Extensions 1→N→G→Q→1 with N=C₈₀ and Q=C₆

Direct product G=N×Q with N=C₈₀ and Q=C₆

		d	ρ	Label	ID
C₂×C₂₄₀		480		C2xC240	480,212

Semidirect products G=N:Q with N=C₈₀ and Q=C₆

extension	φ:Q→Aut N	d	ρ	Label	ID
C₈₀⋊₁C₆ = C₃×D₈₀	φ: C₆/C₃ → C₂ ⊆ Aut C₈₀	240	2	C80:1C6	480,77
C₈₀⋊₂C₆ = C₃×C₁₆⋊D₅	φ: C₆/C₃ → C₂ ⊆ Aut C₈₀	240	2	C80:2C6	480,78
C₈₀⋊₃C₆ = C₁₅×D₁₆	φ: C₆/C₃ → C₂ ⊆ Aut C₈₀	240	2	C80:3C6	480,214
C₈₀⋊₄C₆ = D₅×C₄₈	φ: C₆/C₃ → C₂ ⊆ Aut C₈₀	240	2	C80:4C6	480,75
C₈₀⋊₅C₆ = C₃×C₈₀⋊C₂	φ: C₆/C₃ → C₂ ⊆ Aut C₈₀	240	2	C80:5C6	480,76
C₈₀⋊₆C₆ = C₁₅×SD₃₂	φ: C₆/C₃ → C₂ ⊆ Aut C₈₀	240	2	C80:6C6	480,215
C₈₀⋊₇C₆ = C₁₅×M₅(2)	φ: C₆/C₃ → C₂ ⊆ Aut C₈₀	240	2	C80:7C6	480,213

Non-split extensions G=N.Q with N=C₈₀ and Q=C₆

extension	φ:Q→Aut N	d	ρ	Label	ID
C₈₀.₁C₆ = C₃×Dic₄₀	φ: C₆/C₃ → C₂ ⊆ Aut C₈₀	480	2	C80.1C6	480,79
C₈₀.₂C₆ = C₁₅×Q₃₂	φ: C₆/C₃ → C₂ ⊆ Aut C₈₀	480	2	C80.2C6	480,216
C₈₀.₃C₆ = C₃×C₅⋊₂C₃₂	φ: C₆/C₃ → C₂ ⊆ Aut C₈₀	480	2	C80.3C6	480,2

׿

×

⋊

ℤ

𝔽

○

≀

ℚ

◁