# Extensions 1→N→G→Q→1 with N=C6 and Q=C2×C40

Direct product G=N×Q with N=C6 and Q=C2×C40
dρLabelID
C22×C120480C2^2xC120480,934

Semidirect products G=N:Q with N=C6 and Q=C2×C40
extensionφ:Q→Aut NdρLabelID
C61(C2×C40) = S3×C2×C40φ: C2×C40/C40C2 ⊆ Aut C6240C6:1(C2xC40)480,778
C62(C2×C40) = C2×C10×C3⋊C8φ: C2×C40/C2×C20C2 ⊆ Aut C6480C6:2(C2xC40)480,799

Non-split extensions G=N.Q with N=C6 and Q=C2×C40
extensionφ:Q→Aut NdρLabelID
C6.1(C2×C40) = S3×C80φ: C2×C40/C40C2 ⊆ Aut C62402C6.1(C2xC40)480,116
C6.2(C2×C40) = C5×D6.C8φ: C2×C40/C40C2 ⊆ Aut C62402C6.2(C2xC40)480,117
C6.3(C2×C40) = Dic3×C40φ: C2×C40/C40C2 ⊆ Aut C6480C6.3(C2xC40)480,132
C6.4(C2×C40) = C5×Dic3⋊C8φ: C2×C40/C40C2 ⊆ Aut C6480C6.4(C2xC40)480,133
C6.5(C2×C40) = C5×D6⋊C8φ: C2×C40/C40C2 ⊆ Aut C6240C6.5(C2xC40)480,139
C6.6(C2×C40) = C20×C3⋊C8φ: C2×C40/C2×C20C2 ⊆ Aut C6480C6.6(C2xC40)480,121
C6.7(C2×C40) = C5×C12⋊C8φ: C2×C40/C2×C20C2 ⊆ Aut C6480C6.7(C2xC40)480,123
C6.8(C2×C40) = C10×C3⋊C16φ: C2×C40/C2×C20C2 ⊆ Aut C6480C6.8(C2xC40)480,130
C6.9(C2×C40) = C5×C12.C8φ: C2×C40/C2×C20C2 ⊆ Aut C62402C6.9(C2xC40)480,131
C6.10(C2×C40) = C5×C12.55D4φ: C2×C40/C2×C20C2 ⊆ Aut C6240C6.10(C2xC40)480,149
C6.11(C2×C40) = C15×C22⋊C8central extension (φ=1)240C6.11(C2xC40)480,201
C6.12(C2×C40) = C15×C4⋊C8central extension (φ=1)480C6.12(C2xC40)480,208
C6.13(C2×C40) = C15×M5(2)central extension (φ=1)2402C6.13(C2xC40)480,213

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