GAP Manual: 48.46. StoreFusion

StoreFusion( source, destination, fusion )
StoreFusion( source, destination, fusionmap )

For character tables source and destination, fusion must be a record containing at least the field map which is regarded as a fusion from source to destination. fusion is stored on source if no ambiguity arises, i.e. if there is not yet a fusion into destination stored on source or if any fusion into destination stored on source has a specification field different from that of fusion. The map field of fusion is adjusted by destination.permutation. (Thus the map will remain correct even if the classes of a concerned table are sorted, see SortClassesCharTable and Conventions for Character Tables; the correct fusion can be got using GetFusionMap, so be careful!). Additionally, source.identifier is added to destination.fusionsource.

The second form works like the first, with fusion = rec( map:= fusionmap ).

    gap> s:= CharTable( "A6.2_1" );; t:= CharTable( "A7.2" );;
    gap> fus:= RepresentativesFusions( s, SubgroupFusions( s, t ), t );
    [ [ 1, 2, 3, 4, 5, 6, 9, 10, 11, 12, 13 ] ]
    gap> s.fusions; t.fusionsource;
    [  ]
    [ "2.A7.2", "3.A7.2", "6.A7.2", "A7" ]
    gap> StoreFusion( s, t, fus[1] );
    gap> s.fusions; t.fusionsource;
    [ rec(
          name := "A7.2",
          map := [ 1, 2, 3, 4, 5, 6, 9, 10, 11, 12, 13 ] ) ]
    [ "2.A7.2", "3.A7.2", "6.A7.2", "A6.2_1", "A7" ]