DSC Group numbers are assigned by a member of an organization, not the same agencies that assign MMSI numbers. The distinction of a Group number is that it starts with zero. You will see many entries in the Known Group numbers page use all eight digits as the Group number.
One big application of Group Numbers is for Yacht Clubs or boating fleets. A member of these organizations would define an eight-digit Group number. Some schemes could be the numbers associated with spelling of organization name as it would be entered on a telephone. A specific example would be an organization called Fairwind would have a Group number of 032479463 (remember, there is always a leading zero, which is often filled in by the radio when the Group number is entered). Hopefully, all members of this organization would have this same number entered in their DSC radio as a Group number. Then, if one member of this Group makes a Group call with this number, all other member’s radios would be notified when a call is made to this group. The other advantage is when the calling radio is placing the call, the working channel number is asked. Then, when all other radios are notified, they will be automatically switched to that working channel. Note that Group Calls may not be implemented in early designs of DSC radios. Also note, the action of automatically being switched to the working channel may be different in different radio models. Some radios ask the operator to manually acknowledge switching to the working channel.
Note, there is a special case of these numbers starting with zero, zero, as those are for US Coast Guard Base Station MMSI numbers.