C_n D_n S_n A_n ...

Extensions 1→N→G→Q→1 with N=2₊⁽¹⁺⁴⁾ and Q=C₆

Direct product G=N×Q with N=2₊⁽¹⁺⁴⁾ and Q=C₆

		d	ρ	Label	ID
C₆×2₊⁽¹⁺⁴⁾		48		C6xES+(2,2)	192,1534

Semidirect products G=N:Q with N=2₊⁽¹⁺⁴⁾ and Q=C₆

extension	φ:Q→Out N	d	ρ	Label	ID
2₊⁽¹⁺⁴⁾⋊₁C₆ = C₂≀A₄	φ: C₆/C₁ → C₆ ⊆ Out 2₊⁽¹⁺⁴⁾	8	4+	ES+(2,2):1C6	192,201
2₊⁽¹⁺⁴⁾⋊₂C₆ = SD₁₆.A₄	φ: C₆/C₁ → C₆ ⊆ Out 2₊⁽¹⁺⁴⁾	32	4	ES+(2,2):2C6	192,1018
2₊⁽¹⁺⁴⁾⋊₃C₆ = C₂×Q₈.A₄	φ: C₆/C₂ → C₃ ⊆ Out 2₊⁽¹⁺⁴⁾	48		ES+(2,2):3C6	192,1502
2₊⁽¹⁺⁴⁾⋊₄C₆ = 2_-⁽¹⁺⁴⁾⋊₃C₆	φ: C₆/C₂ → C₃ ⊆ Out 2₊⁽¹⁺⁴⁾	32	4	ES+(2,2):4C6	192,1504
2₊⁽¹⁺⁴⁾⋊₅C₆ = C₂×C₂³⋊A₄	φ: C₆/C₂ → C₃ ⊆ Out 2₊⁽¹⁺⁴⁾	16		ES+(2,2):5C6	192,1508
2₊⁽¹⁺⁴⁾⋊₆C₆ = C₃×D₄⋊₄D₄	φ: C₆/C₃ → C₂ ⊆ Out 2₊⁽¹⁺⁴⁾	24	4	ES+(2,2):6C6	192,886
2₊⁽¹⁺⁴⁾⋊₇C₆ = C₃×C₂≀C₂²	φ: C₆/C₃ → C₂ ⊆ Out 2₊⁽¹⁺⁴⁾	24	4	ES+(2,2):7C6	192,890
2₊⁽¹⁺⁴⁾⋊₈C₆ = C₃×D₄○D₈	φ: C₆/C₃ → C₂ ⊆ Out 2₊⁽¹⁺⁴⁾	48	4	ES+(2,2):8C6	192,1465
2₊⁽¹⁺⁴⁾⋊₉C₆ = C₃×D₄○SD₁₆	φ: C₆/C₃ → C₂ ⊆ Out 2₊⁽¹⁺⁴⁾	48	4	ES+(2,2):9C6	192,1466
2₊⁽¹⁺⁴⁾⋊₁₀C₆ = C₃×C₂.C₂⁵	φ: trivial image	48	4	ES+(2,2):10C6	192,1536

Non-split extensions G=N.Q with N=2₊⁽¹⁺⁴⁾ and Q=C₆

extension	φ:Q→Out N	d	ρ	Label	ID
2₊⁽¹⁺⁴⁾.₁C₆ = 2₊⁽¹⁺⁴⁾.C₆	φ: C₆/C₁ → C₆ ⊆ Out 2₊⁽¹⁺⁴⁾	16	4	ES+(2,2).1C6	192,202
2₊⁽¹⁺⁴⁾.₂C₆ = Q₁₆.A₄	φ: C₆/C₁ → C₆ ⊆ Out 2₊⁽¹⁺⁴⁾	48	4+	ES+(2,2).2C6	192,1017
2₊⁽¹⁺⁴⁾.₃C₆ = 2₊⁽¹⁺⁴⁾.₃C₆	φ: C₆/C₂ → C₃ ⊆ Out 2₊⁽¹⁺⁴⁾	16	4	ES+(2,2).3C6	192,1509
2₊⁽¹⁺⁴⁾.₄C₆ = C₃×D₄.₉D₄	φ: C₆/C₃ → C₂ ⊆ Out 2₊⁽¹⁺⁴⁾	48	4	ES+(2,2).4C6	192,888
2₊⁽¹⁺⁴⁾.₅C₆ = C₃×C₂³.₇D₄	φ: C₆/C₃ → C₂ ⊆ Out 2₊⁽¹⁺⁴⁾	48	4	ES+(2,2).5C6	192,891

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