Yes, they do if they are of similar shape and size. For example, Corydoras sterbai, Corydoras panda, Corydoras trilineatus will all school together.
But don't expect Corydoras fowleri (Long sharp nose type, about 8 to 10 cm), Corydoras metae (round headed type, about 5 cm) and Corydoras pygmaeus (dwarf type, about 3 cm) to hang out together.
Hope that helps. Which species exactly did you get anyway? Most of the comon ones should be fine.
Cheers,
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