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

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

		d	ρ	Label	ID
C₆×C₃₀		180		C6xC30	180,37

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

extension	φ:Q→Aut N	d	ρ	Label	ID
C₃₀⋊₁C₆ = C₆×D₁₅	φ: C₆/C₃ → C₂ ⊆ Aut C₃₀	60	2	C30:1C6	180,34
C₃₀⋊₂C₆ = D₅×C₃×C₆	φ: C₆/C₃ → C₂ ⊆ Aut C₃₀	90		C30:2C6	180,32
C₃₀⋊₃C₆ = S₃×C₃₀	φ: C₆/C₃ → C₂ ⊆ Aut C₃₀	60	2	C30:3C6	180,33

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

extension	φ:Q→Aut N	d	ρ	Label	ID
C₃₀.₁C₆ = C₃×Dic₁₅	φ: C₆/C₃ → C₂ ⊆ Aut C₃₀	60	2	C30.1C6	180,15
C₃₀.₂C₆ = C₉×Dic₅	φ: C₆/C₃ → C₂ ⊆ Aut C₃₀	180	2	C30.2C6	180,2
C₃₀.₃C₆ = D₅×C₁₈	φ: C₆/C₃ → C₂ ⊆ Aut C₃₀	90	2	C30.3C6	180,9
C₃₀.₄C₆ = C₃²×Dic₅	φ: C₆/C₃ → C₂ ⊆ Aut C₃₀	180		C30.4C6	180,13
C₃₀.₅C₆ = Dic₃×C₁₅	φ: C₆/C₃ → C₂ ⊆ Aut C₃₀	60	2	C30.5C6	180,14

׿

×

⋊

ℤ

𝔽

○

≀

ℚ

◁