Extensions 1→N→G→Q→1 with N=Q₈×C₃₁ and Q=C₂

Direct product G=N×Q with N=Q₈×C₃₁ and Q=C₂

		d	ρ	Label	ID
Q₈×C₆₂		496		Q8xC62	496,39

Semidirect products G=N:Q with N=Q₈×C₃₁ and Q=C₂

extension	φ:Q→Out N	d	ρ	Label	ID
(Q₈×C₃₁)⋊₁C₂ = Q₈⋊D₃₁	φ: C₂/C₁ → C₂ ⊆ Out Q₈×C₃₁	248	4+	(Q8xC31):1C2	496,16
(Q₈×C₃₁)⋊₂C₂ = Q₈×D₃₁	φ: C₂/C₁ → C₂ ⊆ Out Q₈×C₃₁	248	4-	(Q8xC31):2C2	496,33
(Q₈×C₃₁)⋊₃C₂ = Q₈⋊₂D₃₁	φ: C₂/C₁ → C₂ ⊆ Out Q₈×C₃₁	248	4+	(Q8xC31):3C2	496,34
(Q₈×C₃₁)⋊₄C₂ = SD₁₆×C₃₁	φ: C₂/C₁ → C₂ ⊆ Out Q₈×C₃₁	248	2	(Q8xC31):4C2	496,25
(Q₈×C₃₁)⋊₅C₂ = C₄○D₄×C₃₁	φ: trivial image	248	2	(Q8xC31):5C2	496,40

Non-split extensions G=N.Q with N=Q₈×C₃₁ and Q=C₂

extension	φ:Q→Out N	d	ρ	Label	ID
(Q₈×C₃₁).₁C₂ = C₃₁⋊Q₁₆	φ: C₂/C₁ → C₂ ⊆ Out Q₈×C₃₁	496	4-	(Q8xC31).1C2	496,17
(Q₈×C₃₁).₂C₂ = Q₁₆×C₃₁	φ: C₂/C₁ → C₂ ⊆ Out Q₈×C₃₁	496	2	(Q8xC31).2C2	496,26

׿

×

⋊

ℤ

𝔽

○

≀

ℚ

◁