# Extensions 1→N→G→Q→1 with N=C10 and Q=S3×C6

Direct product G=N×Q with N=C10 and Q=S3×C6
dρLabelID
S3×C2×C30120S3xC2xC30360,158

Semidirect products G=N:Q with N=C10 and Q=S3×C6
extensionφ:Q→Aut NdρLabelID
C101(S3×C6) = S3×C6×D5φ: S3×C6/C3×S3C2 ⊆ Aut C10604C10:1(S3xC6)360,151
C102(S3×C6) = C2×C6×D15φ: S3×C6/C3×C6C2 ⊆ Aut C10120C10:2(S3xC6)360,159

Non-split extensions G=N.Q with N=C10 and Q=S3×C6
extensionφ:Q→Aut NdρLabelID
C10.1(S3×C6) = C3×D5×Dic3φ: S3×C6/C3×S3C2 ⊆ Aut C10604C10.1(S3xC6)360,58
C10.2(S3×C6) = C3×S3×Dic5φ: S3×C6/C3×S3C2 ⊆ Aut C101204C10.2(S3xC6)360,59
C10.3(S3×C6) = C3×D30.C2φ: S3×C6/C3×S3C2 ⊆ Aut C101204C10.3(S3xC6)360,60
C10.4(S3×C6) = C3×C15⋊D4φ: S3×C6/C3×S3C2 ⊆ Aut C10604C10.4(S3xC6)360,61
C10.5(S3×C6) = C3×C3⋊D20φ: S3×C6/C3×S3C2 ⊆ Aut C10604C10.5(S3xC6)360,62
C10.6(S3×C6) = C3×C5⋊D12φ: S3×C6/C3×S3C2 ⊆ Aut C101204C10.6(S3xC6)360,63
C10.7(S3×C6) = C3×C15⋊Q8φ: S3×C6/C3×S3C2 ⊆ Aut C101204C10.7(S3xC6)360,64
C10.8(S3×C6) = C3×Dic30φ: S3×C6/C3×C6C2 ⊆ Aut C101202C10.8(S3xC6)360,100
C10.9(S3×C6) = C12×D15φ: S3×C6/C3×C6C2 ⊆ Aut C101202C10.9(S3xC6)360,101
C10.10(S3×C6) = C3×D60φ: S3×C6/C3×C6C2 ⊆ Aut C101202C10.10(S3xC6)360,102
C10.11(S3×C6) = C6×Dic15φ: S3×C6/C3×C6C2 ⊆ Aut C10120C10.11(S3xC6)360,103
C10.12(S3×C6) = C3×C157D4φ: S3×C6/C3×C6C2 ⊆ Aut C10602C10.12(S3xC6)360,104
C10.13(S3×C6) = C15×Dic6central extension (φ=1)1202C10.13(S3xC6)360,95
C10.14(S3×C6) = S3×C60central extension (φ=1)1202C10.14(S3xC6)360,96
C10.15(S3×C6) = C15×D12central extension (φ=1)1202C10.15(S3xC6)360,97
C10.16(S3×C6) = Dic3×C30central extension (φ=1)120C10.16(S3xC6)360,98
C10.17(S3×C6) = C15×C3⋊D4central extension (φ=1)602C10.17(S3xC6)360,99

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