3 research outputs found
Computing with finite groups
The character table of a finite group G is constructed
by computing the eigenvectors of matrix equations determined
by the centre of the group algebra. The numerical character
values are expressed in algebraic form. A variant using a
certain sub-algebra of the centre of the group algebra is
used to ease problems associated with determining the
conjugacy classes of elements of G. The simple group of
order 50,232,960 and its subgroups PSL(2,17) and PSL(2,19)
are constructed using general techniques.
A combination of hand and machine calculation gives the
character tables of the known simple groups of order < 106
excepting Sp(4,4) and PSL(2,q). The characters of the non-
Abelian 2-groups of order < 2 6 are computed.
Miscellaneous computations involving the symmetric
group Sn are given