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Quaternion
Group elements
1 | i | j | k | -1 | -i | -j | -k
i | j
8
Notation
Q_8
Related groups
5th finite group of order 8 | dicyclic group of order 8 | 4th finite group of order 8 in the SmallGroups library
Multiplication table
| 1 | i | j | k | -1 | -i | -j | -k 1 | 1 | i | j | k | -1 | -i | -j | -k i | i | -1 | k | -j | -i | 1 | -k | j j | j | -k | -1 | i | -j | k | 1 | -i k | k | j | -i | -1 | -k | -j | i | 1 -1 | -1 | -i | -j | -k | 1 | i | j | k -i | -i | 1 | -k | j | i | -1 | k | -j -j | -j | k | 1 | -i | j | -k | -1 | i -k | -k | -j | i | 1 | k | j | -i | -1
Cycle graph
Group theory properties
nonabelian | nonalternating | noncyclic | nondihedral | nonperfect | nonsimple | nonsporadic | nonsymmetric | solvable | transitive
Associated person
William Rowan Hamilton