Extensions 1→N→G→Q→1 with N=C₄xF₇ and Q=C₂

Direct product G=NxQ with N=C₄xF₇ and Q=C₂

		d	ρ	Label	ID
C₂xC₄xF₇		56		C2xC4xF7	336,122

Semidirect products G=N:Q with N=C₄xF₇ and Q=C₂

extension	φ:Q→Out N	d	ρ	Label	ID
(C₄xF₇):₁C₂ = D₄xF₇	φ: C₂/C₁ → C₂ ⊆ Out C₄xF₇	28	12+	(C4xF7):1C2	336,125
(C₄xF₇):₂C₂ = D₄:₂F₇	φ: C₂/C₁ → C₂ ⊆ Out C₄xF₇	56	12-	(C4xF7):2C2	336,126
(C₄xF₇):₃C₂ = Q₈:₃F₇	φ: C₂/C₁ → C₂ ⊆ Out C₄xF₇	56	12+	(C4xF7):3C2	336,128
(C₄xF₇):₄C₂ = D₂₈:₆C₆	φ: C₂/C₁ → C₂ ⊆ Out C₄xF₇	56	6	(C4xF7):4C2	336,124

Non-split extensions G=N.Q with N=C₄xF₇ and Q=C₂

extension	φ:Q→Out N	d	ρ	Label	ID
(C₄xF₇).₁C₂ = Q₈xF₇	φ: C₂/C₁ → C₂ ⊆ Out C₄xF₇	56	12-	(C4xF7).1C2	336,127
(C₄xF₇).₂C₂ = C₈:F₇	φ: C₂/C₁ → C₂ ⊆ Out C₄xF₇	56	6	(C4xF7).2C2	336,8
(C₄xF₇).₃C₂ = C₈xF₇	φ: trivial image	56	6	(C4xF7).3C2	336,7

׿

x

:

Z

F

o

wr

Q

<