The Cohomology of the Sylow 2-subgroup of J2

John Maginnis
Kansas State University, Manhattan KS 66506

J. London Math. Soc. (2) 51 (1995) 259-278

Abstract: The Hall-Janko-Wales group J2 is one of the twenty-six
sporadic finite simple groups.  The cohomology of its Sylow
2-subgroup S_J is computed, an important step in calculating the 
mod 2 cohomology of J2.  The spectral sequence corresponding to the
central extension for S_J is described and shown to collapse at the 
eighth page.  The group S_J contains two subgroups 2^{1+4} (the
central product of a dihedral and a quaternionic group) and 2^{2+4}
(the Sylow 2-subgroup of the matrix group PSL(3,4)) which detect the
cohomology of S_J.  The cohomology relations for the subgoup 2^{2+4}
are computed.