Extensions 1→N→G→Q→1 with N=C₅ and Q=C₂².C₄²

Direct product G=N×Q with N=C₅ and Q=C₂².C₄²

		d	ρ	Label	ID
C₅×C₂².C₄²		160		C5xC2^2.C4^2	320,148

Semidirect products G=N:Q with N=C₅ and Q=C₂².C₄²

extension	φ:Q→Aut N	d	ρ	Label	ID
C₅⋊₁(C₂².C₄²) = M₄(2)⋊F₅	φ: C₂².C₄²/M₄(2) → C₄ ⊆ Aut C₅	40	8	C5:1(C2^2.C4^2)	320,237
C₅⋊₂(C₂².C₄²) = C₂².F₅⋊C₄	φ: C₂².C₄²/C₂²×C₄ → C₄ ⊆ Aut C₅	160		C5:2(C2^2.C4^2)	320,257
C₅⋊₃(C₂².C₄²) = (C₂×C₂₀).Q₈	φ: C₂².C₄²/C₂×C₄⋊C₄ → C₂ ⊆ Aut C₅	160		C5:3(C2^2.C4^2)	320,88
C₅⋊₄(C₂².C₄²) = M₄(2)⋊Dic₅	φ: C₂².C₄²/C₂×M₄(2) → C₂ ⊆ Aut C₅	160		C5:4(C2^2.C4^2)	320,112

׿

×

⋊

ℤ

𝔽

○

≀

ℚ

◁