Extensions 1→N→G→Q→1 with N=C₃ and Q=C₁₂.₂₉D₆

Direct product G=N×Q with N=C₃ and Q=C₁₂.₂₉D₆

		d	ρ	Label	ID
C₃×C₁₂.₂₉D₆		48	4	C3xC12.29D6	432,415

Semidirect products G=N:Q with N=C₃ and Q=C₁₂.₂₉D₆

extension	φ:Q→Aut N	d	ρ	Label	ID
C₃⋊₁(C₁₂.₂₉D₆) = C₁₂.₆₉S₃²	φ: C₁₂.₂₉D₆/C₃×C₃⋊C₈ → C₂ ⊆ Aut C₃	72		C3:1(C12.29D6)	432,432
C₃⋊₂(C₁₂.₂₉D₆) = C₁₂.₉₃S₃²	φ: C₁₂.₂₉D₆/C₄×C₃⋊S₃ → C₂ ⊆ Aut C₃	48	4	C3:2(C12.29D6)	432,455

Non-split extensions G=N.Q with N=C₃ and Q=C₁₂.₂₉D₆

extension	φ:Q→Aut N	d	ρ	Label	ID
C₃.₁(C₁₂.₂₉D₆) = C₃₆.₃₈D₆	φ: C₁₂.₂₉D₆/C₃×C₃⋊C₈ → C₂ ⊆ Aut C₃	72	4	C3.1(C12.29D6)	432,59
C₃.₂(C₁₂.₂₉D₆) = C₁₂.₈₉S₃²	φ: C₁₂.₂₉D₆/C₄×C₃⋊S₃ → C₂ ⊆ Aut C₃	72	6	C3.2(C12.29D6)	432,81

⋊

ℤ

𝔽

○

≀

ℚ

◁

Extensions 1→N→G→Q→1 with N=C3 and Q=C12.29D6