Extensions 1→N→G→Q→1 with N=C₂² and Q=C₄×C₈

Direct product G=N×Q with N=C₂² and Q=C₄×C₈

		d	ρ	Label	ID
C₂²×C₄×C₈		128		C2^2xC4xC8	128,1601

Semidirect products G=N:Q with N=C₂² and Q=C₄×C₈

extension	φ:Q→Aut N	d	ρ	Label	ID
C₂²⋊₁(C₄×C₈) = C₄×C₂²⋊C₈	φ: C₄×C₈/C₄² → C₂ ⊆ Aut C₂²	64		C2^2:1(C4xC8)	128,480
C₂²⋊₂(C₄×C₈) = C₈×C₂²⋊C₄	φ: C₄×C₈/C₂×C₈ → C₂ ⊆ Aut C₂²	64		C2^2:2(C4xC8)	128,483

Non-split extensions G=N.Q with N=C₂² and Q=C₄×C₈

extension	φ:Q→Aut N	d	ρ	Label	ID
C₂².₁(C₄×C₈) = C₂³.₁₉C₄²	φ: C₄×C₈/C₄² → C₂ ⊆ Aut C₂²	64		C2^2.1(C4xC8)	128,12
C₂².₂(C₄×C₈) = C₄².₂Q₈	φ: C₄×C₈/C₄² → C₂ ⊆ Aut C₂²	64		C2^2.2(C4xC8)	128,13
C₂².₃(C₄×C₈) = M₅(2)⋊C₄	φ: C₄×C₈/C₄² → C₂ ⊆ Aut C₂²	64		C2^2.3(C4xC8)	128,109
C₂².₄(C₄×C₈) = C₈²⋊C₂	φ: C₄×C₈/C₄² → C₂ ⊆ Aut C₂²	64		C2^2.4(C4xC8)	128,182
C₂².₅(C₄×C₈) = C₄×M₅(2)	φ: C₄×C₈/C₄² → C₂ ⊆ Aut C₂²	64		C2^2.5(C4xC8)	128,839
C₂².₆(C₄×C₈) = C₂³.₂₁C₄²	φ: C₄×C₈/C₂×C₈ → C₂ ⊆ Aut C₂²	32		C2^2.6(C4xC8)	128,14
C₂².₇(C₄×C₈) = C₄².₃Q₈	φ: C₄×C₈/C₂×C₈ → C₂ ⊆ Aut C₂²	64		C2^2.7(C4xC8)	128,15
C₂².₈(C₄×C₈) = M₄(2).C₈	φ: C₄×C₈/C₂×C₈ → C₂ ⊆ Aut C₂²	32	4	C2^2.8(C4xC8)	128,110
C₂².₉(C₄×C₈) = C₈×M₄(2)	φ: C₄×C₈/C₂×C₈ → C₂ ⊆ Aut C₂²	64		C2^2.9(C4xC8)	128,181
C₂².₁₀(C₄×C₈) = C₁₆○₂M₅(2)	φ: C₄×C₈/C₂×C₈ → C₂ ⊆ Aut C₂²	64		C2^2.10(C4xC8)	128,840
C₂².₁₁(C₄×C₈) = C₂.C₈²	central extension (φ=1)	128		C2^2.11(C4xC8)	128,5
C₂².₁₂(C₄×C₈) = C₁₆⋊₅C₈	central extension (φ=1)	128		C2^2.12(C4xC8)	128,43
C₂².₁₃(C₄×C₈) = C₈⋊C₁₆	central extension (φ=1)	128		C2^2.13(C4xC8)	128,44
C₂².₁₄(C₄×C₈) = C₂².₇M₅(2)	central extension (φ=1)	128		C2^2.14(C4xC8)	128,106
C₂².₁₅(C₄×C₈) = C₂×C₈⋊C₈	central extension (φ=1)	128		C2^2.15(C4xC8)	128,180
C₂².₁₆(C₄×C₈) = C₂×C₂².₇C₄²	central extension (φ=1)	128		C2^2.16(C4xC8)	128,459
C₂².₁₇(C₄×C₈) = C₂×C₁₆⋊₅C₄	central extension (φ=1)	128		C2^2.17(C4xC8)	128,838

׿

×

⋊

ℤ

𝔽

○

≀

ℚ

◁