Extensions 1→N→G→Q→1 with N=C₃ and Q=A₄×C₂×C₆

Direct product G=N×Q with N=C₃ and Q=A₄×C₂×C₆

		d	ρ	Label	ID
A₄×C₆²		108		A4xC6^2	432,770

Semidirect products G=N:Q with N=C₃ and Q=A₄×C₂×C₆

extension	φ:Q→Aut N	d	ρ	Label	ID
C₃⋊(A₄×C₂×C₆) = S₃×C₆×A₄	φ: A₄×C₂×C₆/C₆×A₄ → C₂ ⊆ Aut C₃	36	6	C3:(A4xC2xC6)	432,763

Non-split extensions G=N.Q with N=C₃ and Q=A₄×C₂×C₆

extension	φ:Q→Aut N	d	ρ	Label	ID
C₃.₁(A₄×C₂×C₆) = A₄×C₂×C₁₈	central extension (φ=1)	108		C3.1(A4xC2xC6)	432,546
C₃.₂(A₄×C₂×C₆) = C₂×C₆×C₃.A₄	central extension (φ=1)	108		C3.2(A4xC2xC6)	432,548
C₃.₃(A₄×C₂×C₆) = C₂²×C₉⋊A₄	central stem extension (φ=1)	108		C3.3(A4xC2xC6)	432,547
C₃.₄(A₄×C₂×C₆) = C₂²×C₃².A₄	central stem extension (φ=1)	36		C3.4(A4xC2xC6)	432,549
C₃.₅(A₄×C₂×C₆) = C₂²×C₃²⋊A₄	central stem extension (φ=1)	36		C3.5(A4xC2xC6)	432,550

׿

×

⋊

ℤ

𝔽

○

≀

ℚ

◁