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

Direct product G=N×Q with N=C70 and Q=C22
dρLabelID
C22×C70280C2^2xC70280,40

Semidirect products G=N:Q with N=C70 and Q=C22
extensionφ:Q→Aut NdρLabelID
C70⋊C22 = C2×D5×D7φ: C22/C1C22 ⊆ Aut C70704+C70:C2^2280,36
C702C22 = C22×D35φ: C22/C2C2 ⊆ Aut C70140C70:2C2^2280,39
C703C22 = D7×C2×C10φ: C22/C2C2 ⊆ Aut C70140C70:3C2^2280,37
C704C22 = D5×C2×C14φ: C22/C2C2 ⊆ Aut C70140C70:4C2^2280,38

Non-split extensions G=N.Q with N=C70 and Q=C22
extensionφ:Q→Aut NdρLabelID
C70.1C22 = D7×Dic5φ: C22/C1C22 ⊆ Aut C701404-C70.1C2^2280,7
C70.2C22 = D5×Dic7φ: C22/C1C22 ⊆ Aut C701404-C70.2C2^2280,8
C70.3C22 = D70.C2φ: C22/C1C22 ⊆ Aut C701404+C70.3C2^2280,9
C70.4C22 = C35⋊D4φ: C22/C1C22 ⊆ Aut C701404-C70.4C2^2280,10
C70.5C22 = C5⋊D28φ: C22/C1C22 ⊆ Aut C701404+C70.5C2^2280,11
C70.6C22 = C7⋊D20φ: C22/C1C22 ⊆ Aut C701404+C70.6C2^2280,12
C70.7C22 = C35⋊Q8φ: C22/C1C22 ⊆ Aut C702804-C70.7C2^2280,13
C70.8C22 = Dic70φ: C22/C2C2 ⊆ Aut C702802-C70.8C2^2280,24
C70.9C22 = C4×D35φ: C22/C2C2 ⊆ Aut C701402C70.9C2^2280,25
C70.10C22 = D140φ: C22/C2C2 ⊆ Aut C701402+C70.10C2^2280,26
C70.11C22 = C2×Dic35φ: C22/C2C2 ⊆ Aut C70280C70.11C2^2280,27
C70.12C22 = C357D4φ: C22/C2C2 ⊆ Aut C701402C70.12C2^2280,28
C70.13C22 = C5×Dic14φ: C22/C2C2 ⊆ Aut C702802C70.13C2^2280,14
C70.14C22 = D7×C20φ: C22/C2C2 ⊆ Aut C701402C70.14C2^2280,15
C70.15C22 = C5×D28φ: C22/C2C2 ⊆ Aut C701402C70.15C2^2280,16
C70.16C22 = C10×Dic7φ: C22/C2C2 ⊆ Aut C70280C70.16C2^2280,17
C70.17C22 = C5×C7⋊D4φ: C22/C2C2 ⊆ Aut C701402C70.17C2^2280,18
C70.18C22 = C7×Dic10φ: C22/C2C2 ⊆ Aut C702802C70.18C2^2280,19
C70.19C22 = D5×C28φ: C22/C2C2 ⊆ Aut C701402C70.19C2^2280,20
C70.20C22 = C7×D20φ: C22/C2C2 ⊆ Aut C701402C70.20C2^2280,21
C70.21C22 = C14×Dic5φ: C22/C2C2 ⊆ Aut C70280C70.21C2^2280,22
C70.22C22 = C7×C5⋊D4φ: C22/C2C2 ⊆ Aut C701402C70.22C2^2280,23
C70.23C22 = D4×C35central extension (φ=1)1402C70.23C2^2280,30
C70.24C22 = Q8×C35central extension (φ=1)2802C70.24C2^2280,31

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