Your plant is a succulent, but not a cactus. It looks like a sempervivum (hens and chicks) blooming to me, but since I don't (and can't) grow these, I'll defer to our experts.

If it IS a semp, the plant will die after blooming. But don't dispair, they leave babies (chicks) behind.

Thank you so much. I did put it in the hens and chick's family as well but thought they were outdoor succulents. But I do see small seedlings growing at the bottom of the pot so that makes sense. ThanKS again!

Looks like sempervivum to me too, and they really do better outdoors - unless you are in hot & humid area.
I have many of them outside, they are hardy & overwinter in colder zone than mine.

My personal opinion is that they are tortured indoors - pls. no offence! Look how nice they grow outside, they will never look same indoors.

It is good idea to put zone & even a state where you live next to your name, so you can get better advice...

Your holiday cacti next to it looks good (can't see much, but soil looks peaty?)

Rina

Sorry for the delayed response. I am going to edit my profile and put my zone info. I live in Rensselaer NY. It's a small town across from Albany. Unfortunately, I can't put any plans outside of my house. Long story short, I rent an apartment above a family that is quite destructive along with their dogs that are quite destructive too! LOL. That's why I have all of my Plant on my back porch.

I'm located in zone 5

As long as they are outside, that's good. They will overwinter outside too. You can pot them up into larger pot & let them 'multiply' - you mentioned that there are already little chicks growing.
As mentioned, the plant with flower will die, but the chicks will replace it. Make sure you use well draining mix.
I do have some in outside pots too.

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All of these are in containers. And they stay outside year round.
Is your back porch open?

Rina

Yes for the most part it's open. It's full of windows and no curtains are hung. So the sun and heat are pretty brutal out here. It's now in a new big pot so it can catch all the chicks that fall and grow. I picked up another plant that I need identified. I'm posting it next.

Is that photo of the same plant few days later?
If so, did you repot it into larger pot?

Rina

Yes it is and yes I did repot it.