Here goes,-before the big bang there was NOTHING- no over here or
over there, nothing, not even space itself. So, when the big bang happened,
everything was created EVERYWHERE at the same time, so there is/was no center
to the universe-it was everywhere at once.So,like all explosions, everything was
flying outward,away from everything else, in all directions, creating SPACE itself
as it expanded. Because of gravity, some matter drew together into clumps which
became stars,planets, galaxies,clusters of galaxies etc,, but at the same time, they were
still expanding outward away from each other in every direction and are still doing so
to this very day....So to answer your question the galaxies are moving, either in clusters.
or separately, away from each other in all directions at all times.
UYYU:)