Extensions 1→N→G→Q→1 with N=C32 and Q=C2×C7⋊C3

Direct product G=N×Q with N=C32 and Q=C2×C7⋊C3
dρLabelID
C3×C6×C7⋊C3126C3xC6xC7:C3378,52

Semidirect products G=N:Q with N=C32 and Q=C2×C7⋊C3
extensionφ:Q→Aut NdρLabelID
C32⋊(C2×C7⋊C3) = C7⋊He3⋊C2φ: C2×C7⋊C3/C7C6 ⊆ Aut C32636C3^2:(C2xC7:C3)378,17
C322(C2×C7⋊C3) = C2×C7⋊He3φ: C2×C7⋊C3/C14C3 ⊆ Aut C321263C3^2:2(C2xC7:C3)378,28
C323(C2×C7⋊C3) = C3×S3×C7⋊C3φ: C2×C7⋊C3/C7⋊C3C2 ⊆ Aut C32426C3^2:3(C2xC7:C3)378,48
C324(C2×C7⋊C3) = C3⋊S3×C7⋊C3φ: C2×C7⋊C3/C7⋊C3C2 ⊆ Aut C3263C3^2:4(C2xC7:C3)378,50

Non-split extensions G=N.Q with N=C32 and Q=C2×C7⋊C3
extensionφ:Q→Aut NdρLabelID
C32.(C2×C7⋊C3) = C2×C21.C32φ: C2×C7⋊C3/C14C3 ⊆ Aut C321263C3^2.(C2xC7:C3)378,27
C32.2(C2×C7⋊C3) = S3×C7⋊C9φ: C2×C7⋊C3/C7⋊C3C2 ⊆ Aut C321266C3^2.2(C2xC7:C3)378,16
C32.3(C2×C7⋊C3) = C6×C7⋊C9central extension (φ=1)378C3^2.3(C2xC7:C3)378,26

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