# Extensions 1→N→G→Q→1 with N=C70 and Q=C6

Direct product G=N×Q with N=C70 and Q=C6
dρLabelID
C2×C210420C2xC210420,41

Semidirect products G=N:Q with N=C70 and Q=C6
extensionφ:Q→Aut NdρLabelID
C701C6 = C2×C5⋊F7φ: C6/C1C6 ⊆ Aut C70706+C70:1C6420,19
C702C6 = C10×F7φ: C6/C1C6 ⊆ Aut C70706C70:2C6420,17
C703C6 = C2×D5×C7⋊C3φ: C6/C1C6 ⊆ Aut C70706C70:3C6420,18
C704C6 = C2×C10×C7⋊C3φ: C6/C2C3 ⊆ Aut C70140C70:4C6420,31
C705C6 = C6×D35φ: C6/C3C2 ⊆ Aut C702102C70:5C6420,36
C706C6 = D7×C30φ: C6/C3C2 ⊆ Aut C702102C70:6C6420,34
C707C6 = D5×C42φ: C6/C3C2 ⊆ Aut C702102C70:7C6420,35

Non-split extensions G=N.Q with N=C70 and Q=C6
extensionφ:Q→Aut NdρLabelID
C70.1C6 = C353C12φ: C6/C1C6 ⊆ Aut C701406-C70.1C6420,3
C70.2C6 = C5×C7⋊C12φ: C6/C1C6 ⊆ Aut C701406C70.2C6420,1
C70.3C6 = Dic5×C7⋊C3φ: C6/C1C6 ⊆ Aut C701406C70.3C6420,2
C70.4C6 = C20×C7⋊C3φ: C6/C2C3 ⊆ Aut C701403C70.4C6420,4
C70.5C6 = C3×Dic35φ: C6/C3C2 ⊆ Aut C704202C70.5C6420,7
C70.6C6 = C15×Dic7φ: C6/C3C2 ⊆ Aut C704202C70.6C6420,5
C70.7C6 = Dic5×C21φ: C6/C3C2 ⊆ Aut C704202C70.7C6420,6

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