Extensions 1→N→G→Q→1 with N=C₅ and Q=C₅×D₅

Direct product G=N×Q with N=C₅ and Q=C₅×D₅

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

Semidirect products G=N:Q with N=C₅ and Q=C₅×D₅

extension	φ:Q→Aut N	d	ρ	Label	ID
C₅⋊(C₅×D₅) = C₅×C₅⋊D₅	φ: C₅×D₅/C₅² → C₂ ⊆ Aut C₅	50		C5:(C5xD5)	250,13

Non-split extensions G=N.Q with N=C₅ and Q=C₅×D₅

extension	φ:Q→Aut N	d	ρ	Label	ID
C₅.₁(C₅×D₅) = C₅×D₂₅	φ: C₅×D₅/C₅² → C₂ ⊆ Aut C₅	50	2	C5.1(C5xD5)	250,3
C₅.₂(C₅×D₅) = C₅²⋊C₁₀	φ: C₅×D₅/C₅² → C₂ ⊆ Aut C₅	25	10+	C5.2(C5xD5)	250,5
C₅.₃(C₅×D₅) = C₂₅⋊C₁₀	φ: C₅×D₅/C₅² → C₂ ⊆ Aut C₅	25	10+	C5.3(C5xD5)	250,6
C₅.₄(C₅×D₅) = D₅×C₂₅	central extension (φ=1)	50	2	C5.4(C5xD5)	250,4

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Extensions 1→N→G→Q→1 with N=C5 and Q=C5×D5