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Extensions 1→N→G→Q→1 with N=C6 and Q=C4⋊Dic5

Direct product G=N×Q with N=C6 and Q=C4⋊Dic5
dρLabelID
C6×C4⋊Dic5480C6xC4:Dic5480,718

Semidirect products G=N:Q with N=C6 and Q=C4⋊Dic5
extensionφ:Q→Aut NdρLabelID
C6⋊1(C4⋊Dic5) = C2×C6.Dic10φ: C4⋊Dic5/C2×Dic5 → C2 ⊆ Aut C6480C6:1(C4:Dic5)480,621
C6⋊2(C4⋊Dic5) = C2×C60⋊5C4φ: C4⋊Dic5/C2×C20 → C2 ⊆ Aut C6480C6:2(C4:Dic5)480,890

Non-split extensions G=N.Q with N=C6 and Q=C4⋊Dic5
extensionφ:Q→Aut NdρLabelID
C6.1(C4⋊Dic5) = C60.15Q8φ: C4⋊Dic5/C2×Dic5 → C2 ⊆ Aut C6480C6.1(C4:Dic5)480,60
C6.2(C4⋊Dic5) = C60.Q8φ: C4⋊Dic5/C2×Dic5 → C2 ⊆ Aut C6480C6.2(C4:Dic5)480,63
C6.3(C4⋊Dic5) = C60.5Q8φ: C4⋊Dic5/C2×Dic5 → C2 ⊆ Aut C6480C6.3(C4:Dic5)480,66
C6.4(C4⋊Dic5) = C12.59D20φ: C4⋊Dic5/C2×Dic5 → C2 ⊆ Aut C62404C6.4(C4:Dic5)480,69
C6.5(C4⋊Dic5) = C30.24C42φ: C4⋊Dic5/C2×Dic5 → C2 ⊆ Aut C6480C6.5(C4:Dic5)480,70
C6.6(C4⋊Dic5) = C60⋊5C8φ: C4⋊Dic5/C2×C20 → C2 ⊆ Aut C6480C6.6(C4:Dic5)480,164
C6.7(C4⋊Dic5) = C120⋊10C4φ: C4⋊Dic5/C2×C20 → C2 ⊆ Aut C6480C6.7(C4:Dic5)480,177
C6.8(C4⋊Dic5) = C120⋊9C4φ: C4⋊Dic5/C2×C20 → C2 ⊆ Aut C6480C6.8(C4:Dic5)480,178
C6.9(C4⋊Dic5) = C4.18D60φ: C4⋊Dic5/C2×C20 → C2 ⊆ Aut C62402C6.9(C4:Dic5)480,179
C6.10(C4⋊Dic5) = C30.29C42φ: C4⋊Dic5/C2×C20 → C2 ⊆ Aut C6480C6.10(C4:Dic5)480,191
C6.11(C4⋊Dic5) = C3×C20⋊3C8central extension (φ=1)480C6.11(C4:Dic5)480,82
C6.12(C4⋊Dic5) = C3×C40⋊6C4central extension (φ=1)480C6.12(C4:Dic5)480,95
C6.13(C4⋊Dic5) = C3×C40⋊5C4central extension (φ=1)480C6.13(C4:Dic5)480,96
C6.14(C4⋊Dic5) = C3×C40.6C4central extension (φ=1)2402C6.14(C4:Dic5)480,97
C6.15(C4⋊Dic5) = C3×C10.10C42central extension (φ=1)480C6.15(C4:Dic5)480,109

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