Geodesic
On the number of finite groups with a~given automorphism group
Sbornik. Mathematics, Tome 12 (1970) no. 4, pp. 521-524

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In this article, the following theorem is proved. Theorem. There exist only a finite number of pairwise nonisomorphic finite groups having at most a given number of automorphisms. Bibliography: 2 titles. 
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     author = {V. T. Nagrebetskii},
     title = {On the number of finite groups with a~given automorphism group},
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V. T. Nagrebetskii. On the number of finite groups with a~given automorphism group. Sbornik. Mathematics, Tome 12 (1970) no. 4, pp. 521-524. http://geodesic.mathdoc.fr/item/SM_1970_12_4_a2/