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Extensions 1→N→G→Q→1 with N=C6 and Q=C4⋊F5

Direct product G=N×Q with N=C6 and Q=C4⋊F5
dρLabelID
C6×C4⋊F5120C6xC4:F5480,1051

Semidirect products G=N:Q with N=C6 and Q=C4⋊F5
extensionφ:Q→Aut NdρLabelID
C6⋊1(C4⋊F5) = C2×C60⋊C4φ: C4⋊F5/C4×D5 → C2 ⊆ Aut C6120C6:1(C4:F5)480,1064
C6⋊2(C4⋊F5) = C2×Dic3⋊F5φ: C4⋊F5/C2×F5 → C2 ⊆ Aut C6120C6:2(C4:F5)480,1001

Non-split extensions G=N.Q with N=C6 and Q=C4⋊F5
extensionφ:Q→Aut NdρLabelID
C6.1(C4⋊F5) = C120⋊C4φ: C4⋊F5/C4×D5 → C2 ⊆ Aut C61204C6.1(C4:F5)480,298
C6.2(C4⋊F5) = D5.D24φ: C4⋊F5/C4×D5 → C2 ⊆ Aut C61204C6.2(C4:F5)480,299
C6.3(C4⋊F5) = C40.Dic3φ: C4⋊F5/C4×D5 → C2 ⊆ Aut C62404C6.3(C4:F5)480,300
C6.4(C4⋊F5) = C24.1F5φ: C4⋊F5/C4×D5 → C2 ⊆ Aut C62404C6.4(C4:F5)480,301
C6.5(C4⋊F5) = C60⋊C8φ: C4⋊F5/C4×D5 → C2 ⊆ Aut C6480C6.5(C4:F5)480,306
C6.6(C4⋊F5) = Dic5.13D12φ: C4⋊F5/C4×D5 → C2 ⊆ Aut C6480C6.6(C4:F5)480,309
C6.7(C4⋊F5) = D10.10D12φ: C4⋊F5/C4×D5 → C2 ⊆ Aut C6120C6.7(C4:F5)480,311
C6.8(C4⋊F5) = Dic5.Dic6φ: C4⋊F5/C2×F5 → C2 ⊆ Aut C61208C6.8(C4:F5)480,235
C6.9(C4⋊F5) = Dic5.4Dic6φ: C4⋊F5/C2×F5 → C2 ⊆ Aut C61208C6.9(C4:F5)480,236
C6.10(C4⋊F5) = D10.Dic6φ: C4⋊F5/C2×F5 → C2 ⊆ Aut C62408C6.10(C4:F5)480,237
C6.11(C4⋊F5) = D10.2Dic6φ: C4⋊F5/C2×F5 → C2 ⊆ Aut C62408C6.11(C4:F5)480,238
C6.12(C4⋊F5) = D10.20D12φ: C4⋊F5/C2×F5 → C2 ⊆ Aut C6120C6.12(C4:F5)480,243
C6.13(C4⋊F5) = C30.4M4(2)φ: C4⋊F5/C2×F5 → C2 ⊆ Aut C6480C6.13(C4:F5)480,252
C6.14(C4⋊F5) = Dic15⋊C8φ: C4⋊F5/C2×F5 → C2 ⊆ Aut C6480C6.14(C4:F5)480,253
C6.15(C4⋊F5) = C3×C40⋊C4central extension (φ=1)1204C6.15(C4:F5)480,273
C6.16(C4⋊F5) = C3×D5.D8central extension (φ=1)1204C6.16(C4:F5)480,274
C6.17(C4⋊F5) = C3×C40.C4central extension (φ=1)2404C6.17(C4:F5)480,275
C6.18(C4⋊F5) = C3×D10.Q8central extension (φ=1)2404C6.18(C4:F5)480,276
C6.19(C4⋊F5) = C3×C20⋊C8central extension (φ=1)480C6.19(C4:F5)480,281
C6.20(C4⋊F5) = C3×Dic5⋊C8central extension (φ=1)480C6.20(C4:F5)480,284
C6.21(C4⋊F5) = C3×D10.3Q8central extension (φ=1)120C6.21(C4:F5)480,286

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