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" )
:
SortClassesCharTable( tbl, "representatives" )
:
SortClassesCharTable( tbl )
:
SortClassesCharTable( tbl, 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, fusions := [ ], fusionsource := [ ], projections := [ ], projectionsource := [ ] ) 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 ]
GAP 3.4.4