Elementary group
Direct product of a p-group and a cyclic group of coprime order
In algebra, more specifically group theory, a p-elementary group is a direct product of a finite cyclic group of order relatively prime to p and a p-group. A finite group is an elementary group if it is p-elementary for some prime number p. An elementary group is nilpotent.
Brauer's theorem on induced characters states that a character on a finite group is a linear combination with integer coefficients of characters induced from elementary subgroups.
More generally, a finite group G is called a p-hyperelementary if it has the extension
where 
Sources and credits
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