Extensions 1→N→G→Q→1 with N=C₅ and Q=C₄○D₂₄

Direct product G=N×Q with N=C₅ and Q=C₄○D₂₄

		d	ρ	Label	ID
C₅×C₄○D₂₄		240	2	C5xC4oD24	480,783

Semidirect products G=N:Q with N=C₅ and Q=C₄○D₂₄

extension	φ:Q→Aut N	d	ρ	Label	ID
C₅⋊₁(C₄○D₂₄) = C₄₀.₃₁D₆	φ: C₄○D₂₄/C₂₄⋊C₂ → C₂ ⊆ Aut C₅	240	4	C5:1(C4oD24)	480,345
C₅⋊₂(C₄○D₂₄) = D₂₄⋊₇D₅	φ: C₄○D₂₄/D₂₄ → C₂ ⊆ Aut C₅	240	4-	C5:2(C4oD24)	480,346
C₅⋊₃(C₄○D₂₄) = D₁₂₀⋊C₂	φ: C₄○D₂₄/Dic₁₂ → C₂ ⊆ Aut C₅	240	4+	C5:3(C4oD24)	480,347
C₅⋊₄(C₄○D₂₄) = C₄₀.₆₉D₆	φ: C₄○D₂₄/C₂×C₂₄ → C₂ ⊆ Aut C₅	240	2	C5:4(C4oD24)	480,869
C₅⋊₅(C₄○D₂₄) = C₂₀.₆₀D₁₂	φ: C₄○D₂₄/C₄○D₁₂ → C₂ ⊆ Aut C₅	240	4	C5:5(C4oD24)	480,379

׿

×

⋊

ℤ

𝔽

○

≀

ℚ

◁