48.24 CharTableSSGroup

CharTableSSGroup( G )

CharTableSSGroup returns the character table of the supersolvable ag-group G and stores it in G.charTable. If G is not supersolvable not all irreducible characters migth be calculated and a warning will be printed out. The algorithm bases on Con90a and Con90b.

All the characters calculated are monomial, so they are the induced of a linear character of some subgroup of G. For every character the subgroup it is induced from and the kernel the linear character has are written down in t.irredinfo[i].inducedFrom.subgroup and t.irredinfo[i].inducedFrom.kernel.

    gap> t:= CharTableSSGroup( SolvableGroup( 8 , 5 ) );;
    gap> PrintCharTable( t );
    rec( size := 8, classes := [ 1, 1, 2, 2, 2 ], powermap :=
    [ , [ 1, 1, 2, 2, 2 ]
     ], operations := CharTableOps, group := Q8, 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 ] ], orders :=
    [ 1, 2, 4, 4, 4 ], irredinfo := [ rec(
          inducedFrom := rec(
              subgroup := Q8,
              kernel := Q8 ) ), rec(
          inducedFrom := rec(
              subgroup := Q8,
              kernel := Subgroup( Q8, [ b, c ] ) ) ), rec(
          inducedFrom := rec(
              subgroup := Q8,
              kernel := Subgroup( Q8, [ a, c ] ) ) ), rec(
          inducedFrom := rec(
              subgroup := Q8,
              kernel := Subgroup( Q8, [ a*b, c ] ) ) ), rec(
          inducedFrom := rec(
              subgroup := Subgroup( Q8, [ b, c ] ),
              kernel := Subgroup( Q8, [  ] ) ) ) ], order :=
    8, centralizers := [ 8, 8, 4, 4, 4
     ], identifier := "Q8", name := "Q8" )

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