Write the composition table for group q8 where q8 is quaterniom group
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Cycle diagram of Q8. Each color specifies a series of powers of any element connected to the identity element e = 1. For example, the cycle in red reflects the fact that i2 = e, i3 = i and i4 = e. The red cycle also reflects that i2 = e, i3 = i and i4 = e.
In group theory, the quaternion group Q8(sometimes just denoted by Q) is a non-abelian group of order eight, isomorphic to a certain eight-element subset of the quaternions under multiplication. It is given by the group presentation
{\displaystyle \mathrm {Q} _{8}=\langle {\bar {e}},i,j,k\mid {\bar {e}}^{2}=e,\;i^{2}=j^{2}=k^{2}=ijk={\bar {e}}\rangle ,}
where e is the identity element and ecommutes with the other elements of the group.

Cycle diagram of Q8. Each color specifies a series of powers of any element connected to the identity element e = 1. For example, the cycle in red reflects the fact that i2 = e, i3 = i and i4 = e. The red cycle also reflects that i2 = e, i3 = i and i4 = e.
In group theory, the quaternion group Q8(sometimes just denoted by Q) is a non-abelian group of order eight, isomorphic to a certain eight-element subset of the quaternions under multiplication. It is given by the group presentation
{\displaystyle \mathrm {Q} _{8}=\langle {\bar {e}},i,j,k\mid {\bar {e}}^{2}=e,\;i^{2}=j^{2}=k^{2}=ijk={\bar {e}}\rangle ,}
where e is the identity element and ecommutes with the other elements of the group.
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