I want to collect the table elements and create a new table. (lua)

I can't find a similar case. Please Help! (lua)

input :

table1={'a','b','c','d','e'}
table2={'aa','bb','cc','dd','ee'}
table3={'aaa','bbb','ccc','ddc','eee'}
...

output :

group1={'a','aa','aaa',...}
group2={'b','bb','bbb',...}
group3={'c','cc','ccc',...}
group4={'d','dd','ddd',...}
group5={'e','ee','eee',...}

Assuming your problem is to group strings made up of different amounts of the same character, I managed to come up with a function I called agroupTables().

The function:

function agroupTables(tableOfTables)
  local existentChars = {}
  local agroupedItems = {} 
  for i, currentTable in ipairs(tableOfTables) do
    for j, item in ipairs(currentTable) do
      local character = string.sub(item, 1, 1) -- get the first character of the current item

      if not table.concat(existentChars):find(character) or i == 1 then -- checks if character is already in existentChars
        table.insert(existentChars, 1, character) 
        table.insert(agroupedItems, 1, {item})     
      else       
        for v, existentChar in ipairs(existentChars) do
          if item :find(existentChar) then -- check in which group the item should be inserted
            table.insert(agroupedItems[v], 1, item)
            table.sort(agroupedItems[v]) -- sort by the number of characters in the item
          end
        end
      end
    end
  end
  return agroupedItems 
end

Usage example

table1 = {'aa','b','c','d','e'}
table2 = {'a','bb','cc','dd','ee'}
table3 = {'aaa','bbb','ccc','ddd','eee', 'z'}

agroupedTables = agroupTables({table1, table2, table3})

for i, v in ipairs(agroupedTables) do
  print("group: ".. i .." {")
  for k, j in ipairs(v) do
    print("  " .. j)
  end
  print("}")
end 

output:

group: 1 {
   z
}
group: 2 {
   e
   ee
   eee
}
group: 3 {
   d
   dd
   ddd
}
group: 4 {
   c
   cc
   ccc
}
group: 5 {
   b
   bb
   bbb
}
group: 6 {
   a
   aa
   aaa
}