Extensions 1→N→G→Q→1 with N=Q₁₆ and Q=Q₈

Direct product G=N×Q with N=Q₁₆ and Q=Q₈

		d	ρ	Label	ID
Q₈×Q₁₆		128		Q8xQ16	128,2114

Semidirect products G=N:Q with N=Q₁₆ and Q=Q₈

extension	φ:Q→Out N	d	ρ	Label	ID
Q₁₆⋊₁Q₈ = Q₁₆⋊Q₈	φ: Q₈/C₄ → C₂ ⊆ Out Q₁₆	128		Q16:1Q8	128,957
Q₁₆⋊₂Q₈ = C₄.Q₃₂	φ: Q₈/C₄ → C₂ ⊆ Out Q₁₆	128		Q16:2Q8	128,959
Q₁₆⋊₃Q₈ = D₈⋊₃Q₈	φ: Q₈/C₄ → C₂ ⊆ Out Q₁₆	16	4	Q16:3Q8	128,962
Q₁₆⋊₄Q₈ = Q₁₆⋊₄Q₈	φ: Q₈/C₄ → C₂ ⊆ Out Q₁₆	128		Q16:4Q8	128,2119
Q₁₆⋊₅Q₈ = Q₁₆⋊₅Q₈	φ: Q₈/C₄ → C₂ ⊆ Out Q₁₆	128		Q16:5Q8	128,2122
Q₁₆⋊₆Q₈ = Q₁₆⋊₆Q₈	φ: trivial image	128		Q16:6Q8	128,2115

Non-split extensions G=N.Q with N=Q₁₆ and Q=Q₈

extension	φ:Q→Out N	d	ρ	Label	ID
Q₁₆.₁Q₈ = Q₁₆.Q₈	φ: Q₈/C₄ → C₂ ⊆ Out Q₁₆	128		Q16.1Q8	128,961
Q₁₆.₂Q₈ = D₈.₂Q₈	φ: Q₈/C₄ → C₂ ⊆ Out Q₁₆	32	4	Q16.2Q8	128,963

׿

×

⋊

ℤ

𝔽

○

≀

ℚ

◁