In this case, the given dihedral group is a Frobenius group, but is larger than the groups in the database.
Cyclic groups are not Frobenius groups, so a different exception is raised in this example.
Use the assign option to request that an explicit isomorphism be computed.
Construct the Frobenius group directly from the database.
Construct a group as the image of the computed isomorphism eta.
Check that F1 and F2 are, in fact, the same group.
The smallest insoluble (in fact, perfect) Frobenius group has order .
In fact, is a perfect group.
All perfect Frobenius groups have the same Frobenius complement up to isomorphism.
(Note that there are additional (much larger) Frobenius groups in the database of perfect groups that are not present in the Frobenius groups database.)