Direct product of A5 and Z7

Definition
This group is defined as the defining ingredient::external direct product of defining ingredient::alternating group:A5 (a simple non-abelian group of order 60) and cyclic group:Z7 (a group of order 7).

It is the smallest example of a non-solvable group that is a p-solvable group for some prime number $$p$$ dividing its order (in this case, $$p = 7$$). In fact, the group is a p-nilpotent group for $$p = 7$$.