50.23 InducedCyclic

InducedCyclic( tbl )
InducedCyclic( tbl, "all" )
InducedCyclic( tbl, classes )
InducedCyclic( tbl, classes, "all" )

returns a set of characters of the character table tbl. They are characters induced from cyclic subgroups of tbl. If "all" is specified, all irreducible characters of those subgroups are induced, otherwise only the permutation characters are computed. If a list classes is specified, only those cyclic subgroups generated by these classes are considered, otherwise all classes of tbl are considered.

Note that the powermaps for primes dividing tbl.order must be stored on tbl; if any powermap for a prime not dividing tbl.order that is smaller than the maximal representative order is not stored, this map will be computed (see Powermap) and stored afterwards.

More about Maps and Parametrized Maps); any value that is not uniquely determined in an induced character is set to an unknown (see Unknown). The representative orders of the classes to induce from must not be parametrized (see More about Maps and Parametrized Maps).

    gap> t:= CharTable( "A5" );; InducedCyclic( t, "all" );
    [ [ 12, 0, 0, 2, 2 ], [ 12, 0, 0, E(5)^2+E(5)^3, E(5)+E(5)^4 ],
      [ 12, 0, 0, E(5)+E(5)^4, E(5)^2+E(5)^3 ], [ 20, 0, -1, 0, 0 ],
      [ 20, 0, 2, 0, 0 ], [ 30, -2, 0, 0, 0 ], [ 30, 2, 0, 0, 0 ],
      [ 60, 0, 0, 0, 0 ] ]

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