Certified GKH Gardening Expert
They need full sun, but they prefer a cool, mild climate. In looking at your photo, the green foliage without flowers looks more like chrysanthemums, which don't bloom till late summer or fall. Could you have those? The foliage doesn't look like carnations at all. However, there is a small pot in the center that looks like a dianthus flower that is blooming.
Here is more about carnations. Make sure you are meeting its growing conditions and they are getting full sun: