C_n D_n S_n A_n ...

Extensions 1→N→G→Q→1 with N=2₊⁽¹⁺⁴⁾ and Q=C₄

Direct product G=N×Q with N=2₊⁽¹⁺⁴⁾ and Q=C₄

		d	ρ	Label	ID
C₄×2₊⁽¹⁺⁴⁾		32		C4xES+(2,2)	128,2161

Semidirect products G=N:Q with N=2₊⁽¹⁺⁴⁾ and Q=C₄

extension	φ:Q→Out N	d	ρ	Label	ID
2₊⁽¹⁺⁴⁾⋊C₄ = C₄².D₄	φ: C₄/C₁ → C₄ ⊆ Out 2₊⁽¹⁺⁴⁾	16	4+	ES+(2,2):C4	128,134
2₊⁽¹⁺⁴⁾⋊₂C₄ = 2₊⁽¹⁺⁴⁾⋊₂C₄	φ: C₄/C₂ → C₂ ⊆ Out 2₊⁽¹⁺⁴⁾	32		ES+(2,2):2C4	128,522
2₊⁽¹⁺⁴⁾⋊₃C₄ = 2₊⁽¹⁺⁴⁾⋊₃C₄	φ: C₄/C₂ → C₂ ⊆ Out 2₊⁽¹⁺⁴⁾	32		ES+(2,2):3C4	128,524
2₊⁽¹⁺⁴⁾⋊₄C₄ = 2_-⁽¹⁺⁴⁾⋊₃C₄	φ: C₄/C₂ → C₂ ⊆ Out 2₊⁽¹⁺⁴⁾	32	4	ES+(2,2):4C4	128,526
2₊⁽¹⁺⁴⁾⋊₅C₄ = 2₊⁽¹⁺⁴⁾⋊₅C₄	φ: C₄/C₂ → C₂ ⊆ Out 2₊⁽¹⁺⁴⁾	32		ES+(2,2):5C4	128,1629
2₊⁽¹⁺⁴⁾⋊₆C₄ = 2₊⁽¹⁺⁴⁾⋊₆C₄	φ: C₄/C₂ → C₂ ⊆ Out 2₊⁽¹⁺⁴⁾	16	4	ES+(2,2):6C4	128,1633

Non-split extensions G=N.Q with N=2₊⁽¹⁺⁴⁾ and Q=C₄

extension	φ:Q→Out N	d	ρ	Label	ID
2₊⁽¹⁺⁴⁾.C₄ = C₄².₂D₄	φ: C₄/C₁ → C₄ ⊆ Out 2₊⁽¹⁺⁴⁾	16	4	ES+(2,2).C4	128,135
2₊⁽¹⁺⁴⁾.₂C₄ = 2₊⁽¹⁺⁴⁾.₂C₄	φ: C₄/C₂ → C₂ ⊆ Out 2₊⁽¹⁺⁴⁾	32	4	ES+(2,2).2C4	128,523
2₊⁽¹⁺⁴⁾.₃C₄ = C₄.₂₂C₂⁵	φ: trivial image	32	4	ES+(2,2).3C4	128,2305

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