Extensions 1→N→G→Q→1 with N=D₄×C₂₅ and Q=C₂

Direct product G=N×Q with N=D₄×C₂₅ and Q=C₂

		d	ρ	Label	ID
D₄×C₅₀		200		D4xC50	400,46

Semidirect products G=N:Q with N=D₄×C₂₅ and Q=C₂

extension	φ:Q→Out N	d	ρ	Label	ID
(D₄×C₂₅)⋊₁C₂ = D₄⋊D₂₅	φ: C₂/C₁ → C₂ ⊆ Out D₄×C₂₅	200	4+	(D4xC25):1C2	400,16
(D₄×C₂₅)⋊₂C₂ = D₄×D₂₅	φ: C₂/C₁ → C₂ ⊆ Out D₄×C₂₅	100	4+	(D4xC25):2C2	400,39
(D₄×C₂₅)⋊₃C₂ = D₄⋊₂D₂₅	φ: C₂/C₁ → C₂ ⊆ Out D₄×C₂₅	200	4-	(D4xC25):3C2	400,40
(D₄×C₂₅)⋊₄C₂ = D₈×C₂₅	φ: C₂/C₁ → C₂ ⊆ Out D₄×C₂₅	200	2	(D4xC25):4C2	400,25
(D₄×C₂₅)⋊₅C₂ = C₄○D₄×C₂₅	φ: trivial image	200	2	(D4xC25):5C2	400,48

Non-split extensions G=N.Q with N=D₄×C₂₅ and Q=C₂

extension	φ:Q→Out N	d	ρ	Label	ID
(D₄×C₂₅).₁C₂ = D₄.D₂₅	φ: C₂/C₁ → C₂ ⊆ Out D₄×C₂₅	200	4-	(D4xC25).1C2	400,15
(D₄×C₂₅).₂C₂ = SD₁₆×C₂₅	φ: C₂/C₁ → C₂ ⊆ Out D₄×C₂₅	200	2	(D4xC25).2C2	400,26

׿

×

⋊

ℤ

𝔽

○

≀

ℚ

◁