Extensions 1→N→G→Q→1 with N=C₅₂ and Q=S₃

Direct product G=N×Q with N=C₅₂ and Q=S₃

		d	ρ	Label	ID
S₃×C₅₂		156	2	S3xC52	312,33

Semidirect products G=N:Q with N=C₅₂ and Q=S₃

extension	φ:Q→Aut N	d	ρ	Label	ID
C₅₂⋊₁S₃ = D₁₅₆	φ: S₃/C₃ → C₂ ⊆ Aut C₅₂	156	2+	C52:1S3	312,39
C₅₂⋊₂S₃ = C₄×D₃₉	φ: S₃/C₃ → C₂ ⊆ Aut C₅₂	156	2	C52:2S3	312,38
C₅₂⋊₃S₃ = C₁₃×D₁₂	φ: S₃/C₃ → C₂ ⊆ Aut C₅₂	156	2	C52:3S3	312,34

Non-split extensions G=N.Q with N=C₅₂ and Q=S₃

extension	φ:Q→Aut N	d	ρ	Label	ID
C₅₂.₁S₃ = Dic₇₈	φ: S₃/C₃ → C₂ ⊆ Aut C₅₂	312	2-	C52.1S3	312,37
C₅₂.₂S₃ = C₃₉⋊₃C₈	φ: S₃/C₃ → C₂ ⊆ Aut C₅₂	312	2	C52.2S3	312,5
C₅₂.₃S₃ = C₁₃×Dic₆	φ: S₃/C₃ → C₂ ⊆ Aut C₅₂	312	2	C52.3S3	312,32
C₅₂.₄S₃ = C₁₃×C₃⋊C₈	central extension (φ=1)	312	2	C52.4S3	312,3

׿

×

⋊

ℤ

𝔽

○

≀

ℚ

◁