Extensions 1→N→G→Q→1 with N=C₄₂ and Q=C₂

Direct product G=N×Q with N=C₄₂ and Q=C₂

		d	ρ	Label	ID
C₂×C₄₂		84		C2xC42	84,15

Semidirect products G=N:Q with N=C₄₂ and Q=C₂

extension	φ:Q→Aut N	d	ρ	Label	ID
C₄₂⋊₁C₂ = D₄₂	φ: C₂/C₁ → C₂ ⊆ Aut C₄₂	42	2+	C42:1C2	84,14
C₄₂⋊₂C₂ = C₆×D₇	φ: C₂/C₁ → C₂ ⊆ Aut C₄₂	42	2	C42:2C2	84,12
C₄₂⋊₃C₂ = S₃×C₁₄	φ: C₂/C₁ → C₂ ⊆ Aut C₄₂	42	2	C42:3C2	84,13

Non-split extensions G=N.Q with N=C₄₂ and Q=C₂

extension	φ:Q→Aut N	d	ρ	Label	ID
C₄₂.₁C₂ = Dic₂₁	φ: C₂/C₁ → C₂ ⊆ Aut C₄₂	84	2-	C42.1C2	84,5
C₄₂.₂C₂ = C₃×Dic₇	φ: C₂/C₁ → C₂ ⊆ Aut C₄₂	84	2	C42.2C2	84,4
C₄₂.₃C₂ = C₇×Dic₃	φ: C₂/C₁ → C₂ ⊆ Aut C₄₂	84	2	C42.3C2	84,3

⋊

ℤ

𝔽

○

≀

ℚ

◁

Extensions 1→N→G→Q→1 with N=C42 and Q=C2