Extensions 1→N→G→Q→1 with N=C₂×C₃₀ and Q=C₆

Direct product G=N×Q with N=C₂×C₃₀ and Q=C₆

		d	ρ	Label	ID
C₂×C₆×C₃₀		360		C2xC6xC30	360,162

Semidirect products G=N:Q with N=C₂×C₃₀ and Q=C₆

extension	φ:Q→Aut N	d	ρ	Label	ID
(C₂×C₃₀)⋊₁C₆ = A₄×D₁₅	φ: C₆/C₁ → C₆ ⊆ Aut C₂×C₃₀	60	6+	(C2xC30):1C6	360,144
(C₂×C₃₀)⋊₂C₆ = C₃×D₅×A₄	φ: C₆/C₁ → C₆ ⊆ Aut C₂×C₃₀	60	6	(C2xC30):2C6	360,142
(C₂×C₃₀)⋊₃C₆ = C₅×S₃×A₄	φ: C₆/C₁ → C₆ ⊆ Aut C₂×C₃₀	60	6	(C2xC30):3C6	360,143
(C₂×C₃₀)⋊₄C₆ = A₄×C₃₀	φ: C₆/C₂ → C₃ ⊆ Aut C₂×C₃₀	90	3	(C2xC30):4C6	360,156
(C₂×C₃₀)⋊₅C₆ = D₄×C₃×C₁₅	φ: C₆/C₃ → C₂ ⊆ Aut C₂×C₃₀	180		(C2xC30):5C6	360,116
(C₂×C₃₀)⋊₆C₆ = C₃×C₁₅⋊₇D₄	φ: C₆/C₃ → C₂ ⊆ Aut C₂×C₃₀	60	2	(C2xC30):6C6	360,104
(C₂×C₃₀)⋊₇C₆ = C₂×C₆×D₁₅	φ: C₆/C₃ → C₂ ⊆ Aut C₂×C₃₀	120		(C2xC30):7C6	360,159
(C₂×C₃₀)⋊₈C₆ = C₃²×C₅⋊D₄	φ: C₆/C₃ → C₂ ⊆ Aut C₂×C₃₀	180		(C2xC30):8C6	360,94
(C₂×C₃₀)⋊₉C₆ = D₅×C₆²	φ: C₆/C₃ → C₂ ⊆ Aut C₂×C₃₀	180		(C2xC30):9C6	360,157
(C₂×C₃₀)⋊₁₀C₆ = C₁₅×C₃⋊D₄	φ: C₆/C₃ → C₂ ⊆ Aut C₂×C₃₀	60	2	(C2xC30):10C6	360,99
(C₂×C₃₀)⋊₁₁C₆ = S₃×C₂×C₃₀	φ: C₆/C₃ → C₂ ⊆ Aut C₂×C₃₀	120		(C2xC30):11C6	360,158

Non-split extensions G=N.Q with N=C₂×C₃₀ and Q=C₆

extension	φ:Q→Aut N	d	ρ	Label	ID
(C₂×C₃₀).C₆ = D₅×C₃.A₄	φ: C₆/C₁ → C₆ ⊆ Aut C₂×C₃₀	90	6	(C2xC30).C6	360,42
(C₂×C₃₀).₂C₆ = C₁₀×C₃.A₄	φ: C₆/C₂ → C₃ ⊆ Aut C₂×C₃₀	90	3	(C2xC30).2C6	360,46
(C₂×C₃₀).₃C₆ = D₄×C₄₅	φ: C₆/C₃ → C₂ ⊆ Aut C₂×C₃₀	180	2	(C2xC30).3C6	360,31
(C₂×C₃₀).₄C₆ = C₆×Dic₁₅	φ: C₆/C₃ → C₂ ⊆ Aut C₂×C₃₀	120		(C2xC30).4C6	360,103
(C₂×C₃₀).₅C₆ = C₁₈×Dic₅	φ: C₆/C₃ → C₂ ⊆ Aut C₂×C₃₀	360		(C2xC30).5C6	360,18
(C₂×C₃₀).₆C₆ = C₉×C₅⋊D₄	φ: C₆/C₃ → C₂ ⊆ Aut C₂×C₃₀	180	2	(C2xC30).6C6	360,19
(C₂×C₃₀).₇C₆ = D₅×C₂×C₁₈	φ: C₆/C₃ → C₂ ⊆ Aut C₂×C₃₀	180		(C2xC30).7C6	360,47
(C₂×C₃₀).₈C₆ = C₃×C₆×Dic₅	φ: C₆/C₃ → C₂ ⊆ Aut C₂×C₃₀	360		(C2xC30).8C6	360,93
(C₂×C₃₀).₉C₆ = Dic₃×C₃₀	φ: C₆/C₃ → C₂ ⊆ Aut C₂×C₃₀	120		(C2xC30).9C6	360,98

׿

×

⋊

ℤ

𝔽

○

≀

ℚ

◁