Extensions 1→N→G→Q→1 with N=C₈ and Q=Dic₃

Direct product G=N×Q with N=C₈ and Q=Dic₃

		d	ρ	Label	ID
C₈×Dic₃		96		C8xDic3	96,20

Semidirect products G=N:Q with N=C₈ and Q=Dic₃

extension	φ:Q→Aut N	d	ρ	Label	ID
C₈⋊₁Dic₃ = C₂₄⋊₁C₄	φ: Dic₃/C₆ → C₂ ⊆ Aut C₈	96		C8:1Dic3	96,25
C₈⋊₂Dic₃ = C₈⋊Dic₃	φ: Dic₃/C₆ → C₂ ⊆ Aut C₈	96		C8:2Dic3	96,24
C₈⋊₃Dic₃ = C₂₄⋊C₄	φ: Dic₃/C₆ → C₂ ⊆ Aut C₈	96		C8:3Dic3	96,22

Non-split extensions G=N.Q with N=C₈ and Q=Dic₃

extension	φ:Q→Aut N	d	ρ	Label	ID
C₈.₁Dic₃ = C₂₄.C₄	φ: Dic₃/C₆ → C₂ ⊆ Aut C₈	48	2	C8.1Dic3	96,26
C₈.₂Dic₃ = C₁₂.C₈	φ: Dic₃/C₆ → C₂ ⊆ Aut C₈	48	2	C8.2Dic3	96,19
C₈.₃Dic₃ = C₃⋊C₃₂	central extension (φ=1)	96	2	C8.3Dic3	96,1
C₈.₄Dic₃ = C₂×C₃⋊C₁₆	central extension (φ=1)	96		C8.4Dic3	96,18

׿

×

⋊

ℤ

𝔽

○

≀

ℚ

◁