48.29 ClassNamesCharTable

ClassNamesCharTable( tbl )

ClassNamesCharTable computes names for the classes of the character table tbl as strings consisting of the order of an element of the class and and least one distinguishing letter.

The list of these names at the same time is returned by this function and stored in the table tbl as record component classnames.

Moreover for each class a component with its name is constructed, containing the position of this name in the list classnames as its value.

    gap> c3:= CharTable( "Cyclic", 3 );;
    gap> ClassNamesCharTable( c3 );
    [ "1a", "3a", "3b" ]
    gap> PrintCharTable( c3 );
    rec( identifier := "C3", name := "C3", size := 3, order :=
    3, centralizers := [ 3, 3, 3 ], orders := [ 1, 3, 3 ], powermap :=
    [ ,, [ 1, 1, 1 ] ], irreducibles :=
    [ [ 1, 1, 1 ], [ 1, E(3), E(3)^2 ], [ 1, E(3)^2, E(3) ]
     ], classparam := [ [ 1, 0 ], [ 1, 1 ], [ 1, 2 ] ], irredinfo :=
    [ rec(
          charparam := [ 1, 0 ] ), rec(
          charparam := [ 1, 1 ] ), rec(
          charparam := [ 1, 2 ] )
     ], text := "computed using generic character table for cyclic groups"\
    , classes := [ 1, 1, 1 ], operations := CharTableOps, fusions :=
    [  ], fusionsource := [  ], projections := [  ], projectionsource :=
    [  ], classnames := [ "1a", "3a", "3b" ], 1a := 1, 3a := 2, 3b := 3 )

If the record component classnames of tbl is unbound, ClassNamesCharTable is automatically called by DisplayCharTable (see DisplayCharTable).

Note that once the class names are computed the resulting record fields are stored on tbl. They are not deleted by another call of ClassNamesCharTable.

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