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Extensions 1→N→G→Q→1 with N=C10 and Q=C2.C42

Direct product G=N×Q with N=C10 and Q=C2.C42
dρLabelID
C10×C2.C42320C10xC2.C4^2320,876

Semidirect products G=N:Q with N=C10 and Q=C2.C42
extensionφ:Q→Aut NdρLabelID
C10⋊(C2.C42) = C2×D10.3Q8φ: C2.C42/C2×C4 → C4 ⊆ Aut C1080C10:(C2.C4^2)320,1100
C10⋊2(C2.C42) = C2×C10.10C42φ: C2.C42/C22×C4 → C2 ⊆ Aut C10320C10:2(C2.C4^2)320,835

Non-split extensions G=N.Q with N=C10 and Q=C2.C42
extensionφ:Q→Aut NdρLabelID
C10.1(C2.C42) = C42⋊6F5φ: C2.C42/C2×C4 → C4 ⊆ Aut C10404C10.1(C2.C4^2)320,200
C10.2(C2.C42) = C42⋊3F5φ: C2.C42/C2×C4 → C4 ⊆ Aut C10804C10.2(C2.C4^2)320,201
C10.3(C2.C42) = (C22×F5)⋊C4φ: C2.C42/C2×C4 → C4 ⊆ Aut C10408+C10.3(C2.C4^2)320,204
C10.4(C2.C42) = C22⋊C4.F5φ: C2.C42/C2×C4 → C4 ⊆ Aut C10808-C10.4(C2.C4^2)320,205
C10.5(C2.C42) = D10.18D8φ: C2.C42/C2×C4 → C4 ⊆ Aut C1080C10.5(C2.C4^2)320,212
C10.6(C2.C42) = C20.C42φ: C2.C42/C2×C4 → C4 ⊆ Aut C1080C10.6(C2.C4^2)320,213
C10.7(C2.C42) = D10.3M4(2)φ: C2.C42/C2×C4 → C4 ⊆ Aut C1080C10.7(C2.C4^2)320,230
C10.8(C2.C42) = D10.10D8φ: C2.C42/C2×C4 → C4 ⊆ Aut C1080C10.8(C2.C4^2)320,231
C10.9(C2.C42) = (C2×C8)⋊F5φ: C2.C42/C2×C4 → C4 ⊆ Aut C10804C10.9(C2.C4^2)320,232
C10.10(C2.C42) = C20.24C42φ: C2.C42/C2×C4 → C4 ⊆ Aut C10804C10.10(C2.C4^2)320,233
C10.11(C2.C42) = C20.10C42φ: C2.C42/C2×C4 → C4 ⊆ Aut C10160C10.11(C2.C4^2)320,234
C10.12(C2.C42) = C20.25C42φ: C2.C42/C2×C4 → C4 ⊆ Aut C10804C10.12(C2.C4^2)320,235
C10.13(C2.C42) = M4(2)⋊F5φ: C2.C42/C2×C4 → C4 ⊆ Aut C10408C10.13(C2.C4^2)320,237
C10.14(C2.C42) = M4(2)⋊3F5φ: C2.C42/C2×C4 → C4 ⊆ Aut C10408C10.14(C2.C4^2)320,238
C10.15(C2.C42) = M4(2).F5φ: C2.C42/C2×C4 → C4 ⊆ Aut C10808C10.15(C2.C4^2)320,239
C10.16(C2.C42) = M4(2)⋊4F5φ: C2.C42/C2×C4 → C4 ⊆ Aut C10808C10.16(C2.C4^2)320,240
C10.17(C2.C42) = C22⋊F5⋊C4φ: C2.C42/C2×C4 → C4 ⊆ Aut C1080C10.17(C2.C4^2)320,255
C10.18(C2.C42) = C10.(C4⋊C8)φ: C2.C42/C2×C4 → C4 ⊆ Aut C10320C10.18(C2.C4^2)320,256
C10.19(C2.C42) = C22.F5⋊C4φ: C2.C42/C2×C4 → C4 ⊆ Aut C10160C10.19(C2.C4^2)320,257
C10.20(C2.C42) = C42⋊6Dic5φ: C2.C42/C22×C4 → C2 ⊆ Aut C1080C10.20(C2.C4^2)320,81
C10.21(C2.C42) = (C2×C20)⋊8C8φ: C2.C42/C22×C4 → C2 ⊆ Aut C10320C10.21(C2.C4^2)320,82
