Extensions 1→N→G→Q→1 with N=C₅ and Q=C₂₄⋊C₂

Direct product G=N×Q with N=C₅ and Q=C₂₄⋊C₂

		d	ρ	Label	ID
C₅×C₂₄⋊C₂		120	2	C5xC24:C2	240,51

Semidirect products G=N:Q with N=C₅ and Q=C₂₄⋊C₂

extension	φ:Q→Aut N	d	ρ	Label	ID
C₅⋊₁(C₂₄⋊C₂) = C₂₄⋊D₅	φ: C₂₄⋊C₂/C₂₄ → C₂ ⊆ Aut C₅	120	2	C5:1(C24:C2)	240,67
C₅⋊₂(C₂₄⋊C₂) = Dic₆⋊D₅	φ: C₂₄⋊C₂/Dic₆ → C₂ ⊆ Aut C₅	120	4+	C5:2(C24:C2)	240,21
C₅⋊₃(C₂₄⋊C₂) = D₁₂.D₅	φ: C₂₄⋊C₂/D₁₂ → C₂ ⊆ Aut C₅	120	4-	C5:3(C24:C2)	240,20

׿

×

⋊

ℤ

𝔽

○

≀

ℚ

◁