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== Properties == A complete group is always [[group isomorphism|isomorphic]] to its [[automorphism group]] (via sending an element to conjugation by that element), although the converse need not hold: for example, the [[dihedral group]] of 8 elements is isomorphic to its automorphism group, but it is not complete. For a discussion, see {{harv|Robinson|1996|loc=section 13.5}}.
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