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Group cohomology of Klein four-group

170 bytes added, 19:50, 24 November 2011
Second cohomology groups for trivial group action
===Second cohomology groups for trivial group action===
<section begin="second cohomology group for trivial group action summary"/>
{| class="sortable" border="1"
! Group acted upon !! Order !! Second part of GAP ID !! [[Second cohomology group for trivial group action]] (as abstract group) !! Order !! Extensions !! Number of extensions up to [[pseudo-congruent extension|pseudo-congruence]], i.e., number of orbits under action of relevant automorpism groups !! Cohomology information
| [[cyclic group:Z8]] || 8 || 1 || [[elementary abelian group:E8]] || 8 || [[direct product of Z8 and V4]], [[direct product of Z16 and Z2]], [[central product of D8 and Z8]], [[M32]] || 4 || [[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 || ? || ? || ? || ? || ?
|}
<section end="second cohomology group for trivial group action summary"/>
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