54.7 IsPrimitive for Characters

IsPrimitive( chi )

returns true if the irreducible character chi of the solvable group G is not induced from any proper subgroup of G, and false otherwise.

Note that an irreducible character of a solvable group is primitive if and only if it is quasi-primitive (see TestQuasiPrimitive).

    gap> IsPrimitive( Irr( Sl23 )[4] );
    true
    gap> IsPrimitive( Irr( Sl23 )[7] );
    false 

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