I know that $H^3(S_3,\mathbb{Z}_3)\cong \mathbb{Z}_3$ (S_3 is the symmetric group for three elements). So this group is generated by any nontrivial cocycle. But I don't know how to explicitly find such a cocycle (any explicit representation will do - even a table describing all possible values).
How can I find the cocycle in this case, and is there a general way of doing it?