Extensions 1→N→G→Q→1 with N=C₅₆ and Q=C₄

Direct product G=N×Q with N=C₅₆ and Q=C₄

		d	ρ	Label	ID
C₄×C₅₆		224		C4xC56	224,45

Semidirect products G=N:Q with N=C₅₆ and Q=C₄

extension	φ:Q→Aut N	d	ρ	Label	ID
C₅₆⋊₁C₄ = C₅₆⋊₁C₄	φ: C₄/C₂ → C₂ ⊆ Aut C₅₆	224		C56:1C4	224,24
C₅₆⋊₂C₄ = C₈⋊Dic₇	φ: C₄/C₂ → C₂ ⊆ Aut C₅₆	224		C56:2C4	224,23
C₅₆⋊₃C₄ = C₈×Dic₇	φ: C₄/C₂ → C₂ ⊆ Aut C₅₆	224		C56:3C4	224,19
C₅₆⋊₄C₄ = C₅₆⋊C₄	φ: C₄/C₂ → C₂ ⊆ Aut C₅₆	224		C56:4C4	224,21
C₅₆⋊₅C₄ = C₇×C₂.D₈	φ: C₄/C₂ → C₂ ⊆ Aut C₅₆	224		C56:5C4	224,56
C₅₆⋊₆C₄ = C₇×C₄.Q₈	φ: C₄/C₂ → C₂ ⊆ Aut C₅₆	224		C56:6C4	224,55
C₅₆⋊₇C₄ = C₇×C₈⋊C₄	φ: C₄/C₂ → C₂ ⊆ Aut C₅₆	224		C56:7C4	224,46

Non-split extensions G=N.Q with N=C₅₆ and Q=C₄

extension	φ:Q→Aut N	d	ρ	Label	ID
C₅₆.₁C₄ = C₅₆.C₄	φ: C₄/C₂ → C₂ ⊆ Aut C₅₆	112	2	C56.1C4	224,25
C₅₆.₂C₄ = C₇⋊C₃₂	φ: C₄/C₂ → C₂ ⊆ Aut C₅₆	224	2	C56.2C4	224,1
C₅₆.₃C₄ = C₂×C₇⋊C₁₆	φ: C₄/C₂ → C₂ ⊆ Aut C₅₆	224		C56.3C4	224,17
C₅₆.₄C₄ = C₂₈.C₈	φ: C₄/C₂ → C₂ ⊆ Aut C₅₆	112	2	C56.4C4	224,18
C₅₆.₅C₄ = C₇×C₈.C₄	φ: C₄/C₂ → C₂ ⊆ Aut C₅₆	112	2	C56.5C4	224,57
C₅₆.₆C₄ = C₇×M₅(2)	φ: C₄/C₂ → C₂ ⊆ Aut C₅₆	112	2	C56.6C4	224,59

׿

×

⋊

ℤ

𝔽

○

≀

ℚ

◁