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( () ) )
GAP 3.4.4