Friday 26th March, 12:05-12:55pm,
The talk is based on a joint work with Sergey V. Shpectorov
on a class of groups, which are certain split
extensions of special 2-groups 23+6n
by L3(2). We
call these groups tri-extraspecial, because they behave very much like
extraspecial 2-groups. For every value of n, there are exactly two
such groups, denoted T±(n).
We show that the outer automorphism group of
T±(n) is 2 x Sp(2n,2).
The group Out(T±(n)) acts transitively on
the classes of complements L3(2) in
T±(n), the stabilizer of
such a class being O±(2n,2). The group
T±(n) arises as a
normal subgroup in a maximal parabolic subgroup (the stabilizer of a
3-dimensional totally singular subspace) of
more remarkably, the groups T+(4) and T-(4) arise,
respectively, in the sporadic groups J4 and
These latter examples were
the primary motivation of our interest in tri-extraspecial groups.