Does the Milky Way belong to a Galaxy cluster I know that the Milky Way is a member of the Local Group and the Virgo Supercluster / Laniakea Supercluster. However, I can't seem to find any information about the Galaxy cluster we belong to.

Does the Local Group / Milky Way belong to a galaxy cluster?
The Local Group contains 54 plus galaxies.
Don't know that that counts as much of a cluster.
Next up in scale, the Milky way is part of the Laniakea Supercluster
That contains about 100,000 galaxies, so it's a bit on the large size to call a simple cluster.
The well known Virgo Cluster contains about 1300 galaxies.
So it's clearly a thing of intermediate scale.