CharTablePGroup( G )
CharTablePGroup returns the character table of the finite polycyclic
group G, and stores it in G.charTable. Do not change the order of
G.conjugacyClasses after having called CharTablePGroup.
Let G be a finite polycyclic group with an abelian normal subgroup N
such that the factorgroup <G> / <N> is supersolvable.
CharTablePGroup uses the algorithm described in Bau91.
If G has not the property stated above, a system of representatives of
irreducible representations and characters only for the factor group <G>
/ <M> can be computed using this algorithm, where M is the derived
subgroup of the supersolvable residuum of G. In this case first a
warning is printed. CharTablePGroup returns an incomplete table
containing exactly those irreducibles with kernel containing M.
gap> t:= CharTablePGroup( SolvableGroup( 8, 4 ) );;
gap> PrintCharTable( t );
rec( size := 8, centralizers := [ 8, 8, 4, 4, 4 ], classes :=
[ 1, 1, 2, 2, 2 ], orders := [ 1, 2, 2, 2, 4 ], irreducibles :=
[ [ 1, 1, 1, 1, 1 ], [ 1, 1, -1, 1, -1 ], [ 1, 1, 1, -1, -1 ],
[ 1, 1, -1, -1, 1 ], [ 2, -2, 0, 0, 0 ]
], operations := CharTableOps, order := 8, powermap :=
[ , [ 1, 1, 1, 1, 2 ]
], identifier := "D8", name := "D8", group := D8 )
MatRepresentationsPGroup can be used to compute representatives of
the complex irreducible representations (see MatRepresentationsPGroup).
GAP 3.4.4