This is a large blue/purple "druzy" agate cabochon, drilled to accept a "bail" or finding to make it into a pendant. While the main form is agate, a chalcedony form of quartz, it also contains a "druzy" section - quartz in its crystalline form.
This stone is indeed banded agate and druzy quartz, but it has been dyed in order to obtain the unusual coloration. These come in many variations and are indeed striking.
"Druzy Agate" is one of my favorite forms of agate. It usually has opaque, translucent, and natural quartz sections, and can be very artistic.