explain different ways to govern groups

Can you explain?

dictatorially
autocratically
democratically
lackadaisically

i'm not sure we are talking about group building and we need to give examples of how to govern groups and i wasn't understanding exactly. does this mean how to set it up and authoritate?

Are you talking about cooperative groups in a classroom? Faculty groups for curriculum writing? Or what?

I'm not sure "authoritate" (whatever that is) is appropriate. Governing a group can be done any of the ways I listed above. Look them up in a dictionary.

cooperative groups

Cooperative groups can be governed

dictatorially
autocratically
democratically
lackadaisically

Dictatorially and autocratically are synonyms. What do you mean by each?