Extensions 1→N→G→Q→1 with N=C₃ and Q=C₃²⋊₃Q₁₆

Direct product G=N×Q with N=C₃ and Q=C₃²⋊₃Q₁₆

		d	ρ	Label	ID
C₃×C₃²⋊₃Q₁₆		48	4	C3xC3^2:3Q16	432,424

Semidirect products G=N:Q with N=C₃ and Q=C₃²⋊₃Q₁₆

extension	φ:Q→Aut N	d	ρ	Label	ID
C₃⋊₁(C₃²⋊₃Q₁₆) = C₃³⋊₈Q₁₆	φ: C₃²⋊₃Q₁₆/C₃×C₃⋊C₈ → C₂ ⊆ Aut C₃	144		C3:1(C3^2:3Q16)	432,447
C₃⋊₂(C₃²⋊₃Q₁₆) = C₃³⋊₇Q₁₆	φ: C₃²⋊₃Q₁₆/C₃×Dic₆ → C₂ ⊆ Aut C₃	144		C3:2(C3^2:3Q16)	432,446
C₃⋊₃(C₃²⋊₃Q₁₆) = C₃³⋊₉Q₁₆	φ: C₃²⋊₃Q₁₆/C₃²⋊₄Q₈ → C₂ ⊆ Aut C₃	48	4	C3:3(C3^2:3Q16)	432,459

Non-split extensions G=N.Q with N=C₃ and Q=C₃²⋊₃Q₁₆

extension	φ:Q→Aut N	d	ρ	Label	ID
C₃.₁(C₃²⋊₃Q₁₆) = C₃⋊Dic₃₆	φ: C₃²⋊₃Q₁₆/C₃×C₃⋊C₈ → C₂ ⊆ Aut C₃	144	4-	C3.1(C3^2:3Q16)	432,65
C₃.₂(C₃²⋊₃Q₁₆) = C₉⋊Dic₁₂	φ: C₃²⋊₃Q₁₆/C₃×Dic₆ → C₂ ⊆ Aut C₃	144	4-	C3.2(C3^2:3Q16)	432,75
C₃.₃(C₃²⋊₃Q₁₆) = He₃⋊₃Q₁₆	φ: C₃²⋊₃Q₁₆/C₃²⋊₄Q₈ → C₂ ⊆ Aut C₃	144	12-	C3.3(C3^2:3Q16)	432,86

׿

×

⋊

ℤ

𝔽

○

≀

ℚ

◁