Extensions 1→N→G→Q→1 with N=C60 and Q=S3

Direct product G=N×Q with N=C60 and Q=S3
dρLabelID
S3×C601202S3xC60360,96

Semidirect products G=N:Q with N=C60 and Q=S3
extensionφ:Q→Aut NdρLabelID
C601S3 = C60⋊S3φ: S3/C3C2 ⊆ Aut C60180C60:1S3360,112
C602S3 = C4×C3⋊D15φ: S3/C3C2 ⊆ Aut C60180C60:2S3360,111
C603S3 = C3×D60φ: S3/C3C2 ⊆ Aut C601202C60:3S3360,102
C604S3 = C5×C12⋊S3φ: S3/C3C2 ⊆ Aut C60180C60:4S3360,107
C605S3 = C12×D15φ: S3/C3C2 ⊆ Aut C601202C60:5S3360,101
C606S3 = C3⋊S3×C20φ: S3/C3C2 ⊆ Aut C60180C60:6S3360,106
C607S3 = C15×D12φ: S3/C3C2 ⊆ Aut C601202C60:7S3360,97

Non-split extensions G=N.Q with N=C60 and Q=S3
extensionφ:Q→Aut NdρLabelID
C60.1S3 = Dic90φ: S3/C3C2 ⊆ Aut C603602-C60.1S3360,25
C60.2S3 = D180φ: S3/C3C2 ⊆ Aut C601802+C60.2S3360,27
C60.3S3 = C12.D15φ: S3/C3C2 ⊆ Aut C60360C60.3S3360,110
C60.4S3 = C453C8φ: S3/C3C2 ⊆ Aut C603602C60.4S3360,3
C60.5S3 = C4×D45φ: S3/C3C2 ⊆ Aut C601802C60.5S3360,26
C60.6S3 = C60.S3φ: S3/C3C2 ⊆ Aut C60360C60.6S3360,37
C60.7S3 = C3×Dic30φ: S3/C3C2 ⊆ Aut C601202C60.7S3360,100
C60.8S3 = C5×Dic18φ: S3/C3C2 ⊆ Aut C603602C60.8S3360,20
C60.9S3 = C5×D36φ: S3/C3C2 ⊆ Aut C601802C60.9S3360,22
C60.10S3 = C5×C324Q8φ: S3/C3C2 ⊆ Aut C60360C60.10S3360,105
C60.11S3 = C3×C153C8φ: S3/C3C2 ⊆ Aut C601202C60.11S3360,35
C60.12S3 = C5×C9⋊C8φ: S3/C3C2 ⊆ Aut C603602C60.12S3360,1
C60.13S3 = D9×C20φ: S3/C3C2 ⊆ Aut C601802C60.13S3360,21
C60.14S3 = C5×C324C8φ: S3/C3C2 ⊆ Aut C60360C60.14S3360,36
C60.15S3 = C15×Dic6φ: S3/C3C2 ⊆ Aut C601202C60.15S3360,95
C60.16S3 = C15×C3⋊C8central extension (φ=1)1202C60.16S3360,34

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