Extensions 1→N→G→Q→1 with N=C52 and Q=S3

Direct product G=NxQ with N=C52 and Q=S3
dρLabelID
S3xC521562S3xC52312,33

Semidirect products G=N:Q with N=C52 and Q=S3
extensionφ:Q→Aut NdρLabelID
C52:1S3 = D156φ: S3/C3C2 ⊆ Aut C521562+C52:1S3312,39
C52:2S3 = C4xD39φ: S3/C3C2 ⊆ Aut C521562C52:2S3312,38
C52:3S3 = C13xD12φ: S3/C3C2 ⊆ Aut C521562C52:3S3312,34

Non-split extensions G=N.Q with N=C52 and Q=S3
extensionφ:Q→Aut NdρLabelID
C52.1S3 = Dic78φ: S3/C3C2 ⊆ Aut C523122-C52.1S3312,37
C52.2S3 = C39:3C8φ: S3/C3C2 ⊆ Aut C523122C52.2S3312,5
C52.3S3 = C13xDic6φ: S3/C3C2 ⊆ Aut C523122C52.3S3312,32
C52.4S3 = C13xC3:C8central extension (φ=1)3122C52.4S3312,3

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