Extensions 1→N→G→Q→1 with N=C₅₂ and Q=C₈

Direct product G=N×Q with N=C₅₂ and Q=C₈

		d	ρ	Label	ID
C₄×C₁₀₄		416		C4xC104	416,46

Semidirect products G=N:Q with N=C₅₂ and Q=C₈

extension	φ:Q→Aut N	d	ρ	Label	ID
C₅₂⋊₁C₈ = C₅₂⋊C₈	φ: C₈/C₂ → C₄ ⊆ Aut C₅₂	416		C52:1C8	416,76
C₅₂⋊₂C₈ = C₄×C₁₃⋊C₈	φ: C₈/C₂ → C₄ ⊆ Aut C₅₂	416		C52:2C8	416,75
C₅₂⋊₃C₈ = C₅₂⋊₃C₈	φ: C₈/C₄ → C₂ ⊆ Aut C₅₂	416		C52:3C8	416,11
C₅₂⋊₄C₈ = C₄×C₁₃⋊₂C₈	φ: C₈/C₄ → C₂ ⊆ Aut C₅₂	416		C52:4C8	416,9
C₅₂⋊₅C₈ = C₁₃×C₄⋊C₈	φ: C₈/C₄ → C₂ ⊆ Aut C₅₂	416		C52:5C8	416,55

Non-split extensions G=N.Q with N=C₅₂ and Q=C₈

extension	φ:Q→Aut N	d	ρ	Label	ID
C₅₂.₁C₈ = C₅₂.C₈	φ: C₈/C₂ → C₄ ⊆ Aut C₅₂	208	4	C52.1C8	416,73
C₅₂.₂C₈ = C₁₃⋊C₃₂	φ: C₈/C₂ → C₄ ⊆ Aut C₅₂	416	4	C52.2C8	416,3
C₅₂.₃C₈ = C₂×C₁₃⋊C₁₆	φ: C₈/C₂ → C₄ ⊆ Aut C₅₂	416		C52.3C8	416,72
C₅₂.₄C₈ = C₅₂.₄C₈	φ: C₈/C₄ → C₂ ⊆ Aut C₅₂	208	2	C52.4C8	416,19
C₅₂.₅C₈ = C₁₃⋊₂C₃₂	φ: C₈/C₄ → C₂ ⊆ Aut C₅₂	416	2	C52.5C8	416,1
C₅₂.₆C₈ = C₂×C₁₃⋊₂C₁₆	φ: C₈/C₄ → C₂ ⊆ Aut C₅₂	416		C52.6C8	416,18
C₅₂.₇C₈ = C₁₃×M₅(2)	φ: C₈/C₄ → C₂ ⊆ Aut C₅₂	208	2	C52.7C8	416,60

׿

×

⋊

ℤ

𝔽

○

≀

ℚ

◁