4 August 1996
Dear GAP-Forum,

it's necessary for me to have "Class Multiplication Coefficients" in an algebra
of classes of some finite permutation group G. Of course, I can use GAP-command
"ClassMultCoeffCharTable", but in this GAP-command it's necessary to point out
some "CharTable". For example in GAP-manual there is a sample:
t:=CharTable("L3(2)");;
ClassMultCoeffCharTable(t,2,2,4);

How can I avoid an use of "CharTable"? For example, I have Conjugacy Classes
which was computed with help of GAP-command "ConjugacyClasses(G)" or with help
of any other, for example my own, GAP-function.

Yesterday I wrote a GAP-function for a calculation of Class Multiplication
Coefficients for the group Mathieu M12. I use a straightforward algorithm.
Let a1 and a2 be elements from group G. Let CCl be the conjugacy class with
element a2. With help of GAP-command Elements(CCl) I look over all elements a3
from conjugacy class CCl and calculate a product a1*a3. For all a1*a3 I find
a conjugacy class with a1*a3 with help GAP-command "IsConjugate". After the
calculation of multiplicity for all the conjugacy classes I can receive Class
Multiplication Coefficients by means of simple arithmetic with orders of the
conjugacy classes. My IBM-computer has a number GAPstones equal 3223. For two
conjugacy classes with 396 and 495 elements from M12 my computer calculated the
Class Multiplication Coefficients about a half of an hour. For two conjugacy
classes with 9504 and 11880 elements from M12 my computer calculated the Class
Multiplication Coefficients more than eight hours (the whole night) and nothing.
At morning I stoped the calculations. Alas! And so my second question:
how can I calculate Class Multiplication Coefficients more fast?

These two questions are important for me, but soon (9 august) I shall go away
to Ukraine. I shall back in St.-Petersburg at the end of August.

Sincerely yours,
Anatolii^ V. Rukolaine.

My home E-mail: rukolaha@tower.hop.stu.neva.ru