66.5 Sorting Tables of Marks

SortedTom returns a table of marks where the rows and columns of the table of marks tom are reordered according to the permutation perm.

Note that in each table of marks in GAP, the matrix of marks is assumed to have lower triangular shape (see Table of Marks Objects in GAP). If the permutation perm does not have this property then the functions for tables of marks might return wrong results when applied to the output of SortedTom.

The returned table of marks has only those attribute values stored that are known for tom and listed in TableOfMarksComponents (see TableOfMarksComponents).

gap> tom:= TableOfMarksCyclic( 6 );;  Display( tom );
1:  6
2:  3 3
3:  2 . 2
4:  1 1 1 1

gap> sorted:= SortedTom( tom, (2,3) );;  Display( sorted );
1:  6
2:  2 2
3:  3 . 3
4:  1 1 1 1

gap> wrong:= SortedTom( tom, (1,2) );;  Display( wrong );
1:  3
2:  . 6
3:  . 2 2
4:  1 1 1 1

For the table of marks tom of the group G stored as UnderlyingGroup value of tom (see UnderlyingGroup), PermutationTom is a permutation p such that the i-th conjugacy class of subgroups of G belongs to the i^p-th column and row of marks in tom.

This attribute value is bound only if tom was obtained from another table of marks by permuting with SortedTom (see SortedTom), and there is no default method to compute its value.

The attribute is necessary because the original and the sorted table of marks have the same identifier and the same group, and information computed from the group may depend on the ordering of marks, for example the fusion from the ordinary character table of G into tom.

gap> MarksTom( tom )[2];
[ 3, 3 ]
gap> MarksTom( sorted )[2];
[ 2, 2 ]
gap> HasPermutationTom( sorted );
true
gap> PermutationTom( sorted );
(2,3)

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