GAP Manual: 48.22. CharTableCollapsedClasses

CharTableCollapsedClasses( tbl, fusionmap )

returns a character table where all classes of the character table tbl with equal images under the map fusionmap are collapsed; the fields orders, classes, and the characters in irreducibles are the images under fusionmap, the powermaps are obtained on conjugation (see TransferDiagram) with fusionmap, order remains unchanged, and centralizers arise from classes and order.

The fusion to the returned table is stored on tbl.

    gap> c3:= CharTable( "Cyclic", 3 );;
    gap> t:= CharTableSplitClasses( c3, [ 1, 2, 2, 3, 3 ] );;
    gap> PrintCharTable( t );
    rec( identifier := "Split(C3,[ 1, 2, 2, 3, 3 ])", size := 3, order :=
    3, name := "Split(C3,[ 1, 2, 2, 3, 3 ])", centralizers :=
    [ 3, 6, 6, 6, 6 ], classes := [ 1, 1/2, 1/2, 1/2, 1/2 ], orders :=
    [ 1, 3, 3, 3, 3 ], powermap := [ ,, [ 1, 1, 1, 1, 1 ]
     ], irreducibles :=
    [ [ 1, 1, 1, 1, 1 ], [ 1, E(3), E(3), E(3)^2, E(3)^2 ],
      [ 1, E(3)^2, E(3)^2, E(3), E(3) ] ], fusions := [ rec(
          name := "C3",
          map := [ 1, 2, 2, 3, 3 ] ) ], operations := CharTableOps )
    gap> c:= CharTableCollapsedClasses( t, [ 1, 2, 2, 3, 3 ] );;
    gap> PrintCharTable( c );
    rec( identifier := "Collapsed(Split(C3,[ 1, 2, 2, 3, 3 ]),[ 1, 2, 2, 3\
    , 3 ])", size := 3, order :=
    3, name := "Collapsed(Split(C3,[ 1, 2, 2, 3, 3 ]),[ 1, 2, 2, 3, 3 ])",\
     centralizers := [ 3, 3, 3 ], orders := [ 1, 3, 3 ], powermap :=
    [ ,, [ 1, 1, 1 ] ], fusionsource := [ "Split(C3,[ 1, 2, 2, 3, 3 ])"
     ], irreducibles := [ [ 1, 1, 1 ], [ 1, E(3), E(3)^2 ],
      [ 1, E(3)^2, E(3) ] ], classes :=
    [ 1, 1, 1 ], operations := CharTableOps )

The inverse process of fusion is the splitting of classes, see CharTableSplitClasses.