Extensions 1→N→G→Q→1 with N=C₄ and Q=D₆₀

Direct product G=N×Q with N=C₄ and Q=D₆₀

		d	ρ	Label	ID
C₄×D₆₀		240		C4xD60	480,838

Semidirect products G=N:Q with N=C₄ and Q=D₆₀

extension	φ:Q→Aut N	d	ρ	Label	ID
C₄⋊₁D₆₀ = C₄²⋊₆D₁₅	φ: D₆₀/C₆₀ → C₂ ⊆ Aut C₄	240		C4:1D60	480,839
C₄⋊₂D₆₀ = C₄⋊D₆₀	φ: D₆₀/D₃₀ → C₂ ⊆ Aut C₄	240		C4:2D60	480,860

Non-split extensions G=N.Q with N=C₄ and Q=D₆₀

extension	φ:Q→Aut N	d	ρ	Label	ID
C₄.₁D₆₀ = D₂₄₀	φ: D₆₀/C₆₀ → C₂ ⊆ Aut C₄	240	2+	C4.1D60	480,159
C₄.₂D₆₀ = C₄₈⋊D₅	φ: D₆₀/C₆₀ → C₂ ⊆ Aut C₄	240	2	C4.2D60	480,160
C₄.₃D₆₀ = Dic₁₂₀	φ: D₆₀/C₆₀ → C₂ ⊆ Aut C₄	480	2-	C4.3D60	480,161
C₄.₄D₆₀ = C₆₀⋊₈Q₈	φ: D₆₀/C₆₀ → C₂ ⊆ Aut C₄	480		C4.4D60	480,834
C₄.₅D₆₀ = C₄²⋊₇D₁₅	φ: D₆₀/C₆₀ → C₂ ⊆ Aut C₄	240		C4.5D60	480,840
C₄.₆D₆₀ = C₂×C₂₄⋊D₅	φ: D₆₀/C₆₀ → C₂ ⊆ Aut C₄	240		C4.6D60	480,867
C₄.₇D₆₀ = C₂×D₁₂₀	φ: D₆₀/C₆₀ → C₂ ⊆ Aut C₄	240		C4.7D60	480,868
C₄.₈D₆₀ = C₂×Dic₆₀	φ: D₆₀/C₆₀ → C₂ ⊆ Aut C₄	480		C4.8D60	480,870
C₄.₉D₆₀ = D₆₀⋊₉C₄	φ: D₆₀/D₃₀ → C₂ ⊆ Aut C₄	240		C4.9D60	480,169
C₄.₁₀D₆₀ = Dic₃₀⋊₉C₄	φ: D₆₀/D₃₀ → C₂ ⊆ Aut C₄	480		C4.10D60	480,170
C₄.₁₁D₆₀ = M₄(2)⋊D₁₅	φ: D₆₀/D₃₀ → C₂ ⊆ Aut C₄	120	4+	C4.11D60	480,183
C₄.₁₂D₆₀ = C₄.D₆₀	φ: D₆₀/D₃₀ → C₂ ⊆ Aut C₄	240	4-	C4.12D60	480,184
C₄.₁₃D₆₀ = D₃₀⋊₆Q₈	φ: D₆₀/D₃₀ → C₂ ⊆ Aut C₄	240		C4.13D60	480,862
C₄.₁₄D₆₀ = C₈⋊D₃₀	φ: D₆₀/D₃₀ → C₂ ⊆ Aut C₄	120	4+	C4.14D60	480,873
C₄.₁₅D₆₀ = C₈.D₃₀	φ: D₆₀/D₃₀ → C₂ ⊆ Aut C₄	240	4-	C4.15D60	480,874
C₄.₁₆D₆₀ = C₆₀⋊₅C₈	central extension (φ=1)	480		C4.16D60	480,164
C₄.₁₇D₆₀ = D₆₀⋊₇C₄	central extension (φ=1)	120	2	C4.17D60	480,165
C₄.₁₈D₆₀ = C₄.₁₈D₆₀	central extension (φ=1)	240	2	C4.18D60	480,179
C₄.₁₉D₆₀ = D₃₀⋊₃C₈	central extension (φ=1)	240		C4.19D60	480,180
C₄.₂₀D₆₀ = C₄₀.₆₉D₆	central extension (φ=1)	240	2	C4.20D60	480,869

⋊

ℤ

𝔽

○

≀

ℚ

◁

Extensions 1→N→G→Q→1 with N=C4 and Q=D60

Extensions 1→N→G→Q→1 with N=C₄ and Q=D₆₀