Extensions 1→N→G→Q→1 with N=C₅ and Q=C₅²⋊₆C₄

Direct product G=N×Q with N=C₅ and Q=C₅²⋊₆C₄

		d	ρ	Label	ID
C₅×C₅²⋊₆C₄		100		C5xC5^2:6C4	500,38

Semidirect products G=N:Q with N=C₅ and Q=C₅²⋊₆C₄

extension	φ:Q→Aut N	d	ρ	Label	ID
C₅⋊(C₅²⋊₆C₄) = C₅³⋊C₄	φ: C₅²⋊₆C₄/C₅² → C₄ ⊆ Aut C₅	100		C5:(C5^2:6C4)	500,45
C₅⋊₂(C₅²⋊₆C₄) = C₅³⋊₁₂C₄	φ: C₅²⋊₆C₄/C₅×C₁₀ → C₂ ⊆ Aut C₅	500		C5:2(C5^2:6C4)	500,39

Non-split extensions G=N.Q with N=C₅ and Q=C₅²⋊₆C₄

extension	φ:Q→Aut N	d	ρ	Label	ID
C₅.(C₅²⋊₆C₄) = C₅₀.D₅	φ: C₅²⋊₆C₄/C₅×C₁₀ → C₂ ⊆ Aut C₅	500		C5.(C5^2:6C4)	500,10
C₅.₂(C₅²⋊₆C₄) = He₅⋊₆C₄	central stem extension (φ=1)	100	5	C5.2(C5^2:6C4)	500,11

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Extensions 1→N→G→Q→1 with N=C5 and Q=C52⋊6C4