GAP Manual: 48.42. TableAutomorphisms

TableAutomorphisms( tbl, chars )
TableAutomorphisms( tbl, chars, "closed" )

returns a permutation group record for the group of those matrix automorphisms of chars (see MatAutomorphisms) which are admissible by (i.e. which fix) the fields orders and all uniquely determined (i.e. not parametrized) maps in powermap of the character table tbl; the action on orders is the natural permutation, that on the powermaps is conjugation.

If chars is closed under galois conjugacy --this is always satisfied for ordinary character tables-- the parameter "closed" may be entered. In that case the subgroup of Galois automorphisms is computed by GaloisMat GaloisMat.

    gap> t:= CharTable( "Dihedral", 8 );; # as in "MatAutomorphisms"
    gap> TableAutomorphisms( t, t.irreducibles );
    Group( (4,5) )