DecomposedFixedPointVector( tom, fix )
Let the group with table of marks tom act as a permutation group on its
conjugacy classes of subgroups, then fix is assumed to be a vector of
fixed point numbers, i.e., a vector which contains for each class of
subgroups the number of fixed points under that action.
DecomposedFixedPointVector returns the decomposition of fix into rows
of the table of marks. This decomposition corresponds to a decomposition
of the action into transitive constituents. Trailing zeros in fix may
be omitted.
gap> DecomposedFixedPointVector( a5, [ 16, 4, 1, 0, 1, 1, 1 ] );
[ ,,,,, 1, 1 ]
The vector fix may be any vector of integers. The resulting decomposition, however, will not be integral, in general.
gap> DecomposedFixedPointVector( a5, [ 0, 0, 0, 0, 1, 1 ] );
[ 2/5, -1, -1/2,, 1/2, 1 ]
GAP 3.4.4