53.6 VirtualCharacter

VirtualCharacter( G, values )

returns the virtual character of the group G with values list values.

VirtualCharacter( G, chi )

returns the virtual character of G corresponding to the virtual character chi of H. The group H can be a factor group of G, or G can be a subgroup or factor group of H.

    gap> syl2:= SylowSubgroup( S4, 2 );;
    gap> psi:= VirtualCharacter( S4, [ 0, 0, 3, 0, 0 ] );
    VirtualCharacter( S4, [ 0, 0, 3, 0, 0 ] )
    gap> VirtualCharacter( syl2, psi );
    VirtualCharacter( D8, [ 0, 0, 0, 0, 0 ] )
    gap> S3:= S4 / V4;
    Group( a, b )
    gap> VirtualCharacter( S3, irr[3] );
    VirtualCharacter( Group( a, b ), [ 2, -1, 0 ] ) 

Note that it is not checked whether the result is really a virtual character.

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