Extensions 1→N→G→Q→1 with N=C₅₁ and Q=Q₈

Direct product G=N×Q with N=C₅₁ and Q=Q₈

		d	ρ	Label	ID
Q₈×C₅₁		408	2	Q8xC51	408,32

Semidirect products G=N:Q with N=C₅₁ and Q=Q₈

extension	φ:Q→Aut N	d	ρ	Label	ID
C₅₁⋊Q₈ = C₅₁⋊Q₈	φ: Q₈/C₂ → C₂² ⊆ Aut C₅₁	408	4-	C51:Q8	408,13
C₅₁⋊₂Q₈ = Dic₁₀₂	φ: Q₈/C₄ → C₂ ⊆ Aut C₅₁	408	2-	C51:2Q8	408,25
C₅₁⋊₃Q₈ = C₃×Dic₃₄	φ: Q₈/C₄ → C₂ ⊆ Aut C₅₁	408	2	C51:3Q8	408,15
C₅₁⋊₄Q₈ = C₁₇×Dic₆	φ: Q₈/C₄ → C₂ ⊆ Aut C₅₁	408	2	C51:4Q8	408,20

׿

×

⋊

ℤ

𝔽

○

≀

ℚ

◁