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⁾		64		C4xES-(2,2)	128,2162

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 = C₄².₃D₄	φ: C₄/C₁ → C₄ ⊆ Out 2_-⁽¹⁺⁴⁾	16	4	ES-(2,2):C4	128,136
2_-⁽¹⁺⁴⁾⋊₂C₄ = 2_-⁽¹⁺⁴⁾⋊₂C₄	φ: C₄/C₂ → C₂ ⊆ Out 2_-⁽¹⁺⁴⁾	32		ES-(2,2):2C4	128,525
2_-⁽¹⁺⁴⁾⋊₃C₄ = 2_-⁽¹⁺⁴⁾⋊₃C₄	φ: C₄/C₂ → C₂ ⊆ Out 2_-⁽¹⁺⁴⁾	32	4	ES-(2,2):3C4	128,526
2_-⁽¹⁺⁴⁾⋊₄C₄ = 2_-⁽¹⁺⁴⁾⋊₄C₄	φ: C₄/C₂ → C₂ ⊆ Out 2_-⁽¹⁺⁴⁾	64		ES-(2,2):4C4	128,1630
2_-⁽¹⁺⁴⁾⋊₅C₄ = 2₊⁽¹⁺⁴⁾⋊₆C₄	φ: C₄/C₂ → C₂ ⊆ Out 2_-⁽¹⁺⁴⁾	16	4	ES-(2,2):5C4	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 = C₄².₄D₄	φ: C₄/C₁ → C₄ ⊆ Out 2_-⁽¹⁺⁴⁾	16	4-	ES-(2,2).C4	128,137
2_-⁽¹⁺⁴⁾.₂C₄ = C₄.₂₂C₂⁵	φ: trivial image	32	4	ES-(2,2).2C4	128,2305

׿

×

⋊

ℤ

𝔽

○

≀