Extensions 1→N→G→Q→1 with N=D₅₂⋊C₂ and Q=C₂

Direct product G=N×Q with N=D₅₂⋊C₂ and Q=C₂

		d	ρ	Label	ID
C₂×D₅₂⋊C₂		208		C2xD52:C2	416,220

Semidirect products G=N:Q with N=D₅₂⋊C₂ and Q=C₂

extension	φ:Q→Out N	d	ρ	Label	ID
D₅₂⋊C₂⋊₁C₂ = Q₈⋊D₂₆	φ: C₂/C₁ → C₂ ⊆ Out D₅₂⋊C₂	104	4+	D52:C2:1C2	416,135
D₅₂⋊C₂⋊₂C₂ = D₂₆.₆D₄	φ: C₂/C₁ → C₂ ⊆ Out D₅₂⋊C₂	208	4	D52:C2:2C2	416,137
D₅₂⋊C₂⋊₃C₂ = D₁₀₄⋊C₂	φ: C₂/C₁ → C₂ ⊆ Out D₅₂⋊C₂	208	4+	D52:C2:3C2	416,140
D₅₂⋊C₂⋊₄C₂ = Q₈.₁₀D₂₆	φ: C₂/C₁ → C₂ ⊆ Out D₅₂⋊C₂	208	4	D52:C2:4C2	416,221
D₅₂⋊C₂⋊₅C₂ = D₄⋊₈D₂₆	φ: C₂/C₁ → C₂ ⊆ Out D₅₂⋊C₂	104	4+	D52:C2:5C2	416,223
D₅₂⋊C₂⋊₆C₂ = C₄○D₄×D₁₃	φ: trivial image	104	4	D52:C2:6C2	416,222

Non-split extensions G=N.Q with N=D₅₂⋊C₂ and Q=C₂

extension	φ:Q→Out N	d	ρ	Label	ID
D₅₂⋊C₂.₁C₂ = Q₁₆⋊D₁₃	φ: C₂/C₁ → C₂ ⊆ Out D₅₂⋊C₂	208	4	D52:C2.1C2	416,139
D₅₂⋊C₂.₂C₂ = D₅₂⋊C₄	φ: C₂/C₁ → C₂ ⊆ Out D₅₂⋊C₂	104	8+	D52:C2.2C2	416,85
D₅₂⋊C₂.₃C₂ = D₅₂.C₄	φ: C₂/C₁ → C₂ ⊆ Out D₅₂⋊C₂	208	8+	D52:C2.3C2	416,207

׿

×

⋊

ℤ

𝔽

○

≀

ℚ

◁