Note that calling this function will cause the computation of factor groups of G , so it works efficiently only for AG groups. N may be given also as list of conjugacy class positions w.r. to G . If chi is the only argument then it is checked whether there is a maximal normal subgroup of G from that chi is induced. If there is a second argument N , a normal subgroup of G , then it is checked whether chi is induced from N . N may also be given as the list of positions of conjugacy classes contained in the normal subgroup in question.
G is subnormally monomial.
G are monomial. A group G is proved to be monomial by TestMonomialQuick if its order is not divisible by the third power of a prime, or if G is nilpotent or Sylow abelian by supersolvable. Nonsolvable groups are proved to me nonmonomial by TestMonomialQuick . An irreducible character is proved to be monomial if it is linear, or if its codegree is a prime power, or if its group knows to be monomial, or if the factor group modulo the kernel can be proved to be monomial by TestMonomialQuick . If chi or G is proved to be nonmonomial the component isMonomial is false , and in the case of G a nonmonomial character is contained in the component character if it had been necessary to compute it.