54.6 TestQuasiPrimitive

TestQuasiPrimitive( chi )

returns a record with information about quasiprimitivity of the character chi of the group G (i.e., whether chi restricts homogeneously to every normal subgroup of G).

The record contains the components

isQuasiPrimitive:

true or false,

comment:

a string telling a reason for the value of the isQuasiPrimitive component,

character:

an irreducible constituent of a nonhomogeneous restriction of chi, bound only if chi is not quasi-primitive.

IsQuasiPrimitive( chi )

returns true or false, depending on whether the character chi of the group G is quasiprimitive.

    gap> chi:= Irr( Sl23 )[4];
    Character( Sl(2,3), [ 2, -2, 0, -1, 1, -1, 1 ] )
    gap> TestQuasiPrimitive( chi );
    #W  Warning: Group has no name
    rec(
      isQuasiPrimitive := true,
      comment := "all restrictions checked" )
    gap> chi:= Irr( Sl23 )[7];
    Character( Sl(2,3), [ 3, 3, -1, 0, 0, 0, 0 ] )
    gap> TestQuasiPrimitive( chi );
    rec(
      isQuasiPrimitive := false,
      comment := "restriction checked",
      character := Character( Subgroup( Sl(2,3), [ b, c, d ] ), 
        [ 1, 1, -1, 1, -1 ] ) ) 

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