Was Custer a general or colonel during the Battle of Big Horn?

Custer was a colonel during the Battle of Little Big Horn, as a regiment is normally commanded by a colonel, while a general commands multiple regiments. I think the confusion over Custer's rank is because during the Civil War he was promoted to brevet general (sort of a temporary general, promoted in the field). After the war Custer got himself in some trouble and was demoted back to colonel, and he never rose to the rank of general again.