GAP Manual: 47.4. TableOfMarks

TableOfMarks( str )

If the argument str given to TableOfMarks is a string then TableOfMarks will search the library of tables of marks (see The Library of Tables of Marks) for a table with name str. If such a table is found then TableOfMarks will return a copy of that table. Otherwise TableOfMarks will return false. 

    gap> a5 := TableOfMarks( "A5" );
    rec(
      derivedSubgroup := 9,
      normalizer := [ 9, 4, 6, 8, 7, 6, 7, 8, 9 ],
      nrSubs := [ [ 1 ], [ 1, 1 ], [ 1, 1 ], [ 1, 3, 1 ], [ 1, 1 ],
          [ 1, 3, 1, 1 ], [ 1, 5, 1, 1 ], [ 1, 3, 4, 1, 1 ],
          [ 1, 15, 10, 5, 6, 10, 6, 5, 1 ] ],
      order := [ 1, 2, 3, 4, 5, 6, 10, 12, 60 ],
      subs := [ [ 1 ], [ 1, 2 ], [ 1, 3 ], [ 1, 2, 4 ], [ 1, 5 ],
          [ 1, 2, 3, 6 ], [ 1, 2, 5, 7 ], [ 1, 2, 3, 4, 8 ],
          [ 1, 2, 3, 4, 5, 6, 7, 8, 9 ] ],
      length := [ 1, 15, 10, 5, 6, 10, 6, 5, 1 ] )
    gap> TableOfMarks( "A10" );
    #W  TableOfMarks: no table of marks A10 found.
    false

TableOfMarks( grp )

If TableOfMarks is called with a group grp as its argument then the table of marks of that group will be computed and returned in the compressed format. The computation of the table of marks requires the knowledge of the complete subgroup lattice of the group grp. If the lattice is not yet known then it will be constructed (see Lattice). This may take a while if the group grp is large.

Moreover, as the Lattice command is involved the applicability of TableOfMarks underlies the same restrictions with respect to the soluble residuum of grp as described in section Lattice. The result of TableOfMarks is assigned to the component tableOfMarks of the group record grp, so that the next call to TableOfMarks with the same argument can just return this component tableOfMarks.

Warning: Note that TableOfMarks has changed with the release GAP 3.2. It now returns the table of marks in compressed form. However, you can apply the MatTom command (see MatTom) to convert it into the square matrix which was returned by TableOfMarks in GAP version 3.1. 

    gap> alt5 := AlternatingPermGroup( 5 );;
    gap> TableOfMarks( alt5 );
    rec(
      subs := [ [ 1 ], [ 1, 2 ], [ 1, 3 ], [ 1, 2, 4 ], [ 1, 5 ],
          [ 1, 2, 3, 6 ], [ 1, 2, 5, 7 ], [ 1, 2, 3, 4, 8 ],
          [ 1, 2, 3, 4, 5, 6, 7, 8, 9 ] ],
      marks := [ [ 60 ], [ 30, 2 ], [ 20, 2 ], [ 15, 3, 3 ], [ 12, 2 ],
          [ 10, 2, 1, 1 ], [ 6, 2, 1, 1 ], [ 5, 1, 2, 1, 1 ],
          [ 1, 1, 1, 1, 1, 1, 1, 1, 1 ] ] )
    gap> last = alt5.tableOfMarks;
    true

For a pretty print display of a table of marks see DisplayTom.

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