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