Extensions 1→N→G→Q→1 with N=C₃ and Q=D₅×C₁₂

Direct product G=N×Q with N=C₃ and Q=D₅×C₁₂

		d	ρ	Label	ID
D₅×C₃×C₁₂		180		D5xC3xC12	360,91

Semidirect products G=N:Q with N=C₃ and Q=D₅×C₁₂

extension	φ:Q→Aut N	d	ρ	Label	ID
C₃⋊₁(D₅×C₁₂) = C₃×D₃₀.C₂	φ: D₅×C₁₂/C₃×Dic₅ → C₂ ⊆ Aut C₃	120	4	C3:1(D5xC12)	360,60
C₃⋊₂(D₅×C₁₂) = C₁₂×D₁₅	φ: D₅×C₁₂/C₆₀ → C₂ ⊆ Aut C₃	120	2	C3:2(D5xC12)	360,101
C₃⋊₃(D₅×C₁₂) = C₃×D₅×Dic₃	φ: D₅×C₁₂/C₆×D₅ → C₂ ⊆ Aut C₃	60	4	C3:3(D5xC12)	360,58

Non-split extensions G=N.Q with N=C₃ and Q=D₅×C₁₂

extension	φ:Q→Aut N	d	ρ	Label	ID
C₃.(D₅×C₁₂) = D₅×C₃₆	central extension (φ=1)	180	2	C3.(D5xC12)	360,16

⋊

ℤ

𝔽

○

≀

ℚ

◁

Extensions 1→N→G→Q→1 with N=C3 and Q=D5×C12