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
C₅×C₅⋊D₅		50		C5xC5:D5	250,13

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

extension	φ:Q→Aut N	d	ρ	Label	ID
C₅⋊(C₅⋊D₅) = C₅³⋊C₂	φ: C₅⋊D₅/C₅² → C₂ ⊆ Aut C₅	125		C5:(C5:D5)	250,14

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

extension	φ:Q→Aut N	d	ρ	Label	ID
C₅.(C₅⋊D₅) = C₂₅⋊D₅	φ: C₅⋊D₅/C₅² → C₂ ⊆ Aut C₅	125		C5.(C5:D5)	250,7
C₅.₂(C₅⋊D₅) = He₅⋊C₂	central stem extension (φ=1)	25	5	C5.2(C5:D5)	250,8

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