Extensions 1→N→G→Q→1 with N=D₆ and Q=S₄

Direct product G=NxQ with N=D₆ and Q=S₄

		d	ρ	Label	ID
C₂xS₃xS₄		18	6+	C2xS3xS4	288,1028

Semidirect products G=N:Q with N=D₆ and Q=S₄

extension	φ:Q→Out N	d	ρ	Label	ID
D₆:₁S₄ = D₆:S₄	φ: S₄/A₄ → C₂ ⊆ Out D₆	36	6	D6:1S4	288,857
D₆:₂S₄ = A₄:D₁₂	φ: S₄/A₄ → C₂ ⊆ Out D₆	36	6+	D6:2S4	288,858

Non-split extensions G=N.Q with N=D₆ and Q=S₄

extension	φ:Q→Out N	d	ρ	Label	ID
D₆.₁S₄ = D₆.S₄	φ: S₄/A₄ → C₂ ⊆ Out D₆	48	4-	D6.1S4	288,849
D₆.₂S₄ = D₆.₂S₄	φ: S₄/A₄ → C₂ ⊆ Out D₆	48	4	D6.2S4	288,850
D₆.₃S₄ = S₃xCSU₂(F₃)	φ: trivial image	48	4-	D6.3S4	288,848
D₆.₄S₄ = S₃xGL₂(F₃)	φ: trivial image	24	4	D6.4S4	288,851
D₆.₅S₄ = S₃xA₄:C₄	φ: trivial image	36	6	D6.5S4	288,856

׿

x

:

Z

F

o

wr

Q

<