Extensions 1→N→G→Q→1 with N=C3 and Q=S3×C2×C12

Direct product G=N×Q with N=C3 and Q=S3×C2×C12
dρLabelID
S3×C6×C12144S3xC6xC12432,701

Semidirect products G=N:Q with N=C3 and Q=S3×C2×C12
extensionφ:Q→Aut NdρLabelID
C31(S3×C2×C12) = S32×C12φ: S3×C2×C12/S3×C12C2 ⊆ Aut C3484C3:1(S3xC2xC12)432,648
C32(S3×C2×C12) = C6×C6.D6φ: S3×C2×C12/C6×Dic3C2 ⊆ Aut C348C3:2(S3xC2xC12)432,654
C33(S3×C2×C12) = C3⋊S3×C2×C12φ: S3×C2×C12/C6×C12C2 ⊆ Aut C3144C3:3(S3xC2xC12)432,711
C34(S3×C2×C12) = S3×C6×Dic3φ: S3×C2×C12/S3×C2×C6C2 ⊆ Aut C348C3:4(S3xC2xC12)432,651

Non-split extensions G=N.Q with N=C3 and Q=S3×C2×C12
extensionφ:Q→Aut NdρLabelID
C3.1(S3×C2×C12) = D9×C2×C12φ: S3×C2×C12/C6×C12C2 ⊆ Aut C3144C3.1(S3xC2xC12)432,342
C3.2(S3×C2×C12) = C2×C4×C32⋊C6φ: S3×C2×C12/C6×C12C2 ⊆ Aut C372C3.2(S3xC2xC12)432,349
C3.3(S3×C2×C12) = C2×C4×C9⋊C6φ: S3×C2×C12/C6×C12C2 ⊆ Aut C372C3.3(S3xC2xC12)432,353
C3.4(S3×C2×C12) = S3×C2×C36central extension (φ=1)144C3.4(S3xC2xC12)432,345

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