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

Direct product G=N×Q with N=C4 and Q=C6×F5
dρLabelID
F5×C2×C12120F5xC2xC12480,1050

Semidirect products G=N:Q with N=C4 and Q=C6×F5
extensionφ:Q→Aut NdρLabelID
C4⋊1(C6×F5) = C3×D4×F5φ: C6×F5/C3×F5 → C2 ⊆ Aut C4608C4:1(C6xF5)480,1054
C4⋊2(C6×F5) = C6×C4⋊F5φ: C6×F5/C6×D5 → C2 ⊆ Aut C4120C4:2(C6xF5)480,1051

Non-split extensions G=N.Q with N=C4 and Q=C6×F5
extensionφ:Q→Aut NdρLabelID
C4.1(C6×F5) = C3×D20⋊C4φ: C6×F5/C3×F5 → C2 ⊆ Aut C41208C4.1(C6xF5)480,287
C4.2(C6×F5) = C3×D4⋊F5φ: C6×F5/C3×F5 → C2 ⊆ Aut C41208C4.2(C6xF5)480,288
C4.3(C6×F5) = C3×Q8⋊F5φ: C6×F5/C3×F5 → C2 ⊆ Aut C41208C4.3(C6xF5)480,289
C4.4(C6×F5) = C3×Q8⋊2F5φ: C6×F5/C3×F5 → C2 ⊆ Aut C41208C4.4(C6xF5)480,290
C4.5(C6×F5) = C3×D4.F5φ: C6×F5/C3×F5 → C2 ⊆ Aut C42408C4.5(C6xF5)480,1053
C4.6(C6×F5) = C3×Q8.F5φ: C6×F5/C3×F5 → C2 ⊆ Aut C42408C4.6(C6xF5)480,1055
C4.7(C6×F5) = C3×Q8×F5φ: C6×F5/C3×F5 → C2 ⊆ Aut C41208C4.7(C6xF5)480,1056
C4.8(C6×F5) = C3×C40⋊C4φ: C6×F5/C6×D5 → C2 ⊆ Aut C41204C4.8(C6xF5)480,273
C4.9(C6×F5) = C3×D5.D8φ: C6×F5/C6×D5 → C2 ⊆ Aut C41204C4.9(C6xF5)480,274
C4.10(C6×F5) = C3×C40.C4φ: C6×F5/C6×D5 → C2 ⊆ Aut C42404C4.10(C6xF5)480,275
C4.11(C6×F5) = C3×D10.Q8φ: C6×F5/C6×D5 → C2 ⊆ Aut C42404C4.11(C6xF5)480,276
C4.12(C6×F5) = C6×C4.F5φ: C6×F5/C6×D5 → C2 ⊆ Aut C4240C4.12(C6xF5)480,1048
C4.13(C6×F5) = C3×D5⋊C16central extension (φ=1)2404C4.13(C6xF5)480,269
C4.14(C6×F5) = C3×C8.F5central extension (φ=1)2404C4.14(C6xF5)480,270
C4.15(C6×F5) = F5×C24central extension (φ=1)1204C4.15(C6xF5)480,271
C4.16(C6×F5) = C3×C8⋊F5central extension (φ=1)1204C4.16(C6xF5)480,272
C4.17(C6×F5) = C6×C5⋊C16central extension (φ=1)480C4.17(C6xF5)480,277
C4.18(C6×F5) = C3×C20.C8central extension (φ=1)2404C4.18(C6xF5)480,278
C4.19(C6×F5) = C6×D5⋊C8central extension (φ=1)240C4.19(C6xF5)480,1047
C4.20(C6×F5) = C3×D5⋊M4(2)central extension (φ=1)1204C4.20(C6xF5)480,1049
C4.21(C6×F5) = C3×D10.C23central extension (φ=1)1204C4.21(C6xF5)480,1052

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