Center of binary octahedral group

This article is about a particular subgroup in a group, up to equivalence of subgroups (i.e., an isomorphism of groups that induces the corresponding isomorphism of subgroups). The subgroup is (up to isomorphism) cyclic group:Z2 and the group is (up to isomorphism) binary octahedral group (see subgroup structure of binary octahedral group).
The subgroup is a normal subgroup and the quotient group is isomorphic to symmetric group:S4.
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Definition

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Arithmetic functions

Function	Value	Explanation
order of the whole group	48
order of the subgroup	2
index of the subgroup	24	Follows from Lagrange's theorem.
size of conjugacy class = index of normalizer	1	center is normal
number of conjugacy classes in automorphism class	1	center is characteristic