Extensions 1→N→G→Q→1 with N=C₄² and Q=S₃

Direct product G=N×Q with N=C₄² and Q=S₃

		d	ρ	Label	ID
S₃×C₄²		48		S3xC4^2	96,78

Semidirect products G=N:Q with N=C₄² and Q=S₃

extension	φ:Q→Aut N	d	ρ	Label	ID
C₄²⋊S₃ = C₄²⋊S₃	φ: S₃/C₁ → S₃ ⊆ Aut C₄²	12	3	C4^2:S3	96,64
C₄²⋊₂S₃ = C₄²⋊₂S₃	φ: S₃/C₃ → C₂ ⊆ Aut C₄²	48		C4^2:2S3	96,79
C₄²⋊₃S₃ = C₄²⋊₃S₃	φ: S₃/C₃ → C₂ ⊆ Aut C₄²	48		C4^2:3S3	96,83
C₄²⋊₄S₃ = C₄²⋊₄S₃	φ: S₃/C₃ → C₂ ⊆ Aut C₄²	24	2	C4^2:4S3	96,12
C₄²⋊₅S₃ = C₄×D₁₂	φ: S₃/C₃ → C₂ ⊆ Aut C₄²	48		C4^2:5S3	96,80
C₄²⋊₆S₃ = C₄⋊D₁₂	φ: S₃/C₃ → C₂ ⊆ Aut C₄²	48		C4^2:6S3	96,81
C₄²⋊₇S₃ = C₄²⋊₇S₃	φ: S₃/C₃ → C₂ ⊆ Aut C₄²	48		C4^2:7S3	96,82

Non-split extensions G=N.Q with N=C₄² and Q=S₃

extension	φ:Q→Aut N	d	ρ	Label	ID
C₄².₁S₃ = C₄².S₃	φ: S₃/C₃ → C₂ ⊆ Aut C₄²	96		C4^2.1S3	96,10
C₄².₂S₃ = C₁₂⋊C₈	φ: S₃/C₃ → C₂ ⊆ Aut C₄²	96		C4^2.2S3	96,11
C₄².₃S₃ = C₄×Dic₆	φ: S₃/C₃ → C₂ ⊆ Aut C₄²	96		C4^2.3S3	96,75
C₄².₄S₃ = C₁₂⋊₂Q₈	φ: S₃/C₃ → C₂ ⊆ Aut C₄²	96		C4^2.4S3	96,76
C₄².₅S₃ = C₁₂.₆Q₈	φ: S₃/C₃ → C₂ ⊆ Aut C₄²	96		C4^2.5S3	96,77
C₄².₆S₃ = C₄×C₃⋊C₈	central extension (φ=1)	96		C4^2.6S3	96,9

׿

×

⋊

ℤ

𝔽

○

≀

ℚ

◁