Extensions 1→N→G→Q→1 with N=C₅² and Q=D₅

Direct product G=N×Q with N=C₅² and Q=D₅

		d	ρ	Label	ID
D₅×C₅²		50		D5xC5^2	250,12

Semidirect products G=N:Q with N=C₅² and Q=D₅

extension	φ:Q→Aut N	d	ρ	Label	ID
C₅²⋊₁D₅ = C₅²⋊C₁₀	φ: D₅/C₁ → D₅ ⊆ Aut C₅²	25	10+	C5^2:1D5	250,5
C₅²⋊₂D₅ = He₅⋊C₂	φ: D₅/C₁ → D₅ ⊆ Aut C₅²	25	5	C5^2:2D5	250,8
C₅²⋊₃D₅ = C₅×C₅⋊D₅	φ: D₅/C₅ → C₂ ⊆ Aut C₅²	50		C5^2:3D5	250,13
C₅²⋊₄D₅ = C₅³⋊C₂	φ: D₅/C₅ → C₂ ⊆ Aut C₅²	125		C5^2:4D5	250,14

Non-split extensions G=N.Q with N=C₅² and Q=D₅

extension	φ:Q→Aut N	d	ρ	Label	ID
C₅².D₅ = C₂₅⋊C₁₀	φ: D₅/C₁ → D₅ ⊆ Aut C₅²	25	10+	C5^2.D5	250,6
C₅².₂D₅ = C₅×D₂₅	φ: D₅/C₅ → C₂ ⊆ Aut C₅²	50	2	C5^2.2D5	250,3
C₅².₃D₅ = C₂₅⋊D₅	φ: D₅/C₅ → C₂ ⊆ Aut C₅²	125		C5^2.3D5	250,7

׿

×

⋊

ℤ

𝔽

○

≀

ℚ

◁