Speed up IrrBaumClausen (used for computing character tables of supersolvable groups, including $p$-groups)

[frankluebeck]

For the non-linear characters fewer multiplications of monomial matrices
are needed.
Also improved further details: multiplication of monomial matrices,
avoiding arithmetic with cyclotomics.

Comments:

This should never be slower than the previous version.
On my computer in the following example IrrBaumClausen (used to compute the irreducible characters of the group) becomes about 6 times faster:

gap> s:=SylowSubgroup(Sp(4,25),5);
ps<group of 4x4 matrices of size 390625 over GF(5^2)>
gap> ps:=Image(IsomorphismPcGroup(s));
Group([ f1, f2, f3, f4, f5, f6, f7, f8 ])
gap> ConjugacyClasses(ps);;time;
310
gap> BaumClausenInfo(ps);;time;
41
gap> ir:=IrrBaumClausen(ps);;time;
3608

Text for release notes

Speedup of IrrBaumClausen which is used by GAP to compute the character table of supersolvable (in particular p-) groups.

[ThomasBreuer]

This looks good.

• Avoiding arithmetic operations with cyclotomics is always a good idea; here this is done by creating the character values with CycList.
• Using {} instead of a for loop yields a speedup (in spite of the additional intermediate list).
• Memorizing partial products of the evaluation of a class representative and using the common initial part for the next representative is a good idea. (Since the lengths of the exponent vectors are in general much larger than the number of conjugacy classes, there are enough cases where common initial parts occur.)