Extensions 1→N→G→Q→1 with N=2₊¹⁺⁴ and Q=D₅

Direct product G=NxQ with N=2₊¹⁺⁴ and Q=D₅

		d	ρ	Label	ID
D₅x2₊¹⁺⁴		40	8+	D5xES+(2,2)	320,1622

Semidirect products G=N:Q with N=2₊¹⁺⁴ and Q=D₅

extension	φ:Q→Out N	d	ρ	Label	ID
2₊¹⁺⁴:₁D₅ = 2₊¹⁺⁴:D₅	φ: D₅/C₅ → C₂ ⊆ Out 2₊¹⁺⁴	40	8+	ES+(2,2):1D5	320,868
2₊¹⁺⁴:₂D₅ = 2₊¹⁺⁴:₂D₅	φ: D₅/C₅ → C₂ ⊆ Out 2₊¹⁺⁴	40	8+	ES+(2,2):2D5	320,871
2₊¹⁺⁴:₃D₅ = D₂₀.₃₂C₂³	φ: D₅/C₅ → C₂ ⊆ Out 2₊¹⁺⁴	80	8+	ES+(2,2):3D5	320,1507
2₊¹⁺⁴:₄D₅ = D₂₀.₃₃C₂³	φ: D₅/C₅ → C₂ ⊆ Out 2₊¹⁺⁴	80	8-	ES+(2,2):4D5	320,1508
2₊¹⁺⁴:₅D₅ = D₂₀.₃₇C₂³	φ: trivial image	80	8-	ES+(2,2):5D5	320,1623

Non-split extensions G=N.Q with N=2₊¹⁺⁴ and Q=D₅

extension	φ:Q→Out N	d	ρ	Label	ID
2₊¹⁺⁴.₁D₅ = 2₊¹⁺⁴.D₅	φ: D₅/C₅ → C₂ ⊆ Out 2₊¹⁺⁴	80	8-	ES+(2,2).1D5	320,869
2₊¹⁺⁴.₂D₅ = 2₊¹⁺⁴.₂D₅	φ: D₅/C₅ → C₂ ⊆ Out 2₊¹⁺⁴	80	8-	ES+(2,2).2D5	320,870

׿

x

:

Z

F

o

wr

Q

<