| 11. | All 24 units have absolute value 1 and therefore lie in the unit quaternion group Sp ( 1 ).
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| 12. | The Schur multiplier of the quaternion group is trivial, but the Schur multiplier of dihedral 2-groups has order 2.
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| 13. | The dihedral groups are both very similar to and very dissimilar from the quaternion groups and the semidihedral groups.
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| 14. | The quaternion group has normal subgroups of order 4 and 2 but is not a [ semi ] direct product.
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| 15. | For instance, he shows " a Hamilton group of order 2 " a " has quaternion groups as subgroups ".
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| 16. | The quaternion group consisting of the 8 Lipschitz units forms a normal subgroup of 2 " O " of index 6.
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| 17. | More generally, when " n " is a power of 2, the dicyclic group is isomorphic to the generalized quaternion group.
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| 18. | Finally, there is the generalized quaternion group of order 16 . talk ) 15 : 20, 26 April 2015 ( UTC)
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| 19. | The quaternion group consisting of the 8 Lipschitz units forms a normal subgroup of 2 " T " of index 3.
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| 20. | The elements " x " and " y " generate a normal subgroup isomorphic to the quaternion group of order 8.
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