Frilly, sempervivum are alpine plants that live in high elevations with lots of snow during winter. And they require at least 1/2 day of sun. Unless you live in an area that has very hot and harsh summers. Then the would need filtered/dappled sun/shade.
Right now it would probably do better in a very cool room/garage, or a covered deck/porch. Like Greg suggested. Just give it sips of water, don't over water.
The three rosettes at the bottom right corner look good and should produce many offsets for you this year. The other two will bloom and die. Many things can trigger blooming, stress, age, etc. Many of the arachnoideum types of sempervivum stay small, as you can see in tarev's excellent photo in her above post.
I see it has the name of 'Cobwebs' on the nursery label. That is not a correct cultivar name, just a descriptive name they gave it.
You are going to love your little Sempervivum arachnoideum. I can't wait to see updated photos as it starts producing little chicks surrounding the hen.
