Group elements are the Rare Earth Elements or Metals, which currently hasn't a group number. Group numbers were originally designed by the IUPAC. They go from 1 to 18. The rare earth metals are left out because they have too similar chemical properties and grouping is unnecessary.
These elements include: Lanthanum, Cerium, Praseodymium, Neodymium, Promethium, Samarium, Europium, Gadolinium, Terbium, Dysprosium, Holmium, Erbium, Thulium and Ytterbium of the Lanthanides; and Actinium, Thorium, Protactinium, Uranium, Neptunium, Plutonium, Americium, Curium, Berkelium, Californium, Einsteinium, Fermium, Mendelevium, Nobelium and Lawrencium of the Actinides.