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.