C10.22(C2.C42) = C24.D10φ: C2.C42/C22×C4 → C2 ⊆ Aut C1080C10.22(C2.C4^2)320,84
C10.23(C2.C42) = C24.2D10φ: C2.C42/C22×C4 → C2 ⊆ Aut C1080C10.23(C2.C4^2)320,85
C10.24(C2.C42) = C20.31C42φ: C2.C42/C22×C4 → C2 ⊆ Aut C10320C10.24(C2.C4^2)320,87
C10.25(C2.C42) = (C2×C20).Q8φ: C2.C42/C22×C4 → C2 ⊆ Aut C10160C10.25(C2.C4^2)320,88
C10.26(C2.C42) = C42⋊1Dic5φ: C2.C42/C22×C4 → C2 ⊆ Aut C10804C10.26(C2.C4^2)320,89
C10.27(C2.C42) = C20.32C42φ: C2.C42/C22×C4 → C2 ⊆ Aut C1080C10.27(C2.C4^2)320,90
C10.28(C2.C42) = C20.60(C4⋊C4)φ: C2.C42/C22×C4 → C2 ⊆ Aut C10804C10.28(C2.C4^2)320,91
C10.29(C2.C42) = (C2×C40)⋊15C4φ: C2.C42/C22×C4 → C2 ⊆ Aut C10320C10.29(C2.C4^2)320,108
C10.30(C2.C42) = C20.39C42φ: C2.C42/C22×C4 → C2 ⊆ Aut C10320C10.30(C2.C4^2)320,109
C10.31(C2.C42) = C20.40C42φ: C2.C42/C22×C4 → C2 ⊆ Aut C10160C10.31(C2.C4^2)320,110
C10.32(C2.C42) = M4(2)⋊Dic5φ: C2.C42/C22×C4 → C2 ⊆ Aut C10160C10.32(C2.C4^2)320,112
C10.33(C2.C42) = C20.33C42φ: C2.C42/C22×C4 → C2 ⊆ Aut C1080C10.33(C2.C4^2)320,113
C10.34(C2.C42) = (C2×C40)⋊C4φ: C2.C42/C22×C4 → C2 ⊆ Aut C10804C10.34(C2.C4^2)320,114
C10.35(C2.C42) = C23.9D20φ: C2.C42/C22×C4 → C2 ⊆ Aut C10804C10.35(C2.C4^2)320,115
C10.36(C2.C42) = C20.34C42φ: C2.C42/C22×C4 → C2 ⊆ Aut C10160C10.36(C2.C4^2)320,116
C10.37(C2.C42) = M4(2)⋊4Dic5φ: C2.C42/C22×C4 → C2 ⊆ Aut C10804C10.37(C2.C4^2)320,117
C10.38(C2.C42) = C20.51C42φ: C2.C42/C22×C4 → C2 ⊆ Aut C10804C10.38(C2.C4^2)320,118
C10.39(C2.C42) = C5×C22.7C42central extension (φ=1)320C10.39(C2.C4^2)320,141
C10.40(C2.C42) = C5×C4.9C42central extension (φ=1)804C10.40(C2.C4^2)320,142
C10.41(C2.C42) = C5×C4.10C42central extension (φ=1)804C10.41(C2.C4^2)320,143
C10.42(C2.C42) = C5×C42⋊6C4central extension (φ=1)80C10.42(C2.C4^2)320,144
C10.43(C2.C42) = C5×C22.4Q16central extension (φ=1)320C10.43(C2.C4^2)320,145
C10.44(C2.C42) = C5×C4.C42central extension (φ=1)160C10.44(C2.C4^2)320,146
C10.45(C2.C42) = C5×C23.9D4central extension (φ=1)80C10.45(C2.C4^2)320,147
C10.46(C2.C42) = C5×C22.C42central extension (φ=1)160C10.46(C2.C4^2)320,148
C10.47(C2.C42) = C5×M4(2)⋊4C4central extension (φ=1)804C10.47(C2.C4^2)320,149

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