There is no group whose quotient by the center is isomorphic to the quaternion group
41572
$G/Z$ cannot be isomorphic to quaternion group
51196
A group of order $p^2q^2$ is never simple
135241
Show that $\mathbb{Z}/n^2\mathbb{Z}$ is not isomorphic to other group
2254
Finite group with isomorphic normal subgroups and non-isomorphic quotients?
66510
A group is abelian if and only if the center of the group is all the group
37971
Prove that the center of a group is a normal subgroup
70688
How can I prove that the additive group of rationals is not isomorphic to a direct product of two nontrivial groups?
46664
Is every endomorphism of the quaternion ring surjective?
78048
Group of order 24 with no element of order 6 is isomorphic to $S_4$
51861
$S_4$ is not isomorphic to $D_{12}$
14611
$A_4$ has no subgroup of order $6$?
23641
Quotient ring of field is zero or itself.
41688
An elementary problem in Group Theory: the unique noncyclic group of order 4
8694
$A_4$ is not isomorphic to $D_6$
84869
Are the groups $\mathbb{C}$ and $\mathbb{R}$ isomorphic?
88474
$\mathbb{A}^{2}$ not isomorphic to affine space minus the origin
128732
$\mathbb Z_{p^n}$ is not the direct product of any family of its proper subgroups