GAP Manual: 48.39. SortClassesCharTable

SortClassesCharTable( tbl )
SortClassesCharTable( tbl, "centralizers" )
SortClassesCharTable( tbl, "representatives" )
SortClassesCharTable( tbl, permutation )
SortClassesCharTable( chars, permutation )

The last form simply permutes the classes of all elements of chars with permutation. All other forms take a character table tbl as parameter, and SortClassesCharTable permutes the classes of tbl:

SortClassesCharTable( tbl, "centralizers" ):
sorts the classes according to descending centralizer orders,

SortClassesCharTable( tbl, "representatives" ):
sorts the classes according to ascending representative orders,

SortClassesCharTable( tbl ):
sorts the classes according to ascending representative orders, and classes with equal representative orders according to descending centralizer orders,

SortClassesCharTable( tbl, permutation ):
sorts the classes by application of permutation

After having calculated the permutation, SortClassesCharTable will adjust the following fields of tbl:

by application of the permutation: orders, centralizers, classes, print, all entries of irreducibles, classtext, classparam, classnames, all fusion maps, all entries of the chars lists in the records of projectives

by conjugation with the permutation: all powermaps, automorphisms,

by multiplication with the permutation: permutation,

and the fields corresponding to tbl.classnames (see ClassNamesCharTable).

The applied permutation is returned by SortClassesCharTable.

Note that many programs expect the class 1A to be the first one (see Conventions for Character Tables).

    gap> t:= CharTable( "Symmetric", 5 );;
    gap> PrintCharTable( t );
    rec( identifier := "S5", name := "S5", size := 120, order :=
    120, centralizers := [ 120, 12, 8, 6, 6, 4, 5 ], orders :=
    [ 1, 2, 2, 3, 6, 4, 5 ], powermap :=
    [ , [ 1, 1, 1, 4, 4, 3, 7 ], [ 1, 2, 3, 1, 2, 6, 7 ],,
      [ 1, 2, 3, 4, 5, 6, 1 ] ], irreducibles :=
    [ [ 1, -1, 1, 1, -1, -1, 1 ], [ 4, -2, 0, 1, 1, 0, -1 ],
      [ 5, -1, 1, -1, -1, 1, 0 ], [ 6, 0, -2, 0, 0, 0, 1 ],
      [ 5, 1, 1, -1, 1, -1, 0 ], [ 4, 2, 0, 1, -1, 0, -1 ],
      [ 1, 1, 1, 1, 1, 1, 1 ] ], classparam :=
    [ [ 1, [ 1, 1, 1, 1, 1 ] ], [ 1, [ 2, 1, 1, 1 ] ], [ 1, [ 2, 2, 1 ] ],
      [ 1, [ 3, 1, 1 ] ], [ 1, [ 3, 2 ] ], [ 1, [ 4, 1 ] ], [ 1, [ 5 ] ]
     ], irredinfo := [ rec(
          charparam := [ 1, [ 1, 1, 1, 1, 1 ] ] ), rec(
          charparam := [ 1, [ 2, 1, 1, 1 ] ] ), rec(
          charparam := [ 1, [ 2, 2, 1 ] ] ), rec(
          charparam := [ 1, [ 3, 1, 1 ] ] ), rec(
          charparam := [ 1, [ 3, 2 ] ] ), rec(
          charparam := [ 1, [ 4, 1 ] ] ), rec(
          charparam := [ 1, [ 5 ] ] )
     ], text := "computed using generic character table for symmetric grou\
    ps", classes := [ 1, 10, 15, 20, 20, 30, 24
     ], operations := CharTableOps )
    gap> SortClassesCharTable( t, "centralizers" );
    (6,7)
    gap> SortClassesCharTable( t, "representatives" );
    (5,7)
    gap> t.centralizers; t.orders;
    [ 120, 12, 8, 6, 4, 5, 6 ]
    [ 1, 2, 2, 3, 4, 5, 6 ]