Extensions 1→N→G→Q→1 with N=C₅ and Q=C₅×M₄(2)

Direct product G=N×Q with N=C₅ and Q=C₅×M₄(2)

		d	ρ	Label	ID
M₄(2)×C₅²		200		M4(2)xC5^2	400,112

Semidirect products G=N:Q with N=C₅ and Q=C₅×M₄(2)

extension	φ:Q→Aut N	d	ρ	Label	ID
C₅⋊₁(C₅×M₄(2)) = C₅×C₄.F₅	φ: C₅×M₄(2)/C₂₀ → C₄ ⊆ Aut C₅	80	4	C5:1(C5xM4(2))	400,136
C₅⋊₂(C₅×M₄(2)) = C₅×C₂².F₅	φ: C₅×M₄(2)/C₂×C₁₀ → C₄ ⊆ Aut C₅	40	4	C5:2(C5xM4(2))	400,140
C₅⋊₃(C₅×M₄(2)) = C₅×C₈⋊D₅	φ: C₅×M₄(2)/C₄₀ → C₂ ⊆ Aut C₅	80	2	C5:3(C5xM4(2))	400,77
C₅⋊₄(C₅×M₄(2)) = C₅×C₄.Dic₅	φ: C₅×M₄(2)/C₂×C₂₀ → C₂ ⊆ Aut C₅	40	2	C5:4(C5xM4(2))	400,82

Non-split extensions G=N.Q with N=C₅ and Q=C₅×M₄(2)

extension	φ:Q→Aut N	d	ρ	Label	ID
C₅.(C₅×M₄(2)) = M₄(2)×C₂₅	central extension (φ=1)	200	2	C5.(C5xM4(2))	400,24

׿

×

⋊

ℤ

𝔽

○

≀

ℚ

◁