Extensions 1→N→G→Q→1 with N=C₆² and Q=C₈

Direct product G=N×Q with N=C₆² and Q=C₈

		d	ρ	Label	ID
C₂×C₆×C₂₄		288		C2xC6xC24	288,826

Semidirect products G=N:Q with N=C₆² and Q=C₈

extension	φ:Q→Aut N	d	ρ	Label	ID
C₆²⋊₁C₈ = C₂²⋊F₉	φ: C₈/C₁ → C₈ ⊆ Aut C₆²	24	8+	C6^2:1C8	288,867
C₆²⋊₂C₈ = C₂²×F₉	φ: C₈/C₁ → C₈ ⊆ Aut C₆²	36		C6^2:2C8	288,1030
C₆²⋊₃C₈ = C₆²⋊₃C₈	φ: C₈/C₂ → C₄ ⊆ Aut C₆²	48		C6^2:3C8	288,435
C₆²⋊₄C₈ = C₂²×C₃²⋊₂C₈	φ: C₈/C₂ → C₄ ⊆ Aut C₆²	96		C6^2:4C8	288,939
C₆²⋊₅C₈ = C₃²×C₂²⋊C₈	φ: C₈/C₄ → C₂ ⊆ Aut C₆²	144		C6^2:5C8	288,316
C₆²⋊₆C₈ = C₃×C₁₂.₅₅D₄	φ: C₈/C₄ → C₂ ⊆ Aut C₆²	48		C6^2:6C8	288,264
C₆²⋊₇C₈ = C₆²⋊₇C₈	φ: C₈/C₄ → C₂ ⊆ Aut C₆²	144		C6^2:7C8	288,305
C₆²⋊₈C₈ = C₂×C₆×C₃⋊C₈	φ: C₈/C₄ → C₂ ⊆ Aut C₆²	96		C6^2:8C8	288,691
C₆²⋊₉C₈ = C₂²×C₃²⋊₄C₈	φ: C₈/C₄ → C₂ ⊆ Aut C₆²	288		C6^2:9C8	288,777

Non-split extensions G=N.Q with N=C₆² and Q=C₈

extension	φ:Q→Aut N	d	ρ	Label	ID
C₆².₁C₈ = C₂×C₂.F₉	φ: C₈/C₁ → C₈ ⊆ Aut C₆²	96		C6^2.1C8	288,865
C₆².₂C₈ = C₂².F₉	φ: C₈/C₁ → C₈ ⊆ Aut C₆²	48	8-	C6^2.2C8	288,866
C₆².₃C₈ = C₂×C₃²⋊₂C₁₆	φ: C₈/C₂ → C₄ ⊆ Aut C₆²	96		C6^2.3C8	288,420
C₆².₄C₈ = C₆².₄C₈	φ: C₈/C₂ → C₄ ⊆ Aut C₆²	48	4	C6^2.4C8	288,421
C₆².₅C₈ = C₃²×M₅(2)	φ: C₈/C₄ → C₂ ⊆ Aut C₆²	144		C6^2.5C8	288,328
C₆².₆C₈ = C₆×C₃⋊C₁₆	φ: C₈/C₄ → C₂ ⊆ Aut C₆²	96		C6^2.6C8	288,245
C₆².₇C₈ = C₃×C₁₂.C₈	φ: C₈/C₄ → C₂ ⊆ Aut C₆²	48	2	C6^2.7C8	288,246
C₆².₈C₈ = C₂×C₂₄.S₃	φ: C₈/C₄ → C₂ ⊆ Aut C₆²	288		C6^2.8C8	288,286
C₆².₉C₈ = C₂₄.₉₄D₆	φ: C₈/C₄ → C₂ ⊆ Aut C₆²	144		C6^2.9C8	288,287

׿

×

⋊

ℤ

𝔽

○

≀

ℚ

◁