Extensions 1→N→G→Q→1 with N=C₃₀ and Q=C₁₂

Direct product G=N×Q with N=C₃₀ and Q=C₁₂

		d	ρ	Label	ID
C₆×C₆₀		360		C6xC60	360,115

Semidirect products G=N:Q with N=C₃₀ and Q=C₁₂

extension	φ:Q→Aut N	d	ρ	Label	ID
C₃₀⋊₁C₁₂ = C₆×C₃⋊F₅	φ: C₁₂/C₃ → C₄ ⊆ Aut C₃₀	60	4	C30:1C12	360,146
C₃₀⋊₂C₁₂ = C₃×C₆×F₅	φ: C₁₂/C₃ → C₄ ⊆ Aut C₃₀	90		C30:2C12	360,145
C₃₀⋊₃C₁₂ = C₆×Dic₁₅	φ: C₁₂/C₆ → C₂ ⊆ Aut C₃₀	120		C30:3C12	360,103
C₃₀⋊₄C₁₂ = C₃×C₆×Dic₅	φ: C₁₂/C₆ → C₂ ⊆ Aut C₃₀	360		C30:4C12	360,93
C₃₀⋊₅C₁₂ = Dic₃×C₃₀	φ: C₁₂/C₆ → C₂ ⊆ Aut C₃₀	120		C30:5C12	360,98

Non-split extensions G=N.Q with N=C₃₀ and Q=C₁₂

extension	φ:Q→Aut N	d	ρ	Label	ID
C₃₀.₁C₁₂ = C₃×C₁₅⋊C₈	φ: C₁₂/C₃ → C₄ ⊆ Aut C₃₀	120	4	C30.1C12	360,53
C₃₀.₂C₁₂ = C₉×C₅⋊C₈	φ: C₁₂/C₃ → C₄ ⊆ Aut C₃₀	360	4	C30.2C12	360,5
C₃₀.₃C₁₂ = C₁₈×F₅	φ: C₁₂/C₃ → C₄ ⊆ Aut C₃₀	90	4	C30.3C12	360,43
C₃₀.₄C₁₂ = C₃²×C₅⋊C₈	φ: C₁₂/C₃ → C₄ ⊆ Aut C₃₀	360		C30.4C12	360,52
C₃₀.₅C₁₂ = C₃×C₁₅⋊₃C₈	φ: C₁₂/C₆ → C₂ ⊆ Aut C₃₀	120	2	C30.5C12	360,35
C₃₀.₆C₁₂ = C₉×C₅⋊₂C₈	φ: C₁₂/C₆ → C₂ ⊆ Aut C₃₀	360	2	C30.6C12	360,2
C₃₀.₇C₁₂ = C₁₈×Dic₅	φ: C₁₂/C₆ → C₂ ⊆ Aut C₃₀	360		C30.7C12	360,18
C₃₀.₈C₁₂ = C₃²×C₅⋊₂C₈	φ: C₁₂/C₆ → C₂ ⊆ Aut C₃₀	360		C30.8C12	360,33
C₃₀.₉C₁₂ = C₁₅×C₃⋊C₈	φ: C₁₂/C₆ → C₂ ⊆ Aut C₃₀	120	2	C30.9C12	360,34

׿

×

⋊

ℤ

𝔽

○

≀

ℚ

◁