Extensions 1→N→G→Q→1 with N=C₉₀ and Q=C₂²

Direct product G=N×Q with N=C₉₀ and Q=C₂²

		d	ρ	Label	ID
C₂²×C₉₀		360		C2^2xC90	360,50

Semidirect products G=N:Q with N=C₉₀ and Q=C₂²

extension	φ:Q→Aut N	d	ρ	Label	ID
C₉₀⋊C₂² = C₂×D₅×D₉	φ: C₂²/C₁ → C₂² ⊆ Aut C₉₀	90	4+	C90:C2^2	360,45
C₉₀⋊₂C₂² = C₂²×D₄₅	φ: C₂²/C₂ → C₂ ⊆ Aut C₉₀	180		C90:2C2^2	360,49
C₉₀⋊₃C₂² = D₉×C₂×C₁₀	φ: C₂²/C₂ → C₂ ⊆ Aut C₉₀	180		C90:3C2^2	360,48
C₉₀⋊₄C₂² = D₅×C₂×C₁₈	φ: C₂²/C₂ → C₂ ⊆ Aut C₉₀	180		C90:4C2^2	360,47

Non-split extensions G=N.Q with N=C₉₀ and Q=C₂²

extension	φ:Q→Aut N	d	ρ	Label	ID
C₉₀.₁C₂² = C₄₅⋊Q₈	φ: C₂²/C₁ → C₂² ⊆ Aut C₉₀	360	4-	C90.1C2^2	360,7
C₉₀.₂C₂² = D₉×Dic₅	φ: C₂²/C₁ → C₂² ⊆ Aut C₉₀	180	4-	C90.2C2^2	360,8
C₉₀.₃C₂² = D₉₀.C₂	φ: C₂²/C₁ → C₂² ⊆ Aut C₉₀	180	4+	C90.3C2^2	360,9
C₉₀.₄C₂² = C₅⋊D₃₆	φ: C₂²/C₁ → C₂² ⊆ Aut C₉₀	180	4+	C90.4C2^2	360,10
C₉₀.₅C₂² = D₅×Dic₉	φ: C₂²/C₁ → C₂² ⊆ Aut C₉₀	180	4-	C90.5C2^2	360,11
C₉₀.₆C₂² = C₄₅⋊D₄	φ: C₂²/C₁ → C₂² ⊆ Aut C₉₀	180	4-	C90.6C2^2	360,12
C₉₀.₇C₂² = C₉⋊D₂₀	φ: C₂²/C₁ → C₂² ⊆ Aut C₉₀	180	4+	C90.7C2^2	360,13
C₉₀.₈C₂² = Dic₉₀	φ: C₂²/C₂ → C₂ ⊆ Aut C₉₀	360	2-	C90.8C2^2	360,25
C₉₀.₉C₂² = C₄×D₄₅	φ: C₂²/C₂ → C₂ ⊆ Aut C₉₀	180	2	C90.9C2^2	360,26
C₉₀.₁₀C₂² = D₁₈₀	φ: C₂²/C₂ → C₂ ⊆ Aut C₉₀	180	2+	C90.10C2^2	360,27
C₉₀.₁₁C₂² = C₂×Dic₄₅	φ: C₂²/C₂ → C₂ ⊆ Aut C₉₀	360		C90.11C2^2	360,28
C₉₀.₁₂C₂² = C₄₅⋊₇D₄	φ: C₂²/C₂ → C₂ ⊆ Aut C₉₀	180	2	C90.12C2^2	360,29
C₉₀.₁₃C₂² = C₅×Dic₁₈	φ: C₂²/C₂ → C₂ ⊆ Aut C₉₀	360	2	C90.13C2^2	360,20
C₉₀.₁₄C₂² = D₉×C₂₀	φ: C₂²/C₂ → C₂ ⊆ Aut C₉₀	180	2	C90.14C2^2	360,21
C₉₀.₁₅C₂² = C₅×D₃₆	φ: C₂²/C₂ → C₂ ⊆ Aut C₉₀	180	2	C90.15C2^2	360,22
C₉₀.₁₆C₂² = C₁₀×Dic₉	φ: C₂²/C₂ → C₂ ⊆ Aut C₉₀	360		C90.16C2^2	360,23
C₉₀.₁₇C₂² = C₅×C₉⋊D₄	φ: C₂²/C₂ → C₂ ⊆ Aut C₉₀	180	2	C90.17C2^2	360,24
C₉₀.₁₈C₂² = C₉×Dic₁₀	φ: C₂²/C₂ → C₂ ⊆ Aut C₉₀	360	2	C90.18C2^2	360,15
C₉₀.₁₉C₂² = D₅×C₃₆	φ: C₂²/C₂ → C₂ ⊆ Aut C₉₀	180	2	C90.19C2^2	360,16
C₉₀.₂₀C₂² = C₉×D₂₀	φ: C₂²/C₂ → C₂ ⊆ Aut C₉₀	180	2	C90.20C2^2	360,17
C₉₀.₂₁C₂² = C₁₈×Dic₅	φ: C₂²/C₂ → C₂ ⊆ Aut C₉₀	360		C90.21C2^2	360,18
C₉₀.₂₂C₂² = C₉×C₅⋊D₄	φ: C₂²/C₂ → C₂ ⊆ Aut C₉₀	180	2	C90.22C2^2	360,19
C₉₀.₂₃C₂² = D₄×C₄₅	central extension (φ=1)	180	2	C90.23C2^2	360,31
C₉₀.₂₄C₂² = Q₈×C₄₅	central extension (φ=1)	360	2	C90.24C2^2	360,32

⋊

ℤ

𝔽

○

≀

ℚ

◁

Extensions 1→N→G→Q→1 with N=C90 and Q=C22

Extensions 1→N→G→Q→1 with N=C₉₀ and Q=C₂²