This group is the smallest non-cyclic group, and every element's square is equal to the identity.
Eight of the eleven rings with the same number of elements as this group have its operation as their additive operation, and all of this group's 5 subgroups are normal. This group names an a cappella singing group at Northwestern University best known for their song  Finite Simple Group of Order Two . This group is isomorphic to   D2, the second dihedral group, and to Z2 Ã— Z2. This group is equal to the symmetry group of a rectangle which is not a square. This group is the smallest non-cyclic group, and every element's square is equal to the identity. For ten points, identify this group with four elements named after a mathematician who also names a bottle.
Eight of the eleven rings with the same number of elements as this group have its operation as their additive operation, and all of this group's 5 subgroups are normal.
Klein four-group [prompt on four-group, accept vierergruppe, accept D2 and Z2 Ã— Z2 before read]