Extensions 1→N→G→Q→1 with N=C₇₅ and Q=S₃

Direct product G=N×Q with N=C₇₅ and Q=S₃

		d	ρ	Label	ID
S₃×C₇₅		150	2	S3xC75	450,6

Semidirect products G=N:Q with N=C₇₅ and Q=S₃

extension	φ:Q→Aut N	d	ρ	Label	ID
C₇₅⋊₁S₃ = C₃⋊D₇₅	φ: S₃/C₃ → C₂ ⊆ Aut C₇₅	225		C75:1S3	450,9
C₇₅⋊₂S₃ = C₃×D₇₅	φ: S₃/C₃ → C₂ ⊆ Aut C₇₅	150	2	C75:2S3	450,7
C₇₅⋊₃S₃ = C₃⋊S₃×C₂₅	φ: S₃/C₃ → C₂ ⊆ Aut C₇₅	225		C75:3S3	450,8

Non-split extensions G=N.Q with N=C₇₅ and Q=S₃

extension	φ:Q→Aut N	d	ρ	Label	ID
C₇₅.₁S₃ = D₂₂₅	φ: S₃/C₃ → C₂ ⊆ Aut C₇₅	225	2+	C75.1S3	450,3
C₇₅.₂S₃ = D₉×C₂₅	φ: S₃/C₃ → C₂ ⊆ Aut C₇₅	225	2	C75.2S3	450,1

⋊

ℤ

𝔽

○

≀

ℚ

◁

Extensions 1→N→G→Q→1 with N=C75 and Q=S3