Extensions 1→N→G→Q→1 with N=C₅ and Q=C₅×F₅

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

		d	ρ	Label	ID
F₅×C₅²		100		F5xC5^2	500,41

Semidirect products G=N:Q with N=C₅ and Q=C₅×F₅

extension	φ:Q→Aut N	d	ρ	Label	ID
C₅⋊₁(C₅×F₅) = C₅×C₅⋊F₅	φ: C₅×F₅/C₅² → C₄ ⊆ Aut C₅	100		C5:1(C5xF5)	500,43
C₅⋊₂(C₅×F₅) = C₅×C₅²⋊C₄	φ: C₅×F₅/C₅² → C₄ ⊆ Aut C₅	20	4	C5:2(C5xF5)	500,44
C₅⋊₃(C₅×F₅) = C₅×D₅.D₅	φ: C₅×F₅/C₅×D₅ → C₂ ⊆ Aut C₅	20	4	C5:3(C5xF5)	500,42

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

extension	φ:Q→Aut N	d	ρ	Label	ID
C₅.₁(C₅×F₅) = C₅×C₂₅⋊C₄	φ: C₅×F₅/C₅² → C₄ ⊆ Aut C₅	100	4	C5.1(C5xF5)	500,16
C₅.₂(C₅×F₅) = C₅²⋊C₂₀	φ: C₅×F₅/C₅² → C₄ ⊆ Aut C₅	25	20+	C5.2(C5xF5)	500,17
C₅.₃(C₅×F₅) = C₂₅⋊C₂₀	φ: C₅×F₅/C₅² → C₄ ⊆ Aut C₅	25	20+	C5.3(C5xF5)	500,18
C₅.₄(C₅×F₅) = F₅×C₂₅	central extension (φ=1)	100	4	C5.4(C5xF5)	500,15

׿

×

⋊

ℤ

𝔽

○

≀

ℚ

◁