The glyph is a canonical composition of the glyphs Glyph for U+0055Latin Capital Letter U, Glyph for U+0308Combining Diaeresis. It has no designated width in East Asian texts. In bidirectional text it is written from left to right. When changing direction it is not mirrored. The word that U+00DC forms with similar adjacent characters prevents a line break inside it.
The Wikipedia has the following information about this codepoint:
Ü (lowercase ü) is a Latin script character composed of the letter U and the diaeresis diacritical mark. In some alphabets such as those of a number of Romance languages or Guarani it denotes an instance of regular U to be construed in isolation from adjacent characters with which it would usually form a larger unit; other alphabets like the Azerbaijani, Estonian, German, Hungarian and Turkish ones treat it as a letter in its own right. In those cases it typically represents a close front rounded vowel [y] .
Although not a part of their alphabet, Ü also appears in languages such as Finnish and Swedish when retained in foreign proper names like München ("Munich"). A small number of Dutch and Afrikaans words employ the character to mark vowel hiatus (e.g. reünie /reːyˈni/ ("reunion"), a loanword marked with diaeresis to suppress the native reading of eu as a digraph pronounced /øː/).