Extensions 1→N→G→Q→1 with N=C₅₁ and Q=C₈

Direct product G=N×Q with N=C₅₁ and Q=C₈

		d	ρ	Label	ID
C₄₀₈		408	1	C408	408,4

Semidirect products G=N:Q with N=C₅₁ and Q=C₈

extension	φ:Q→Aut N	d	ρ	Label	ID
C₅₁⋊₁C₈ = C₅₁⋊C₈	φ: C₈/C₁ → C₈ ⊆ Aut C₅₁	51	8	C51:1C8	408,34
C₅₁⋊₂C₈ = C₃×C₁₇⋊C₈	φ: C₈/C₁ → C₈ ⊆ Aut C₅₁	51	8	C51:2C8	408,33
C₅₁⋊₃C₈ = C₅₁⋊₃C₈	φ: C₈/C₂ → C₄ ⊆ Aut C₅₁	408	4	C51:3C8	408,6
C₅₁⋊₄C₈ = C₃×C₁₇⋊₂C₈	φ: C₈/C₂ → C₄ ⊆ Aut C₅₁	408	4	C51:4C8	408,5
C₅₁⋊₅C₈ = C₅₁⋊₅C₈	φ: C₈/C₄ → C₂ ⊆ Aut C₅₁	408	2	C51:5C8	408,3
C₅₁⋊₆C₈ = C₃×C₁₇⋊₃C₈	φ: C₈/C₄ → C₂ ⊆ Aut C₅₁	408	2	C51:6C8	408,2
C₅₁⋊₇C₈ = C₁₇×C₃⋊C₈	φ: C₈/C₄ → C₂ ⊆ Aut C₅₁	408	2	C51:7C8	408,1

׿

×

⋊

ℤ

𝔽

○

≀

ℚ

◁