Extensions 1→N→G→Q→1 with N=C₂xC₄ and Q=D₇

Direct product G=NxQ with N=C₂xC₄ and Q=D₇

		d	ρ	Label	ID
C₂xC₄xD₇		56		C2xC4xD7	112,28

Semidirect products G=N:Q with N=C₂xC₄ and Q=D₇

extension	φ:Q→Aut N	d	ρ	Label	ID
(C₂xC₄):₁D₇ = D₁₄:C₄	φ: D₇/C₇ → C₂ ⊆ Aut C₂xC₄	56		(C2xC4):1D7	112,13
(C₂xC₄):₂D₇ = C₂xD₂₈	φ: D₇/C₇ → C₂ ⊆ Aut C₂xC₄	56		(C2xC4):2D7	112,29
(C₂xC₄):₃D₇ = C₄oD₂₈	φ: D₇/C₇ → C₂ ⊆ Aut C₂xC₄	56	2	(C2xC4):3D7	112,30

Non-split extensions G=N.Q with N=C₂xC₄ and Q=D₇

extension	φ:Q→Aut N	d	ρ	Label	ID
(C₂xC₄).₁D₇ = Dic₇:C₄	φ: D₇/C₇ → C₂ ⊆ Aut C₂xC₄	112		(C2xC4).1D7	112,11
(C₂xC₄).₂D₇ = C₄.Dic₇	φ: D₇/C₇ → C₂ ⊆ Aut C₂xC₄	56	2	(C2xC4).2D7	112,9
(C₂xC₄).₃D₇ = C₄:Dic₇	φ: D₇/C₇ → C₂ ⊆ Aut C₂xC₄	112		(C2xC4).3D7	112,12
(C₂xC₄).₄D₇ = C₂xDic₁₄	φ: D₇/C₇ → C₂ ⊆ Aut C₂xC₄	112		(C2xC4).4D7	112,27
(C₂xC₄).₅D₇ = C₂xC₇:C₈	central extension (φ=1)	112		(C2xC4).5D7	112,8
(C₂xC₄).₆D₇ = C₄xDic₇	central extension (φ=1)	112		(C2xC4).6D7	112,10

׿

x

:

Z

F

o

wr

Q

<