k-Transitive Group

A group is called -transitive group if there exists a set of elements on which the group acts faithfully and -transitively. It should be noted that transitivity computed from a particular permutation representation may not be the (maximal) transitivity of the abstract group. For example, the Higman-Sims group has both a 2-transitive representation of degree 176 and a 1-transitive representation of degree 100.