Extensions 1→N→G→Q→1 with N=D₇₂ and Q=C₂

Direct product G=N×Q with N=D₇₂ and Q=C₂

		d	ρ	Label	ID
C₂×D₇₂		144		C2xD72	288,114

Semidirect products G=N:Q with N=D₇₂ and Q=C₂

extension	φ:Q→Out N	d	ρ	Label	ID
D₇₂⋊₁C₂ = D₁₄₄	φ: C₂/C₁ → C₂ ⊆ Out D₇₂	144	2+	D72:1C2	288,6
D₇₂⋊₂C₂ = C₈⋊D₁₈	φ: C₂/C₁ → C₂ ⊆ Out D₇₂	72	4+	D72:2C2	288,118
D₇₂⋊₃C₂ = C₉⋊D₁₆	φ: C₂/C₁ → C₂ ⊆ Out D₇₂	144	4+	D72:3C2	288,33
D₇₂⋊₄C₂ = D₈×D₉	φ: C₂/C₁ → C₂ ⊆ Out D₇₂	72	4+	D72:4C2	288,120
D₇₂⋊₅C₂ = D₇₂⋊₅C₂	φ: C₂/C₁ → C₂ ⊆ Out D₇₂	144	4+	D72:5C2	288,129
D₇₂⋊₆C₂ = D₇₂⋊C₂	φ: C₂/C₁ → C₂ ⊆ Out D₇₂	72	4+	D72:6C2	288,124
D₇₂⋊₇C₂ = D₇₂⋊₇C₂	φ: trivial image	144	2	D72:7C2	288,115

Non-split extensions G=N.Q with N=D₇₂ and Q=C₂

extension	φ:Q→Out N	d	ρ	Label	ID
D₇₂.₁C₂ = C₁₄₄⋊C₂	φ: C₂/C₁ → C₂ ⊆ Out D₇₂	144	2	D72.1C2	288,7
D₇₂.₂C₂ = C₉⋊SD₃₂	φ: C₂/C₁ → C₂ ⊆ Out D₇₂	144	4+	D72.2C2	288,35

׿

×

⋊

ℤ

𝔽

○

≀

ℚ

◁