This is the 626th most frequent Icelandic word.
hópnum
"Group" (dative singular form).
Here, "hópnum" is used as the beneficiary of the trip, functioning as the dative case in this sentence.
Við skipulögðum ferð fyrir hópnum til fjalla.
We organized a trip for the group to the mountains.
In this instance, "hópnum" represents possession or association in a dative construct, indicating who the laughter belonged to.
Hlátur hópnum fyllti herbergið.
The laughter of the group filled the room.
"Hópnum" is the dative singular form of "hópur" (group), used here as the indirect object of the verb "koma ... saman" (to bring ... together).