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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

    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

    Cycle graph

    Group theory properties

    nonabelian | nonalternating | noncyclic | nonperfect | nonsimple | nonsporadic | nonsymmetric | solvable | transitive

    Associated person

    William Rowan Hamilton

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