Dear all, Does exist 4 distinct elements of order 4 in extraspecial 2groups? yours,
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An extraspecial 2group is isomorphic to a central product of copies of the dihedral group $D_8$ and the quaternion group $Q_8$, both of order 8. Since the central product of two $D_8$s is isomorphic to that of two $Q_8$s, there are just two isomorphism types of extraspecial 2groups of each order $2^{1+2n}$. Your statement is false in $D_8$, which has only 2 elements of order 4. All other extraspecial 2groups contain $Q_8$ as a subgroup, which has 6 distinct elements of order 4. 

