Extensions 1→N→G→Q→1 with N=C₁₆ and Q=D₇

Direct product G=N×Q with N=C₁₆ and Q=D₇

		d	ρ	Label	ID
D₇×C₁₆		112	2	D7xC16	224,3

Semidirect products G=N:Q with N=C₁₆ and Q=D₇

extension	φ:Q→Aut N	d	ρ	Label	ID
C₁₆⋊₁D₇ = D₁₁₂	φ: D₇/C₇ → C₂ ⊆ Aut C₁₆	112	2+	C16:1D7	224,5
C₁₆⋊₂D₇ = C₁₁₂⋊C₂	φ: D₇/C₇ → C₂ ⊆ Aut C₁₆	112	2	C16:2D7	224,6
C₁₆⋊₃D₇ = C₁₆⋊D₇	φ: D₇/C₇ → C₂ ⊆ Aut C₁₆	112	2	C16:3D7	224,4

Non-split extensions G=N.Q with N=C₁₆ and Q=D₇

extension	φ:Q→Aut N	d	ρ	Label	ID
C₁₆.D₇ = Dic₅₆	φ: D₇/C₇ → C₂ ⊆ Aut C₁₆	224	2-	C16.D7	224,7
C₁₆.₂D₇ = C₇⋊C₃₂	central extension (φ=1)	224	2	C16.2D7	224,1

⋊

ℤ

𝔽

○

≀

ℚ

◁

Extensions 1→N→G→Q→1 with N=C16 and Q=D7