V4 in S4
You might be referring to either of these:
- Normal Klein four-subgroup of symmetric group:S4: The subgroup comprising the identity element and the three double transpositions in symmetric group:S4. Concretely, it is the subgroup .
- Non-normal Klein four-subgroups of symmetric group:S4: A conjugacy class of subgroups, each of which is generated by a pair of disjoint transpositions. For instance, the subgroup .