Extensions 1→N→G→Q→1 with N=C₂²×C₆ and Q=C₂₀

Direct product G=N×Q with N=C₂²×C₆ and Q=C₂₀

		d	ρ	Label	ID
C₂³×C₆₀		480		C2^3xC60	480,1180

Semidirect products G=N:Q with N=C₂²×C₆ and Q=C₂₀

extension	φ:Q→Aut N	d	ρ	Label	ID
(C₂²×C₆)⋊₁C₂₀ = C₁₅×C₂³⋊C₄	φ: C₂₀/C₅ → C₄ ⊆ Aut C₂²×C₆	120	4	(C2^2xC6):1C20	480,202
(C₂²×C₆)⋊₂C₂₀ = C₅×C₂³.₇D₆	φ: C₂₀/C₅ → C₄ ⊆ Aut C₂²×C₆	120	4	(C2^2xC6):2C20	480,153
(C₂²×C₆)⋊₃C₂₀ = C₂²⋊C₄×C₃₀	φ: C₂₀/C₁₀ → C₂ ⊆ Aut C₂²×C₆	240		(C2^2xC6):3C20	480,920
(C₂²×C₆)⋊₄C₂₀ = C₁₀×C₆.D₄	φ: C₂₀/C₁₀ → C₂ ⊆ Aut C₂²×C₆	240		(C2^2xC6):4C20	480,831
(C₂²×C₆)⋊₅C₂₀ = Dic₃×C₂²×C₁₀	φ: C₂₀/C₁₀ → C₂ ⊆ Aut C₂²×C₆	480		(C2^2xC6):5C20	480,1163

Non-split extensions G=N.Q with N=C₂²×C₆ and Q=C₂₀

extension	φ:Q→Aut N	d	ρ	Label	ID
(C₂²×C₆).₁C₂₀ = C₁₅×C₄.D₄	φ: C₂₀/C₅ → C₄ ⊆ Aut C₂²×C₆	120	4	(C2^2xC6).1C20	480,203
(C₂²×C₆).₂C₂₀ = C₅×C₁₂.D₄	φ: C₂₀/C₅ → C₄ ⊆ Aut C₂²×C₆	120	4	(C2^2xC6).2C20	480,152
(C₂²×C₆).₃C₂₀ = C₁₅×C₂²⋊C₈	φ: C₂₀/C₁₀ → C₂ ⊆ Aut C₂²×C₆	240		(C2^2xC6).3C20	480,201
(C₂²×C₆).₄C₂₀ = M₄(2)×C₃₀	φ: C₂₀/C₁₀ → C₂ ⊆ Aut C₂²×C₆	240		(C2^2xC6).4C20	480,935
(C₂²×C₆).₅C₂₀ = C₅×C₁₂.₅₅D₄	φ: C₂₀/C₁₀ → C₂ ⊆ Aut C₂²×C₆	240		(C2^2xC6).5C20	480,149
(C₂²×C₆).₆C₂₀ = C₂×C₁₀×C₃⋊C₈	φ: C₂₀/C₁₀ → C₂ ⊆ Aut C₂²×C₆	480		(C2^2xC6).6C20	480,799
(C₂²×C₆).₇C₂₀ = C₁₀×C₄.Dic₃	φ: C₂₀/C₁₀ → C₂ ⊆ Aut C₂²×C₆	240		(C2^2xC6).7C20	480,800

׿

×

⋊

ℤ

𝔽

○

≀

ℚ

◁