Group cohomology of Klein four-group

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This article gives specific information, namely, group cohomology, about a particular group, namely: Klein four-group.
View group cohomology of particular groups | View other specific information about Klein four-group

Homology groups

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Cohomology ring with coefficients in integers

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Second cohomology groups and extensions

Second cohomology groups for trivial group action

Group acted upon Order Second part of GAP ID Second cohomology group for trivial group action Extensions Cohomology information
cyclic group:Z2 2 1 elementary abelian group:E8 elementary abelian group:E8, direct product of Z4 and Z2, quaternion group and dihedral group:D8 second cohomology group for trivial group action of V4 on Z2
cyclic group:Z4 4 1 elementary abelian group:E8 direct product of Z4 and V4, direct product of Z8 and Z2, central product of D8 and Z4, M16 second cohomology group for trivial group action of V4 on Z4
Klein four-group 4 2 elementary abelian group:E64 elementary abelian group:E16, direct product of Z4 and Z4, direct product of Z4 and V4, direct product of D8 and Z2, direct product of Q8 and Z2, SmallGroup(16,3), nontrivial semidirect product of Z4 and Z4 second cohomology group for trivial group action of V4 on V4
cyclic group:Z8 8 1 elementary abelian group:E8 direct product of Z8 and V4, direct product of Z16 and Z2, central product of D8 and Z8, M32 second cohomology group for trivial group action of V4 on Z8
direct product of Z4 and Z2 8 2  ?  ?  ?
elementary abelian group:E8 8 5  ?  ?  ?