# Extensions 1→N→G→Q→1 with N=C15 and Q=C3×S3

Direct product G=N×Q with N=C15 and Q=C3×S3
dρLabelID
S3×C3×C1590S3xC3xC15270,24

Semidirect products G=N:Q with N=C15 and Q=C3×S3
extensionφ:Q→Aut NdρLabelID
C151(C3×S3) = C3×C3⋊D15φ: C3×S3/C32C2 ⊆ Aut C1590C15:1(C3xS3)270,27
C152(C3×S3) = C32×D15φ: C3×S3/C32C2 ⊆ Aut C1590C15:2(C3xS3)270,25
C153(C3×S3) = C15×C3⋊S3φ: C3×S3/C32C2 ⊆ Aut C1590C15:3(C3xS3)270,26

Non-split extensions G=N.Q with N=C15 and Q=C3×S3
extensionφ:Q→Aut NdρLabelID
C15.1(C3×S3) = C3×D45φ: C3×S3/C32C2 ⊆ Aut C15902C15.1(C3xS3)270,12
C15.2(C3×S3) = He3⋊D5φ: C3×S3/C32C2 ⊆ Aut C15456+C15.2(C3xS3)270,14
C15.3(C3×S3) = D45⋊C3φ: C3×S3/C32C2 ⊆ Aut C15456+C15.3(C3xS3)270,15
C15.4(C3×S3) = C9×D15φ: C3×S3/C32C2 ⊆ Aut C15902C15.4(C3xS3)270,13
C15.5(C3×S3) = C15×D9φ: C3×S3/C32C2 ⊆ Aut C15902C15.5(C3xS3)270,8
C15.6(C3×S3) = C5×C32⋊C6φ: C3×S3/C32C2 ⊆ Aut C15456C15.6(C3xS3)270,10
C15.7(C3×S3) = C5×C9⋊C6φ: C3×S3/C32C2 ⊆ Aut C15456C15.7(C3xS3)270,11
C15.8(C3×S3) = S3×C45central extension (φ=1)902C15.8(C3xS3)270,9

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