GAP Manual: 48.44. TransformingPermutationsCharTables

TransformingPermutationsCharTables( tbl1, tbl2 )

tries to construct a permutation pi that transforms the set of rows of tbl1.irreducibles to the set of rows of tbl2.irreducibles by permutation of columns (see TransformingPermutations) and that also transforms the powermaps and the orders field. If such a permutation exists, it returns a record with components columns (a valid permutation of columns), rows (the permutation of tbl.irreducibles corresponding to that permutation), and group (the permutation group record of table automorphisms of tbl2, see TableAutomorphisms). If no such permutation exists, it returns false.

    gap> t1:= CharTable("Dihedral",8);;t2:= CharTable("Quaternionic",8);;
    gap> TransformingPermutations( t1.irreducibles, t2.irreducibles );
    rec(
      columns := (),
      rows := (),
      group := Group( (4,5), (2,4) ) )
    gap> TransformingPermutationsCharTables( t1, t2 );
    false
    gap> t1:= CharTable( "Dihedral", 6 );; t2:= CharTable("Symmetric",3);;
    gap> TransformingPermutationsCharTables( t1, t2 );
    rec(
      columns := (2,3),
      rows := (1,3,2),
      group := Group( () ) )