Extensions 1→N→G→Q→1 with N=C₂³ and Q=F₅

Direct product G=N×Q with N=C₂³ and Q=F₅

		d	ρ	Label	ID
C₂³×F₅		40		C2^3xF5	160,236

Semidirect products G=N:Q with N=C₂³ and Q=F₅

extension	φ:Q→Aut N	d	ρ	Label	ID
C₂³⋊F₅ = C₂³⋊F₅	φ: F₅/C₅ → C₄ ⊆ Aut C₂³	40	4	C2^3:F5	160,86
C₂³⋊₂F₅ = C₂×C₂²⋊F₅	φ: F₅/D₅ → C₂ ⊆ Aut C₂³	40		C2^3:2F5	160,212

Non-split extensions G=N.Q with N=C₂³ and Q=F₅

extension	φ:Q→Aut N	d	ρ	Label	ID
C₂³.F₅ = C₂³.F₅	φ: F₅/C₅ → C₄ ⊆ Aut C₂³	40	4	C2^3.F5	160,88
C₂³.₂F₅ = C₂³.₂F₅	φ: F₅/D₅ → C₂ ⊆ Aut C₂³	80		C2^3.2F5	160,87
C₂³.₃F₅ = C₂×C₂².F₅	φ: F₅/D₅ → C₂ ⊆ Aut C₂³	80		C2^3.3F5	160,211
C₂³.₄F₅ = C₂²×C₅⋊C₈	central extension (φ=1)	160		C2^3.4F5	160,210

׿

×

⋊

ℤ

𝔽

○

≀

ℚ

◁