ClassNamesTom( tom )
ClassNamesTom constructs generic names for the conjugacy classes of
subgroups of the table of marks tom.
In general, the generic name of a class of non--cyclic subgroups consists
of three parts, "(order)", "_{type}", and "letter",
and hence has the form "(order)_{type}letter", where order
indicates the order of the subgroups, type is a number that
distinguishes different types of subgroups of the same order, and
letter is a letter which distinguishes classes of subgroups of the same
type and order. The type of a subgroup is determined by the numbers of
its subgroups of other types (see ClassTypesTom). This is slightly
weaker than isomorphism.
The letter is omitted if there is only one class of subgroups of that order and type, and the type is omitted if there is only one class of that order. Moreover, the braces round the type are omitted if the type number has only one digit.
For classes of cyclic subgoups, the parentheses round the order and the
type are omitted. Hence the most general form of their generic names is
"order,letter". Again, the letter is omitted if there is only
one class of cyclic subgroups of that order.
gap> ClassNamesTom( a6 );
[ "1", "2", "3a", "3b", "5", "4", "(4)_2a", "(4)_2b", "(6)a", "(6)b",
"(9)", "(10)", "(8)", "(12)a", "(12)b", "(18)", "(24)a", "(24)b",
"(36)", "(60)a", "(60)b", "(360)" ]
GAP 3.4.4