Twitch mirc groups

If you’re referring to the user-type then possible values are staff, admin, global_mod, mod or no value for normal chat users. The host can appear as mod if he modded himself.

I highly doubt that is possible or ever will be.
You can define custom groups in your own application though depending on what you want to do with it.

You can get a list of all moderators by sending .mods to the channel. The response will look like this

The moderators of this room are: mod1, mod2, mod3

But keep in mind that the irc message length is limited. Meaning, you might not get all moderators if the channel has a whole lot of them.