  We characterize the para-associative ternary quasigroups (flocks) applicable
to knot theory, and show which of these structures are isomorphic. We enumerate
them up to order 64. We note that the operation used in knot-theoretic flocks
has its non-associative version in extra loops. We use a group action on the
set of flock colorings to improve the cocycle invariant associated with the
knot-theoretic flock (co)homology.
