Extensions 1→N→G→Q→1 with N=C₈ and Q=C₆₀

Direct product G=N×Q with N=C₈ and Q=C₆₀

		d	ρ	Label	ID
C₄×C₁₂₀		480		C4xC120	480,199

Semidirect products G=N:Q with N=C₈ and Q=C₆₀

extension	φ:Q→Aut N	d	Label	ID
C₈⋊₁C₆₀ = C₁₅×C₂.D₈	φ: C₆₀/C₃₀ → C₂ ⊆ Aut C₈	480	C8:1C60	480,210
C₈⋊₂C₆₀ = C₁₅×C₄.Q₈	φ: C₆₀/C₃₀ → C₂ ⊆ Aut C₈	480	C8:2C60	480,209
C₈⋊₃C₆₀ = C₁₅×C₈⋊C₄	φ: C₆₀/C₃₀ → C₂ ⊆ Aut C₈	480	C8:3C60	480,200

Non-split extensions G=N.Q with N=C₈ and Q=C₆₀

extension	φ:Q→Aut N	d	ρ	Label	ID
C₈.₁C₆₀ = C₁₅×C₈.C₄	φ: C₆₀/C₃₀ → C₂ ⊆ Aut C₈	240	2	C8.1C60	480,211
C₈.₂C₆₀ = C₁₅×M₅(2)	φ: C₆₀/C₃₀ → C₂ ⊆ Aut C₈	240	2	C8.2C60	480,213

⋊

ℤ

𝔽

○

≀

ℚ

◁

Extensions 1→N→G→Q→1 with N=C8 and Q=C60