Let G be a group and denote its Frattini subgroup by Φ(G). I know that Φ(G) is the intersection of the maximal subgroups of G, and I know that it is the set of 'non-generators'
Can we compute frattini sub group for any group ? For example we can find frattini sub group for any cyclic group . What is history of frattini subgroup ? Why frattini sub group is important?