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We describe the cohomology ringH  *    (   J  2   ;3   )${H^*(J_2;\mathbb {F}_3)}$    both as a subring ofH  *    (   3  +   1  +  2    ;3   )${H^*(3^{1+2}_+;\mathbb {F}_3)}$    and with an abstract presentation. We also give its Poincaré series. Our calculational tool is the first author's spectral sequence for the cohomology of a finite group with a strongly closed  p -subgroup.

The cohomology of the sporadic group J 2 over 𝔽 3