Extensions 1→N→G→Q→1 with N=C₃₈ and Q=D₄

Direct product G=N×Q with N=C₃₈ and Q=D₄

		d	ρ	Label	ID
D₄×C₃₈		152		D4xC38	304,38

Semidirect products G=N:Q with N=C₃₈ and Q=D₄

extension	φ:Q→Aut N	d	ρ	Label	ID
C₃₈⋊₁D₄ = C₂×D₇₆	φ: D₄/C₄ → C₂ ⊆ Aut C₃₈	152		C38:1D4	304,29
C₃₈⋊₂D₄ = C₂×C₁₉⋊D₄	φ: D₄/C₂² → C₂ ⊆ Aut C₃₈	152		C38:2D4	304,36

Non-split extensions G=N.Q with N=C₃₈ and Q=D₄

extension	φ:Q→Aut N	d	ρ	Label	ID
C₃₈.₁D₄ = C₁₅₂⋊C₂	φ: D₄/C₄ → C₂ ⊆ Aut C₃₈	152	2	C38.1D4	304,5
C₃₈.₂D₄ = D₁₅₂	φ: D₄/C₄ → C₂ ⊆ Aut C₃₈	152	2+	C38.2D4	304,6
C₃₈.₃D₄ = Dic₇₆	φ: D₄/C₄ → C₂ ⊆ Aut C₃₈	304	2-	C38.3D4	304,7
C₃₈.₄D₄ = C₇₆⋊C₄	φ: D₄/C₄ → C₂ ⊆ Aut C₃₈	304		C38.4D4	304,12
C₃₈.₅D₄ = Dic₁₉⋊C₄	φ: D₄/C₂² → C₂ ⊆ Aut C₃₈	304		C38.5D4	304,11
C₃₈.₆D₄ = D₃₈⋊C₄	φ: D₄/C₂² → C₂ ⊆ Aut C₃₈	152		C38.6D4	304,13
C₃₈.₇D₄ = D₄⋊D₁₉	φ: D₄/C₂² → C₂ ⊆ Aut C₃₈	152	4+	C38.7D4	304,14
C₃₈.₈D₄ = D₄.D₁₉	φ: D₄/C₂² → C₂ ⊆ Aut C₃₈	152	4-	C38.8D4	304,15
C₃₈.₉D₄ = Q₈⋊D₁₉	φ: D₄/C₂² → C₂ ⊆ Aut C₃₈	152	4+	C38.9D4	304,16
C₃₈.₁₀D₄ = C₁₉⋊Q₁₆	φ: D₄/C₂² → C₂ ⊆ Aut C₃₈	304	4-	C38.10D4	304,17
C₃₈.₁₁D₄ = C₂³.D₁₉	φ: D₄/C₂² → C₂ ⊆ Aut C₃₈	152		C38.11D4	304,18
C₃₈.₁₂D₄ = C₂²⋊C₄×C₁₉	central extension (φ=1)	152		C38.12D4	304,20
C₃₈.₁₃D₄ = C₄⋊C₄×C₁₉	central extension (φ=1)	304		C38.13D4	304,21
C₃₈.₁₄D₄ = D₈×C₁₉	central extension (φ=1)	152	2	C38.14D4	304,24
C₃₈.₁₅D₄ = SD₁₆×C₁₉	central extension (φ=1)	152	2	C38.15D4	304,25
C₃₈.₁₆D₄ = Q₁₆×C₁₉	central extension (φ=1)	304	2	C38.16D4	304,26

׿

×

⋊

ℤ

𝔽

○

≀

ℚ

◁