A prominent subset of the quaternions is
Q8 = {-1, 1, -i, i, -j, j, -k, k | i2 = j2 = k2 = ijk = -1}.
This subset is refered to as the quaternion group and is represented using the notation Q8 as the cardinality of the set is eight. Q8 satisfies the multiplicative group axioms of closure, associativity, identity, and invertibility. A distinguishing characteristic of this group is that it is non-commutative. This is illustrated in the Cayley table show above. It should also be noted that 1 is the identity element and -1 is commutative with every other element.[4]