Extensions 1→N→G→Q→1 with N=C8 and Q=C7⋊C8

Direct product G=N×Q with N=C8 and Q=C7⋊C8

Semidirect products G=N:Q with N=C8 and Q=C7⋊C8
extensionφ:Q→Aut NdρLabelID
C81(C7⋊C8) = C561C8φ: C7⋊C8/C28C2 ⊆ Aut C8448C8:1(C7:C8)448,15
C82(C7⋊C8) = C562C8φ: C7⋊C8/C28C2 ⊆ Aut C8448C8:2(C7:C8)448,14
C83(C7⋊C8) = C56⋊C8φ: C7⋊C8/C28C2 ⊆ Aut C8448C8:3(C7:C8)448,12

Non-split extensions G=N.Q with N=C8 and Q=C7⋊C8
extensionφ:Q→Aut NdρLabelID
C8.1(C7⋊C8) = C56.16Q8φ: C7⋊C8/C28C2 ⊆ Aut C81122C8.1(C7:C8)448,20
C8.2(C7⋊C8) = C56.C8φ: C7⋊C8/C28C2 ⊆ Aut C8448C8.2(C7:C8)448,18
C8.3(C7⋊C8) = C7⋊M6(2)φ: C7⋊C8/C28C2 ⊆ Aut C82242C8.3(C7:C8)448,56
C8.4(C7⋊C8) = C7⋊C64central extension (φ=1)4482C8.4(C7:C8)448,1
C8.5(C7⋊C8) = C4×C7⋊C16central extension (φ=1)448C8.5(C7:C8)448,17
C8.6(C7⋊C8) = C2×C7⋊C32central extension (φ=1)448C8.6(C7:C8)448,55