A 
-transitive
group is a group for which 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.
k-Transitive Group
See also
Transitive GroupExplore with Wolfram|Alpha
Cite this as:
Weisstein, Eric W. "k-Transitive Group." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/k-TransitiveGroup.html