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One of the two non-Abelian groups of the five groups total of Order 8.  The group 
 has the
Multiplication Table of 
, where 1, 
, 
, and 
 are the Quaternions.
The Cycle Graph is shown above.
See also Finite Group D4, Finite Group Z2Z2Z2, Finite Group Z2Z4, Finite Group Z8, Quaternion