# Extensions 1→N→G→Q→1 with N=C42 and Q=C5×S3

Direct product G=N×Q with N=C42 and Q=C5×S3
dρLabelID
S3×C4×C20240S3xC4xC20480,750

Semidirect products G=N:Q with N=C42 and Q=C5×S3
extensionφ:Q→Aut NdρLabelID
C42⋊(C5×S3) = C5×C42⋊S3φ: C5×S3/C5S3 ⊆ Aut C42603C4^2:(C5xS3)480,254
C422(C5×S3) = C5×C422S3φ: C5×S3/C15C2 ⊆ Aut C42240C4^2:2(C5xS3)480,751
C423(C5×S3) = C5×C423S3φ: C5×S3/C15C2 ⊆ Aut C42240C4^2:3(C5xS3)480,755
C424(C5×S3) = C5×C424S3φ: C5×S3/C15C2 ⊆ Aut C421202C4^2:4(C5xS3)480,124
C425(C5×S3) = C20×D12φ: C5×S3/C15C2 ⊆ Aut C42240C4^2:5(C5xS3)480,752
C426(C5×S3) = C5×C4⋊D12φ: C5×S3/C15C2 ⊆ Aut C42240C4^2:6(C5xS3)480,753
C427(C5×S3) = C5×C427S3φ: C5×S3/C15C2 ⊆ Aut C42240C4^2:7(C5xS3)480,754

Non-split extensions G=N.Q with N=C42 and Q=C5×S3
extensionφ:Q→Aut NdρLabelID
C42.1(C5×S3) = C5×C42.S3φ: C5×S3/C15C2 ⊆ Aut C42480C4^2.1(C5xS3)480,122
C42.2(C5×S3) = C5×C12⋊C8φ: C5×S3/C15C2 ⊆ Aut C42480C4^2.2(C5xS3)480,123
C42.3(C5×S3) = C20×Dic6φ: C5×S3/C15C2 ⊆ Aut C42480C4^2.3(C5xS3)480,747
C42.4(C5×S3) = C5×C122Q8φ: C5×S3/C15C2 ⊆ Aut C42480C4^2.4(C5xS3)480,748
C42.5(C5×S3) = C5×C12.6Q8φ: C5×S3/C15C2 ⊆ Aut C42480C4^2.5(C5xS3)480,749
C42.6(C5×S3) = C20×C3⋊C8central extension (φ=1)480C4^2.6(C5xS3)480,121

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