Hyperelementary group (reviewed)

A finite group $G$ is hyperelementary if it is an extension $G \simeq C \rtimes P$ of a $p$-group $P$ by a cyclic group $C$ of order prime to $p$. Solomon's induction theorem states that the trivial character is an integer linear combination of inductions of trivial characters from hyperelementary subgroups of $G$ (for various primes dividing the order of $G$).