my question to reflect this. –  Eduardo Serra Dec 31 '13 at 13:07
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I'm not prepared to post an answer to this just yet, but basically, individual galaxies and galaxy clusters are well defined structures in the universe. Galaxy groups are loose associations of individual galaxies, but which do not contain the amount of total mass which clusters have ($\gtrsim 1\times 10 ^{13} M_{\odot}$). They are therefore not strictly defined in terms of numbers of galaxies, but do have their place in the mass hierarchy. –  astromax Dec 31 '13 at 15:45
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up vote 7 down vote accepted

A galaxy group is a set of galaxies that are close together and gravitationally bound, i.e. barring outside influences they will stay together indefinitely. That means a galaxy that is in the space occupied by the group but "passing through" it at a high velocity would not be considered part of the group.

The upper limit for calling it a group is roughly 50, bigger accumulations of galaxies are called clusters (which may consist of many groups). The borders between adjacent groups may be uncertain.

These aren't mathematical definitions and actual usage is often based on tradition more than on measurements. It's just like geography: you could debate endlessly whether a given piece of high ground should be called a hill or a mountain, and whether something is a separate mountain or a subpeak, but sensible people recognize it as a waste of time, make up a clear but arbitrary numeric distinction without strongly insisting on its usage.

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Another analogy would be: where do you draw the line between planets, dwarf planets, minor planets, and meteoroids? There's no clear line, with one group clearly distinct from the next group. –  Phil Perry Mar 4 at 18:04
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