Not a cactus but is a succulent. All cactus are succulents, but not all succulents are cactus.

Your succulent is a Sempervivum.

These guys are very hardy and would prefer to live outside. Repot into a better mix suited for succulents. The new mix should be amended with perlite or pumice. A ratio of half cactus soil to half pumice or perlite. Clean off as much of the old soil on the roots as you can before putting in new mix. Your new pot should have drainage holes and ideally shouldn’t be much bigger than the pot it’s in now.

It’s always hard for me to give advice when to water because idk your environment. But the best way to go for most succulents is water once the mix is thoroughly dry.

the most common are commonly called.. hens and chicks ..

https://duckduckgo.com/?t=ffcm&q=Hens+and+chicks+(Sempervivum+tectorum)&iax=images&ia=images

the version i have grow outside year round in my ground freeze MI .. though i couldnt tell you which specific kind they are ...

ken

Thank you:)