The symmetric group in its natural permutation representation is not regular.
But there is a regular permutation representation of degree (the order of the group).
The quaternion group of order has a regular representation of degree .
We construct a diagonal embedding into the direct square.
This is the diagonal subgroup.
Frobenius groups are never regular.
Let's find all the regular groups of degree . First, we create an iterator for all the transitive groups of that degree.
Create an Array in which to store the transitive group IDs of those that are found to be regular.
Now iterate over the groups and check for regularity. Since we already know that the groups are transitive, we avoid the redundant transitivity check and test only for semi-regularity.
