Extensions 1→N→G→Q→1 with N=C₂³ and Q=C₆₀

Direct product G=N×Q with N=C₂³ and Q=C₆₀

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

Semidirect products G=N:Q with N=C₂³ and Q=C₆₀

extension	φ:Q→Aut N	d	ρ	Label	ID
C₂³⋊C₆₀ = C₁₅×C₂³⋊C₄	φ: C₆₀/C₁₅ → C₄ ⊆ Aut C₂³	120	4	C2^3:C60	480,202
C₂³⋊₂C₆₀ = A₄×C₂×C₂₀	φ: C₆₀/C₂₀ → C₃ ⊆ Aut C₂³	120		C2^3:2C60	480,1126
C₂³⋊₃C₆₀ = C₂²⋊C₄×C₃₀	φ: C₆₀/C₃₀ → C₂ ⊆ Aut C₂³	240		C2^3:3C60	480,920

Non-split extensions G=N.Q with N=C₂³ and Q=C₆₀

extension	φ:Q→Aut N	d	ρ	Label	ID
C₂³.C₆₀ = C₁₅×C₄.D₄	φ: C₆₀/C₁₅ → C₄ ⊆ Aut C₂³	120	4	C2^3.C60	480,203
C₂³.₂C₆₀ = A₄×C₄₀	φ: C₆₀/C₂₀ → C₃ ⊆ Aut C₂³	120	3	C2^3.2C60	480,659
C₂³.₃C₆₀ = C₁₅×C₂²⋊C₈	φ: C₆₀/C₃₀ → C₂ ⊆ Aut C₂³	240		C2^3.3C60	480,201
C₂³.₄C₆₀ = M₄(2)×C₃₀	φ: C₆₀/C₃₀ → C₂ ⊆ Aut C₂³	240		C2^3.4C60	480,935

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