Almost solvable group

Symbol-free definition
A finite group is termed almost solvable if it satisfies the following equivalent conditions:


 * The quotient by its solvable radical is either trivial, or isomorphic to the alternating group on five letters
 * The group is a $$M_4$$-group: every irreducible character is induced from a character on a subgroup of dimension at most $$4$$

Stronger properties

 * Finite solvable group