# Extensions 1→N→G→Q→1 with N=C12 and Q=C5×S3

Direct product G=N×Q with N=C12 and Q=C5×S3
dρLabelID
S3×C601202S3xC60360,96

Semidirect products G=N:Q with N=C12 and Q=C5×S3
extensionφ:Q→Aut NdρLabelID
C121(C5×S3) = C5×C12⋊S3φ: C5×S3/C15C2 ⊆ Aut C12180C12:1(C5xS3)360,107
C122(C5×S3) = C3⋊S3×C20φ: C5×S3/C15C2 ⊆ Aut C12180C12:2(C5xS3)360,106
C123(C5×S3) = C15×D12φ: C5×S3/C15C2 ⊆ Aut C121202C12:3(C5xS3)360,97

Non-split extensions G=N.Q with N=C12 and Q=C5×S3
extensionφ:Q→Aut NdρLabelID
C12.1(C5×S3) = C5×Dic18φ: C5×S3/C15C2 ⊆ Aut C123602C12.1(C5xS3)360,20
C12.2(C5×S3) = C5×D36φ: C5×S3/C15C2 ⊆ Aut C121802C12.2(C5xS3)360,22
C12.3(C5×S3) = C5×C324Q8φ: C5×S3/C15C2 ⊆ Aut C12360C12.3(C5xS3)360,105
C12.4(C5×S3) = C5×C9⋊C8φ: C5×S3/C15C2 ⊆ Aut C123602C12.4(C5xS3)360,1
C12.5(C5×S3) = D9×C20φ: C5×S3/C15C2 ⊆ Aut C121802C12.5(C5xS3)360,21
C12.6(C5×S3) = C5×C324C8φ: C5×S3/C15C2 ⊆ Aut C12360C12.6(C5xS3)360,36
C12.7(C5×S3) = C15×Dic6φ: C5×S3/C15C2 ⊆ Aut C121202C12.7(C5xS3)360,95
C12.8(C5×S3) = C15×C3⋊C8central extension (φ=1)1202C12.8(C5xS3)360,34

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