GAP Manual: 48.47. FusionConjugacyClasses

FusionConjugacyClasses( subgroup, group )
FusionConjugacyClasses( group , factorgroup )

FusionConjugacyClasses returns a list denoting the fusion of conjugacy classes from the first group to the second one. If both groups have components charTable this list is written to the character tables, too.

    gap> g := SolvableGroup( 24, 14 );
    Sl(2,3)
    gap> FusionConjugacyClasses( g, g / Subgroup( g, [ g.4 ] ) );
    [ 1, 1, 2, 3, 3, 4, 4 ]
    gap> FusionConjugacyClasses( Subgroup( g, [ g.2, g.3, g.4 ] ), g );
    [ 1, 2, 3, 3, 3 ]