Extensions 1→N→G→Q→1 with N=C56 and Q=S3

Direct product G=N×Q with N=C56 and Q=S3
dρLabelID
S3×C561682S3xC56336,74

Semidirect products G=N:Q with N=C56 and Q=S3
extensionφ:Q→Aut NdρLabelID
C561S3 = D168φ: S3/C3C2 ⊆ Aut C561682+C56:1S3336,93
C562S3 = C8⋊D21φ: S3/C3C2 ⊆ Aut C561682C56:2S3336,92
C563S3 = C8×D21φ: S3/C3C2 ⊆ Aut C561682C56:3S3336,90
C564S3 = C56⋊S3φ: S3/C3C2 ⊆ Aut C561682C56:4S3336,91
C565S3 = C7×D24φ: S3/C3C2 ⊆ Aut C561682C56:5S3336,77
C566S3 = C7×C24⋊C2φ: S3/C3C2 ⊆ Aut C561682C56:6S3336,76
C567S3 = C7×C8⋊S3φ: S3/C3C2 ⊆ Aut C561682C56:7S3336,75

Non-split extensions G=N.Q with N=C56 and Q=S3
extensionφ:Q→Aut NdρLabelID
C56.1S3 = Dic84φ: S3/C3C2 ⊆ Aut C563362-C56.1S3336,94
C56.2S3 = C21⋊C16φ: S3/C3C2 ⊆ Aut C563362C56.2S3336,5
C56.3S3 = C7×Dic12φ: S3/C3C2 ⊆ Aut C563362C56.3S3336,78
C56.4S3 = C7×C3⋊C16central extension (φ=1)3362C56.4S3336,3

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