Extensions 1→N→G→Q→1 with N=C56 and Q=C2

Direct product G=NxQ with N=C56 and Q=C2
dρLabelID
C2xC56112C2xC56112,22

Semidirect products G=N:Q with N=C56 and Q=C2
extensionφ:Q→Aut NdρLabelID
C56:1C2 = D56φ: C2/C1C2 ⊆ Aut C56562+C56:1C2112,6
C56:2C2 = C56:C2φ: C2/C1C2 ⊆ Aut C56562C56:2C2112,5
C56:3C2 = C8xD7φ: C2/C1C2 ⊆ Aut C56562C56:3C2112,3
C56:4C2 = C8:D7φ: C2/C1C2 ⊆ Aut C56562C56:4C2112,4
C56:5C2 = C7xD8φ: C2/C1C2 ⊆ Aut C56562C56:5C2112,24
C56:6C2 = C7xSD16φ: C2/C1C2 ⊆ Aut C56562C56:6C2112,25
C56:7C2 = C7xM4(2)φ: C2/C1C2 ⊆ Aut C56562C56:7C2112,23

Non-split extensions G=N.Q with N=C56 and Q=C2
extensionφ:Q→Aut NdρLabelID
C56.1C2 = Dic28φ: C2/C1C2 ⊆ Aut C561122-C56.1C2112,7
C56.2C2 = C7:C16φ: C2/C1C2 ⊆ Aut C561122C56.2C2112,1
C56.3C2 = C7xQ16φ: C2/C1C2 ⊆ Aut C561122C56.3C2112,26

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