ClearAll[FindPeriodGroup]
FindPeriodGroup[n_Integer] := Which[57 <= n <= 70,
  {8, n - 53}
  ,
  89 <= n <= 102,
  {9, n - 85}
  ,
  1 <= n <= 118,
  {ElementData[n, "Period"], ElementData[n, "Group"]}
  ,
  True,
  Missing["Element does not exist"]
]
Row[{"Element ", #, " -> ", FindPeriodGroup[#]}] & /@ {1, 2, 29, 42, 57, 58, 59, 71, 72, 89, 90, 103, 113} // Column
Graphics[Text[#, {1, -1} Reverse@FindPeriodGroup[#]] & /@ Range[118]]