Extensions 1→N→G→Q→1 with N=C₂²×C₆ and Q=C₁₀

Direct product G=N×Q with N=C₂²×C₆ and Q=C₁₀

		d	ρ	Label	ID
C₂³×C₃₀		240		C2^3xC30	240,208

Semidirect products G=N:Q with N=C₂²×C₆ and Q=C₁₀

extension	φ:Q→Aut N	d	Label	ID
(C₂²×C₆)⋊₁C₁₀ = D₄×C₃₀	φ: C₁₀/C₅ → C₂ ⊆ Aut C₂²×C₆	120	(C2^2xC6):1C10	240,186
(C₂²×C₆)⋊₂C₁₀ = C₁₀×C₃⋊D₄	φ: C₁₀/C₅ → C₂ ⊆ Aut C₂²×C₆	120	(C2^2xC6):2C10	240,174
(C₂²×C₆)⋊₃C₁₀ = S₃×C₂²×C₁₀	φ: C₁₀/C₅ → C₂ ⊆ Aut C₂²×C₆	120	(C2^2xC6):3C10	240,206

Non-split extensions G=N.Q with N=C₂²×C₆ and Q=C₁₀

extension	φ:Q→Aut N	d	Label	ID
(C₂²×C₆).₁C₁₀ = C₁₅×C₂²⋊C₄	φ: C₁₀/C₅ → C₂ ⊆ Aut C₂²×C₆	120	(C2^2xC6).1C10	240,82
(C₂²×C₆).₂C₁₀ = C₅×C₆.D₄	φ: C₁₀/C₅ → C₂ ⊆ Aut C₂²×C₆	120	(C2^2xC6).2C10	240,64
(C₂²×C₆).₃C₁₀ = Dic₃×C₂×C₁₀	φ: C₁₀/C₅ → C₂ ⊆ Aut C₂²×C₆	240	(C2^2xC6).3C10	240,173

⋊

ℤ

𝔽

○

≀

ℚ

◁

Extensions 1→N→G→Q→1 with N=C22×C6 and Q=C10