Company, party, band, troop, troupe are comparable when they denote a group of persons who are associated in a joint endeavor or who are assembled for a common end.
Company is the general term for either a temporary assemblage or a permanent association of individuals who join forces.
A party is a company assembled temporarily for a common purpose.
A band is a company united by a common tie or purpose; the term implies closer organization and a less casual coming together than does company.
A troop is a company or band that works or acts together in close formation or in unanimity; the term frequently suggests a throng or multitude.
In specific use troop is applied to a band of soldiers or, in the plural troops, to soldiers collectively.
When the reference is to a company of performers (especially on the stage), troupe is the preferred spelling.