Extensions 1→N→G→Q→1 with N=C₅ and Q=C₂²⋊F₅

Direct product G=N×Q with N=C₅ and Q=C₂²⋊F₅

		d	ρ	Label	ID
C₅×C₂²⋊F₅		40	4	C5xC2^2:F5	400,141

Semidirect products G=N:Q with N=C₅ and Q=C₂²⋊F₅

extension	φ:Q→Aut N	d	ρ	Label	ID
C₅⋊₁(C₂²⋊F₅) = D₁₀⋊F₅	φ: C₂²⋊F₅/D₁₀ → C₄ ⊆ Aut C₅	20	8+	C5:1(C2^2:F5)	400,125
C₅⋊₂(C₂²⋊F₅) = C₁₀²⋊C₄	φ: C₂²⋊F₅/C₂×C₁₀ → C₄ ⊆ Aut C₅	100		C5:2(C2^2:F5)	400,155
C₅⋊₃(C₂²⋊F₅) = C₁₀²⋊₄C₄	φ: C₂²⋊F₅/C₂×C₁₀ → C₄ ⊆ Aut C₅	20	4+	C5:3(C2^2:F5)	400,162
C₅⋊₄(C₂²⋊F₅) = D₅.D₂₀	φ: C₂²⋊F₅/C₂×F₅ → C₂ ⊆ Aut C₅	40	8+	C5:4(C2^2:F5)	400,118
C₅⋊₅(C₂²⋊F₅) = D₁₀.D₁₀	φ: C₂²⋊F₅/C₂²×D₅ → C₂ ⊆ Aut C₅	40	4	C5:5(C2^2:F5)	400,148

Non-split extensions G=N.Q with N=C₅ and Q=C₂²⋊F₅

extension	φ:Q→Aut N	d	ρ	Label	ID
C₅.(C₂²⋊F₅) = D₂₅.D₄	φ: C₂²⋊F₅/C₂×C₁₀ → C₄ ⊆ Aut C₅	100	4+	C5.(C2^2:F5)	400,34

׿

×

⋊

ℤ

𝔽

○

≀

ℚ

◁