A table of marks is represented by a record. This record has at least a
component subs which is a list where for each conjugacy class of
subgroups the class numbers of its subgroups are stored. These are
exactly the positions in the corresponding row of the table of marks
which have nonzero entries.
The marks themselves can be stored in the component marks which is a
list that contains for each entry in the component subs the
corresponding nonzero value of the table of marks.
The same information is, however, given by the three components nrSubs,
length, and order, where nrSubs is a list which contains for each
entry in the component subs the corresponding number of conjugates
which are contained in a subgroup, length is a list which contains for
each class of subgroups its length, and order is a list which contains
for each class of subgroups their order.
So a table of marks consists either of the components subs and marks
or of the components subs, nrSubs, length, and order. The
functions Marks (see Marks) and NrSubs (see NrSubs) will derive
one representation from the other when needed.
Additional information about a table of marks is needed by some
functions. The class numbers of normalizers are stored in the component
normalizer. The number of the derived subgroup of the whole group is
stored in the component derivedSubgroup.
GAP 3.4.4