Reference for group cohomology

Mentioned early Brown's Cohomology of groups is probably best as introductory reference

There are some books which I like and are not widely known.

• Adem, Milgram, Cohomology of finite groups — contains rarely mentioned in most basic group theory textbooks Quillen-Venkov and Kan-Thurston theorems, and applications in number theory (Brauer grous etc.)

• Karpilovsky, Group representations, p. 2 — half of book is devoted to detailed analysis of second cohomology group and its properties

• Stammbach, Homology in Group Theory — here extensions with abelian kernel within a given group variety are discussed

• Gruenberg, Cohomological Topics in Group Theory and

• Gruenberg, Categories of group extensions — in some sense, more accessible (and extended) versions of previous text

• Ю. Кузьмин, Гомологическая теория групп — unfortunately no English translation exists, but you can look at formulas in ch. 4 §8 and ch. 5 §7 or try it with translator (mathematical texts are not very hard to translate usually)