If these are the only three notes in the chord, it is called an Italian sixth. If an augmented fourth is added above the bass, giving, for example, A flat, C, D, F sharp, the chord is a French sixth. If instead a perfect fifth is added above the bass, giving A flat, C, E flat, F sharp, for example, the chord is a German sixth. The etymology of all these names is unclear.
All augmented sixth chords usually have the flattened sub-mediant (sixth degree of the scale, A flat in C major, for example) as the bass note. When they do, they tend to resolve to the dominant.