last week, Anatolii Rukolaine wrote
I tested two years ago the program to compute character table
described in the GAP-manual section Dixon-Schneider "An Example of Advanced
Calculations" and I had some problems for some finite groups, for example, for
G:=MathieuGroup(22) of Order 443520 and for G:=PrimitiveGroup(8,4) of Order 336
"...#Finally we calculate the characters induced from all cyclic subgroups
# and obtain the missing irreducibles by applying the LLL-algorithm to them."
and after GAP-commands:
ic:= InducedCyclic( c, "all" );;
ro:= ReducedOrdinary( c, c.irreducibles, ic );;
and before GAP-command:l:= LLL( c, ro.remainders );;
I received the message:
Error, List Element: <list> must have a value at
B := [ scpr( L, b, b ) ] ... in
LLLReducedBasis( arg, arg, y ) called from
LLL( c, ro.remainders ) called from
Thanks for reporting this deficiency of the command `LLL'.
In GAP 4, this function will accept also an empty list
as second argument.
Concerning the remarks about the manual section about
``An Example of Advanced Dixon Schneider Calculations'',
it is not the aim of this section to present a recipe
that is useful for arbitrary finite groups.
Just the contrary, the calculations shown there assume
interactive use of GAP, since the user has to decide
what functions might return something that is useful
in the context of Dixon Schneider calculations.
Perhaps this aspect should be emphasized in the manual
for the next version of GAP.
By the way, the reported problems to compute the
character tables of M22 and PGL(2,7) refer only to
the try to calculate the tables of these groups
exactly along the lines of the example in the manual.
Computing these tables with the default strategy
used by `CharTable' requires only a few seconds
on a (semi-)modern PC.