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{{smallest|non-[[cyclic group]]}}

{{group of order|4}}

==Definition==

* The [[quaternion group]], which has the Klein-four group as its [[inner automorphism group]]. The normal subgroups can be taken as those generated by the squareroots of <math>-1</math>

* The [[dihedral group:D8|dihedral group of order eight]], which has the Klein-four group as its [[inner automorphism group]]. Here, it is the quotient by the intersection of two subgroups of order four, one being a cyclic subgroup, the other being itself a Klein-four group.

==Implementation in GAP==

===Group ID===

The Klein-four group is the second group of order 4 as per GAP's small-group enumeration, so it can be described in GAP as:

<pre>SmallGroup(4,2)</pre>

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