Extensions 1→N→G→Q→1 with N=C₆ and Q=Dic₆

Direct product G=N×Q with N=C₆ and Q=Dic₆

		d	ρ	Label	ID
C₆×Dic₆		48		C6xDic6	144,158

Semidirect products G=N:Q with N=C₆ and Q=Dic₆

extension	φ:Q→Aut N	d	ρ	Label	ID
C₆⋊₁Dic₆ = C₂×C₃²⋊₂Q₈	φ: Dic₆/Dic₃ → C₂ ⊆ Aut C₆	48		C6:1Dic6	144,152
C₆⋊₂Dic₆ = C₂×C₃²⋊₄Q₈	φ: Dic₆/C₁₂ → C₂ ⊆ Aut C₆	144		C6:2Dic6	144,168

Non-split extensions G=N.Q with N=C₆ and Q=Dic₆

extension	φ:Q→Aut N	d	ρ	Label	ID
C₆.₁Dic₆ = Dic₃⋊Dic₃	φ: Dic₆/Dic₃ → C₂ ⊆ Aut C₆	48		C6.1Dic6	144,66
C₆.₂Dic₆ = C₆².C₂²	φ: Dic₆/Dic₃ → C₂ ⊆ Aut C₆	48		C6.2Dic6	144,67
C₆.₃Dic₆ = Dic₉⋊C₄	φ: Dic₆/C₁₂ → C₂ ⊆ Aut C₆	144		C6.3Dic6	144,12
C₆.₄Dic₆ = C₄⋊Dic₉	φ: Dic₆/C₁₂ → C₂ ⊆ Aut C₆	144		C6.4Dic6	144,13
C₆.₅Dic₆ = C₂×Dic₁₈	φ: Dic₆/C₁₂ → C₂ ⊆ Aut C₆	144		C6.5Dic6	144,37
C₆.₆Dic₆ = C₆.Dic₆	φ: Dic₆/C₁₂ → C₂ ⊆ Aut C₆	144		C6.6Dic6	144,93
C₆.₇Dic₆ = C₁₂⋊Dic₃	φ: Dic₆/C₁₂ → C₂ ⊆ Aut C₆	144		C6.7Dic6	144,94
C₆.₈Dic₆ = C₃×Dic₃⋊C₄	central extension (φ=1)	48		C6.8Dic6	144,77
C₆.₉Dic₆ = C₃×C₄⋊Dic₃	central extension (φ=1)	48		C6.9Dic6	144,78

׿

×

⋊

ℤ

𝔽

○

≀

ℚ

◁