# Extensions 1→N→G→Q→1 with N=C10 and Q=S32

Direct product G=N×Q with N=C10 and Q=S32
dρLabelID
S32×C10604S3^2xC10360,153

Semidirect products G=N:Q with N=C10 and Q=S32
extensionφ:Q→Aut NdρLabelID
C101S32 = C2×S3×D15φ: S32/C3×S3C2 ⊆ Aut C10604+C10:1S3^2360,154
C102S32 = C2×D15⋊S3φ: S32/C3⋊S3C2 ⊆ Aut C10604C10:2S3^2360,155

Non-split extensions G=N.Q with N=C10 and Q=S32
extensionφ:Q→Aut NdρLabelID
C10.1S32 = Dic3×D15φ: S32/C3×S3C2 ⊆ Aut C101204-C10.1S3^2360,77
C10.2S32 = S3×Dic15φ: S32/C3×S3C2 ⊆ Aut C101204-C10.2S3^2360,78
C10.3S32 = C6.D30φ: S32/C3×S3C2 ⊆ Aut C10604+C10.3S3^2360,79
C10.4S32 = D6⋊D15φ: S32/C3×S3C2 ⊆ Aut C101204-C10.4S3^2360,80
C10.5S32 = C3⋊D60φ: S32/C3×S3C2 ⊆ Aut C10604+C10.5S3^2360,81
C10.6S32 = D62D15φ: S32/C3×S3C2 ⊆ Aut C10604+C10.6S3^2360,82
C10.7S32 = C3⋊Dic30φ: S32/C3×S3C2 ⊆ Aut C101204-C10.7S3^2360,83
C10.8S32 = D30.S3φ: S32/C3⋊S3C2 ⊆ Aut C101204C10.8S3^2360,84
C10.9S32 = Dic15⋊S3φ: S32/C3⋊S3C2 ⊆ Aut C10604C10.9S3^2360,85
C10.10S32 = D30⋊S3φ: S32/C3⋊S3C2 ⊆ Aut C10604C10.10S3^2360,86
C10.11S32 = C323D20φ: S32/C3⋊S3C2 ⊆ Aut C101204C10.11S3^2360,87
C10.12S32 = C323Dic10φ: S32/C3⋊S3C2 ⊆ Aut C101204C10.12S3^2360,88
C10.13S32 = C5×S3×Dic3central extension (φ=1)1204C10.13S3^2360,72
C10.14S32 = C5×C6.D6central extension (φ=1)604C10.14S3^2360,73
C10.15S32 = C5×D6⋊S3central extension (φ=1)1204C10.15S3^2360,74
C10.16S32 = C5×C3⋊D12central extension (φ=1)604C10.16S3^2360,75
C10.17S32 = C5×C322Q8central extension (φ=1)1204C10.17S3^2360,76

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