| Wonderstell |
A Doppelganger is immune to sleep and charm effects. From the magic school descriptions, we can tell that Charm and Compulsion are two different subschools of the Enchantment school.
All enchantments are mind-affecting spells. Two subschools of enchantment spells grant you influence over a subject creature.
Subschools
Charm: A charm spell changes how the subject views you, typically making it see you as a good friend.
Compulsion: a compulsion spell forces the subject to act in some manner or changes the way its mind works. Some compulsion spells determine the subject's actions or the effects on the subject, others allow you to determine the subject's actions when you cast the spell, and still others give you ongoing control over the subject.
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Suggestion belongs to the Enchantment(Compulsion) school, so a Doppelganger is not immune to the spell Suggestion.