A new algorithm for computing character tables

                  William Unger
              University of Sydney

I will describe a new algorithm for computing the character 
table of a finite group. The main ingredients of the algorithm 
are Brauer's theorem on induced characters, lattice reduction 
by LLL and Dixon's method of working over a finite field.  We 
find that for many interesting groups it performs far better 
than the Dixon-Schneider algorithm.


          Tutorial: Computing with groups in Magma

This session will be a tour through using Magma to calculate with groups.
We will take as example the search for a particular subgroup of the 
Coxeter group [5,3,3,3] which Conder and Maclachlan used to construct
a compact hyperbolic 4-manifold of small volume. The search will illustrate
the use of Magma's facilities for computing with finitely-presented groups,
matrix groups, permutation groups and homomorphisms between groups.