Find a nontrivial central extension
1 --> Z_2 --> G --> A_4 --> 1
meaning determine a group G. Is it unique?
(You may use the fact that A_4 has a normal series Z_2 x Z_2/Z3)
We consider G= Z_6 x A_4/Z_3 where Z_3 is a subgroup of Z_6 x A_4 which defines a 1 to 1 homomorphism map shown as a--->(a,a).
Now, we can define 1--->Z_2--->G--->A_4--->1 as a central extension if we assume that ...
A central extension problem is solved. The nontrivial central extension functions are determined.