Extensions 1→N→G→Q→1 with N=C₈ and Q=C₅×S₃

Direct product G=N×Q with N=C₈ and Q=C₅×S₃

		d	ρ	Label	ID
S₃×C₄₀		120	2	S3xC40	240,49

Semidirect products G=N:Q with N=C₈ and Q=C₅×S₃

extension	φ:Q→Aut N	d	ρ	Label	ID
C₈⋊₁(C₅×S₃) = C₅×D₂₄	φ: C₅×S₃/C₁₅ → C₂ ⊆ Aut C₈	120	2	C8:1(C5xS3)	240,52
C₈⋊₂(C₅×S₃) = C₅×C₂₄⋊C₂	φ: C₅×S₃/C₁₅ → C₂ ⊆ Aut C₈	120	2	C8:2(C5xS3)	240,51
C₈⋊₃(C₅×S₃) = C₅×C₈⋊S₃	φ: C₅×S₃/C₁₅ → C₂ ⊆ Aut C₈	120	2	C8:3(C5xS3)	240,50

Non-split extensions G=N.Q with N=C₈ and Q=C₅×S₃

extension	φ:Q→Aut N	d	ρ	Label	ID
C₈.(C₅×S₃) = C₅×Dic₁₂	φ: C₅×S₃/C₁₅ → C₂ ⊆ Aut C₈	240	2	C8.(C5xS3)	240,53
C₈.₂(C₅×S₃) = C₅×C₃⋊C₁₆	central extension (φ=1)	240	2	C8.2(C5xS3)	240,1

⋊

ℤ

𝔽

○

≀

ℚ

◁

Extensions 1→N→G→Q→1 with N=C8 and Q=C5×S3