Extensions 1→N→G→Q→1 with N=C₄ and Q=C₃²:₄Q₈

Direct product G=NxQ with N=C₄ and Q=C₃²:₄Q₈

		d	ρ	Label	ID
C₄xC₃²:₄Q₈		288		C4xC3^2:4Q8	288,725

Semidirect products G=N:Q with N=C₄ and Q=C₃²:₄Q₈

extension	φ:Q→Aut N	d	ρ	Label	ID
C₄:₁(C₃²:₄Q₈) = C₁₂:₂Dic₆	φ: C₃²:₄Q₈/C₃:Dic₃ → C₂ ⊆ Aut C₄	288		C4:1(C3^2:4Q8)	288,745
C₄:₂(C₃²:₄Q₈) = C₁₂:₆Dic₆	φ: C₃²:₄Q₈/C₃xC₁₂ → C₂ ⊆ Aut C₄	288		C4:2(C3^2:4Q8)	288,726

Non-split extensions G=N.Q with N=C₄ and Q=C₃²:₄Q₈

extension	φ:Q→Aut N	d	ρ	Label	ID
C₄.₁(C₃²:₄Q₈) = C₁₂.₉Dic₆	φ: C₃²:₄Q₈/C₃:Dic₃ → C₂ ⊆ Aut C₄	288		C4.1(C3^2:4Q8)	288,282
C₄.₂(C₃²:₄Q₈) = C₁₂.₁₀Dic₆	φ: C₃²:₄Q₈/C₃:Dic₃ → C₂ ⊆ Aut C₄	288		C4.2(C3^2:4Q8)	288,283
C₄.₃(C₃²:₄Q₈) = C₆².₂₃₄C₂³	φ: C₃²:₄Q₈/C₃:Dic₃ → C₂ ⊆ Aut C₄	288		C4.3(C3^2:4Q8)	288,747
C₄.₄(C₃²:₄Q₈) = C₂₄:₂Dic₃	φ: C₃²:₄Q₈/C₃xC₁₂ → C₂ ⊆ Aut C₄	288		C4.4(C3^2:4Q8)	288,292
C₄.₅(C₃²:₄Q₈) = C₂₄:₁Dic₃	φ: C₃²:₄Q₈/C₃xC₁₂ → C₂ ⊆ Aut C₄	288		C4.5(C3^2:4Q8)	288,293
C₄.₆(C₃²:₄Q₈) = C₁₂.₂₅Dic₆	φ: C₃²:₄Q₈/C₃xC₁₂ → C₂ ⊆ Aut C₄	288		C4.6(C3^2:4Q8)	288,727
C₄.₇(C₃²:₄Q₈) = C₁₂.₅₇D₁₂	central extension (φ=1)	288		C4.7(C3^2:4Q8)	288,279
C₄.₈(C₃²:₄Q₈) = C₁₂.₃₀Dic₆	central extension (φ=1)	288		C4.8(C3^2:4Q8)	288,289

׿

x

:

Z

F

o

wr

Q

<