Extensions 1→N→G→Q→1 with N=C72 and Q=S3

Direct product G=NxQ with N=C72 and Q=S3
dρLabelID
S3xC721442S3xC72432,109

Semidirect products G=N:Q with N=C72 and Q=S3
extensionφ:Q→Aut NdρLabelID
C72:1S3 = C72:1S3φ: S3/C3C2 ⊆ Aut C72216C72:1S3432,172
C72:2S3 = C24:D9φ: S3/C3C2 ⊆ Aut C72216C72:2S3432,171
C72:3S3 = C8xC9:S3φ: S3/C3C2 ⊆ Aut C72216C72:3S3432,169
C72:4S3 = C72:S3φ: S3/C3C2 ⊆ Aut C72216C72:4S3432,170
C72:5S3 = C9xD24φ: S3/C3C2 ⊆ Aut C721442C72:5S3432,112
C72:6S3 = C9xC24:C2φ: S3/C3C2 ⊆ Aut C721442C72:6S3432,111
C72:7S3 = C9xC8:S3φ: S3/C3C2 ⊆ Aut C721442C72:7S3432,110

Non-split extensions G=N.Q with N=C72 and Q=S3
extensionφ:Q→Aut NdρLabelID
C72.1S3 = Dic108φ: S3/C3C2 ⊆ Aut C724322-C72.1S3432,4
C72.2S3 = D216φ: S3/C3C2 ⊆ Aut C722162+C72.2S3432,8
C72.3S3 = C24.D9φ: S3/C3C2 ⊆ Aut C72432C72.3S3432,168
C72.4S3 = C216:C2φ: S3/C3C2 ⊆ Aut C722162C72.4S3432,7
C72.5S3 = C27:C16φ: S3/C3C2 ⊆ Aut C724322C72.5S3432,1
C72.6S3 = C8xD27φ: S3/C3C2 ⊆ Aut C722162C72.6S3432,5
C72.7S3 = C8:D27φ: S3/C3C2 ⊆ Aut C722162C72.7S3432,6
C72.8S3 = C72.S3φ: S3/C3C2 ⊆ Aut C72432C72.8S3432,32
C72.9S3 = C9xDic12φ: S3/C3C2 ⊆ Aut C721442C72.9S3432,113
C72.10S3 = C9xC3:C16central extension (φ=1)1442C72.10S3432,29

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