Extensions 1→N→G→Q→1 with N=C₇₀ and Q=C₂²

Direct product G=N×Q with N=C₇₀ and Q=C₂²

		d	ρ	Label	ID
C₂²×C₇₀		280		C2^2xC70	280,40

Semidirect products G=N:Q with N=C₇₀ and Q=C₂²

extension	φ:Q→Aut N	d	ρ	Label	ID
C₇₀⋊C₂² = C₂×D₅×D₇	φ: C₂²/C₁ → C₂² ⊆ Aut C₇₀	70	4+	C70:C2^2	280,36
C₇₀⋊₂C₂² = C₂²×D₃₅	φ: C₂²/C₂ → C₂ ⊆ Aut C₇₀	140		C70:2C2^2	280,39
C₇₀⋊₃C₂² = D₇×C₂×C₁₀	φ: C₂²/C₂ → C₂ ⊆ Aut C₇₀	140		C70:3C2^2	280,37
C₇₀⋊₄C₂² = D₅×C₂×C₁₄	φ: C₂²/C₂ → C₂ ⊆ Aut C₇₀	140		C70:4C2^2	280,38

Non-split extensions G=N.Q with N=C₇₀ and Q=C₂²

extension	φ:Q→Aut N	d	ρ	Label	ID
C₇₀.₁C₂² = D₇×Dic₅	φ: C₂²/C₁ → C₂² ⊆ Aut C₇₀	140	4-	C70.1C2^2	280,7
C₇₀.₂C₂² = D₅×Dic₇	φ: C₂²/C₁ → C₂² ⊆ Aut C₇₀	140	4-	C70.2C2^2	280,8
C₇₀.₃C₂² = D₇₀.C₂	φ: C₂²/C₁ → C₂² ⊆ Aut C₇₀	140	4+	C70.3C2^2	280,9
C₇₀.₄C₂² = C₃₅⋊D₄	φ: C₂²/C₁ → C₂² ⊆ Aut C₇₀	140	4-	C70.4C2^2	280,10
C₇₀.₅C₂² = C₅⋊D₂₈	φ: C₂²/C₁ → C₂² ⊆ Aut C₇₀	140	4+	C70.5C2^2	280,11
C₇₀.₆C₂² = C₇⋊D₂₀	φ: C₂²/C₁ → C₂² ⊆ Aut C₇₀	140	4+	C70.6C2^2	280,12
C₇₀.₇C₂² = C₃₅⋊Q₈	φ: C₂²/C₁ → C₂² ⊆ Aut C₇₀	280	4-	C70.7C2^2	280,13
C₇₀.₈C₂² = Dic₇₀	φ: C₂²/C₂ → C₂ ⊆ Aut C₇₀	280	2-	C70.8C2^2	280,24
C₇₀.₉C₂² = C₄×D₃₅	φ: C₂²/C₂ → C₂ ⊆ Aut C₇₀	140	2	C70.9C2^2	280,25
C₇₀.₁₀C₂² = D₁₄₀	φ: C₂²/C₂ → C₂ ⊆ Aut C₇₀	140	2+	C70.10C2^2	280,26
C₇₀.₁₁C₂² = C₂×Dic₃₅	φ: C₂²/C₂ → C₂ ⊆ Aut C₇₀	280		C70.11C2^2	280,27
C₇₀.₁₂C₂² = C₃₅⋊₇D₄	φ: C₂²/C₂ → C₂ ⊆ Aut C₇₀	140	2	C70.12C2^2	280,28
C₇₀.₁₃C₂² = C₅×Dic₁₄	φ: C₂²/C₂ → C₂ ⊆ Aut C₇₀	280	2	C70.13C2^2	280,14
C₇₀.₁₄C₂² = D₇×C₂₀	φ: C₂²/C₂ → C₂ ⊆ Aut C₇₀	140	2	C70.14C2^2	280,15
C₇₀.₁₅C₂² = C₅×D₂₈	φ: C₂²/C₂ → C₂ ⊆ Aut C₇₀	140	2	C70.15C2^2	280,16
C₇₀.₁₆C₂² = C₁₀×Dic₇	φ: C₂²/C₂ → C₂ ⊆ Aut C₇₀	280		C70.16C2^2	280,17
C₇₀.₁₇C₂² = C₅×C₇⋊D₄	φ: C₂²/C₂ → C₂ ⊆ Aut C₇₀	140	2	C70.17C2^2	280,18
C₇₀.₁₈C₂² = C₇×Dic₁₀	φ: C₂²/C₂ → C₂ ⊆ Aut C₇₀	280	2	C70.18C2^2	280,19
C₇₀.₁₉C₂² = D₅×C₂₈	φ: C₂²/C₂ → C₂ ⊆ Aut C₇₀	140	2	C70.19C2^2	280,20
C₇₀.₂₀C₂² = C₇×D₂₀	φ: C₂²/C₂ → C₂ ⊆ Aut C₇₀	140	2	C70.20C2^2	280,21
C₇₀.₂₁C₂² = C₁₄×Dic₅	φ: C₂²/C₂ → C₂ ⊆ Aut C₇₀	280		C70.21C2^2	280,22
C₇₀.₂₂C₂² = C₇×C₅⋊D₄	φ: C₂²/C₂ → C₂ ⊆ Aut C₇₀	140	2	C70.22C2^2	280,23
C₇₀.₂₃C₂² = D₄×C₃₅	central extension (φ=1)	140	2	C70.23C2^2	280,30
C₇₀.₂₄C₂² = Q₈×C₃₅	central extension (φ=1)	280	2	C70.24C2^2	280,31

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Extensions 1→N→G→Q→1 with N=C70 and Q=C22

Extensions 1→N→G→Q→1 with N=C₇₀ and Q=C₂²