Gamma group

Definition with symbols
A finite non-Abelian group $$G$$ is termed a $$\Gamma$$-group if $$G = NP$$ where $$N$$ is a normal elementary Abelian 2-subgroup and $$P$$ is a cyclic group of prime order acting irreducibly on $$N$$ (in other words, no proper subgroup of $$N$$ is $$P$$-invariant).