Extensions 1→N→G→Q→1 with N=C₅ and Q=D₅²

Direct product G=N×Q with N=C₅ and Q=D₅²

		d	ρ	Label	ID
C₅×D₅²		20	4	C5xD5^2	500,50

Semidirect products G=N:Q with N=C₅ and Q=D₅²

extension	φ:Q→Aut N	d	ρ	Label	ID
C₅⋊₁D₅² = D₅×C₅⋊D₅	φ: D₅²/C₅×D₅ → C₂ ⊆ Aut C₅	50		C5:1D5^2	500,51
C₅⋊₂D₅² = C₅²⋊₅D₁₀	φ: D₅²/C₅⋊D₅ → C₂ ⊆ Aut C₅	20	4	C5:2D5^2	500,52

Non-split extensions G=N.Q with N=C₅ and Q=D₅²

extension	φ:Q→Aut N	d	ρ	Label	ID
C₅.₁D₅² = D₅×D₂₅	φ: D₅²/C₅×D₅ → C₂ ⊆ Aut C₅	50	4+	C5.1D5^2	500,26
C₅.₂D₅² = C₅²⋊D₁₀	φ: D₅²/C₅⋊D₅ → C₂ ⊆ Aut C₅	25	10+	C5.2D5^2	500,27

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Extensions 1→N→G→Q→1 with N=C5 and Q=D52