66.4 Printing Tables of Marks

The default ViewObj (see ViewObj) method for tables of marks prints the string "TableOfMarks", followed by --if known-- the identifier (see Identifier) or the group of the table of marks enclosed in brackets; if neither group nor identifier are known then just the number of conjugacy classes of subgroups is printed instead.

The default PrintObj (see PrintObj) method for tables of marks does the same as ViewObj, except that the group is is Print-ed instead of View-ed.

The default Display (see Display) method for a table of marks tom produces a formatted output of the marks in tom. Each line of output begins with the number of the corresponding class of subgroups. This number is repeated if the output spreads over several pages. The number of columns printed at one time depends on the actual line length, which can be accessed and changed by the function SizeScreen (see SizeScreen).

The optional second argument arec of Display can be used to change the default style for displaying a character as shown above. arec must be a record, its relevant components are the following.

classes

a list of class numbers to select only the rows and columns of the matrix that correspond to this list for printing,

form

one of the strings "subgroups", "supergroups"; in the former case, at position (i,j) of the matrix the number of conjugates of H_j contained in H_i is printed, and in the latter case, at position (i,j) the number of conjugates of H_i which contain H_j is printed.

gap> tom:= TableOfMarks( "A5" );;
gap> Display( tom );
1:  60
2:  30 2
3:  20 . 2
4:  15 3 . 3
5:  12 . . . 2
6:  10 2 1 . . 1
7:   6 2 . . 1 . 1
8:   5 1 2 1 . . . 1
9:   1 1 1 1 1 1 1 1 1

gap> Display( tom, rec( classes:= [ 1, 2, 3, 4, 8 ] ) );
1:  60
2:  30 2
3:  20 . 2
4:  15 3 . 3
8:   5 1 2 1 1

gap> Display( tom, rec( form:= "subgroups" ) );
1:  1
2:  1  1
3:  1  .  1
4:  1  3  . 1
5:  1  .  . . 1
6:  1  3  1 . .  1
7:  1  5  . . 1  . 1
8:  1  3  4 1 .  . . 1
9:  1 15 10 5 6 10 6 5 1

gap> Display( tom, rec( form:= "supergroups" ) );
1:   1
2:  15 1
3:  10 . 1
4:   5 1 . 1
5:   6 . . . 1
6:  10 2 1 . . 1
7:   6 2 . . 1 . 1
8:   5 1 2 1 . . . 1
9:   1 1 1 1 1 1 1 1 1

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