Extensions 1→N→G→Q→1 with N=C₂₄ and Q=S₃

Direct product G=N×Q with N=C₂₄ and Q=S₃

		d	ρ	Label	ID
S₃×C₂₄		48	2	S3xC24	144,69

Semidirect products G=N:Q with N=C₂₄ and Q=S₃

extension	φ:Q→Aut N	d	ρ	Label	ID
C₂₄⋊₁S₃ = C₃²⋊₅D₈	φ: S₃/C₃ → C₂ ⊆ Aut C₂₄	72		C24:1S3	144,88
C₂₄⋊₂S₃ = C₂₄⋊₂S₃	φ: S₃/C₃ → C₂ ⊆ Aut C₂₄	72		C24:2S3	144,87
C₂₄⋊₃S₃ = C₃×D₂₄	φ: S₃/C₃ → C₂ ⊆ Aut C₂₄	48	2	C24:3S3	144,72
C₂₄⋊₄S₃ = C₈×C₃⋊S₃	φ: S₃/C₃ → C₂ ⊆ Aut C₂₄	72		C24:4S3	144,85
C₂₄⋊₅S₃ = C₂₄⋊S₃	φ: S₃/C₃ → C₂ ⊆ Aut C₂₄	72		C24:5S3	144,86
C₂₄⋊₆S₃ = C₃×C₂₄⋊C₂	φ: S₃/C₃ → C₂ ⊆ Aut C₂₄	48	2	C24:6S3	144,71
C₂₄⋊₇S₃ = C₃×C₈⋊S₃	φ: S₃/C₃ → C₂ ⊆ Aut C₂₄	48	2	C24:7S3	144,70

Non-split extensions G=N.Q with N=C₂₄ and Q=S₃

extension	φ:Q→Aut N	d	ρ	Label	ID
C₂₄.₁S₃ = Dic₃₆	φ: S₃/C₃ → C₂ ⊆ Aut C₂₄	144	2-	C24.1S3	144,4
C₂₄.₂S₃ = D₇₂	φ: S₃/C₃ → C₂ ⊆ Aut C₂₄	72	2+	C24.2S3	144,8
C₂₄.₃S₃ = C₃²⋊₅Q₁₆	φ: S₃/C₃ → C₂ ⊆ Aut C₂₄	144		C24.3S3	144,89
C₂₄.₄S₃ = C₇₂⋊C₂	φ: S₃/C₃ → C₂ ⊆ Aut C₂₄	72	2	C24.4S3	144,7
C₂₄.₅S₃ = C₃×Dic₁₂	φ: S₃/C₃ → C₂ ⊆ Aut C₂₄	48	2	C24.5S3	144,73
C₂₄.₆S₃ = C₉⋊C₁₆	φ: S₃/C₃ → C₂ ⊆ Aut C₂₄	144	2	C24.6S3	144,1
C₂₄.₇S₃ = C₈×D₉	φ: S₃/C₃ → C₂ ⊆ Aut C₂₄	72	2	C24.7S3	144,5
C₂₄.₈S₃ = C₈⋊D₉	φ: S₃/C₃ → C₂ ⊆ Aut C₂₄	72	2	C24.8S3	144,6
C₂₄.₉S₃ = C₂₄.S₃	φ: S₃/C₃ → C₂ ⊆ Aut C₂₄	144		C24.9S3	144,29
C₂₄.₁₀S₃ = C₃×C₃⋊C₁₆	central extension (φ=1)	48	2	C24.10S3	144,28

׿

×

⋊

ℤ

𝔽

○

≀

ℚ

◁