Let V be the standard
4-dimensional module for Sz(q), the Suzuki group based on the field of q = 22n+1
elements. In this paper we determine H2(Sz(q),V ). This is usually (q ≧ 32) of
dimension one (otherwise zero) and is generated by a cocycle which is the
restriction of a generator of H2(Sp4(q),V ). In addition, the well known groups
H2(Sz(q),GF(q)) and H1(Sz(q),V ) are calculated. The proof involves the use of
the Hochschild-Serre spectral sequence to determine the cohomology of the
normalizer of a Sylow 2-subgroup acting on the various one-dimensional modules
involved.
