Second cohomology group for trivial group action of Z4 on V4
Description of the group
where and .
The cohomology group is isomorphic to the Klein four-group.
Note that since cyclic over central implies abelian, all the corresponding group extensions are abelian. Equivalently, all the 2-cocycles are symmetric 2-cocycles.
We list here the elements, grouped by similarity under the action of the automorphism groups on both sides.
|Cohomology class type||Number of cohomology classes||Representative 2-cocycle||Corresponding group extension||Second part of GAP ID (order is 16)|
|trivial||1||everywhere||direct product of Z4 and V4||10|
|nontrivial||3||direct product of Z8 and Z2||5|