Extensions 1→N→G→Q→1 with N=C₄₀ and Q=C₂

Direct product G=N×Q with N=C₄₀ and Q=C₂

		d	ρ	Label	ID
C₂×C₄₀		80		C2xC40	80,23

Semidirect products G=N:Q with N=C₄₀ and Q=C₂

extension	φ:Q→Aut N	d	ρ	Label	ID
C₄₀⋊₁C₂ = D₄₀	φ: C₂/C₁ → C₂ ⊆ Aut C₄₀	40	2+	C40:1C2	80,7
C₄₀⋊₂C₂ = C₄₀⋊C₂	φ: C₂/C₁ → C₂ ⊆ Aut C₄₀	40	2	C40:2C2	80,6
C₄₀⋊₃C₂ = C₈×D₅	φ: C₂/C₁ → C₂ ⊆ Aut C₄₀	40	2	C40:3C2	80,4
C₄₀⋊₄C₂ = C₈⋊D₅	φ: C₂/C₁ → C₂ ⊆ Aut C₄₀	40	2	C40:4C2	80,5
C₄₀⋊₅C₂ = C₅×D₈	φ: C₂/C₁ → C₂ ⊆ Aut C₄₀	40	2	C40:5C2	80,25
C₄₀⋊₆C₂ = C₅×SD₁₆	φ: C₂/C₁ → C₂ ⊆ Aut C₄₀	40	2	C40:6C2	80,26
C₄₀⋊₇C₂ = C₅×M₄(2)	φ: C₂/C₁ → C₂ ⊆ Aut C₄₀	40	2	C40:7C2	80,24

Non-split extensions G=N.Q with N=C₄₀ and Q=C₂

extension	φ:Q→Aut N	d	ρ	Label	ID
C₄₀.₁C₂ = Dic₂₀	φ: C₂/C₁ → C₂ ⊆ Aut C₄₀	80	2-	C40.1C2	80,8
C₄₀.₂C₂ = C₅⋊₂C₁₆	φ: C₂/C₁ → C₂ ⊆ Aut C₄₀	80	2	C40.2C2	80,1
C₄₀.₃C₂ = C₅×Q₁₆	φ: C₂/C₁ → C₂ ⊆ Aut C₄₀	80	2	C40.3C2	80,27

׿

×

⋊

ℤ

𝔽

○

≀

ℚ

◁