Home
About
Cn
Dn
Sn
An
Degree
Linear
Irr Reps
Characters
×
⋊
.
○
≀

Extensions 1→N→G→Q→1 with N=C10 and Q=D4⋊C4

Direct product G=N×Q with N=C10 and Q=D4⋊C4
dρLabelID
C10×D4⋊C4160C10xD4:C4320,915

Semidirect products G=N:Q with N=C10 and Q=D4⋊C4
extensionφ:Q→Aut NdρLabelID
C10⋊(D4⋊C4) = C2×D20⋊C4φ: D4⋊C4/D4 → C4 ⊆ Aut C1080C10:(D4:C4)320,1104
C10⋊2(D4⋊C4) = C2×D20⋊6C4φ: D4⋊C4/C4⋊C4 → C2 ⊆ Aut C10160C10:2(D4:C4)320,592
C10⋊3(D4⋊C4) = C2×D20⋊5C4φ: D4⋊C4/C2×C8 → C2 ⊆ Aut C10160C10:3(D4:C4)320,739
C10⋊4(D4⋊C4) = C2×D4⋊Dic5φ: D4⋊C4/C2×D4 → C2 ⊆ Aut C10160C10:4(D4:C4)320,841

Non-split extensions G=N.Q with N=C10 and Q=D4⋊C4
extensionφ:Q→Aut NdρLabelID
C10.1(D4⋊C4) = D10.1D8φ: D4⋊C4/D4 → C4 ⊆ Aut C1080C10.1(D4:C4)320,206
C10.2(D4⋊C4) = D20⋊C8φ: D4⋊C4/D4 → C4 ⊆ Aut C10160C10.2(D4:C4)320,209
C10.3(D4⋊C4) = Dic5.D8φ: D4⋊C4/D4 → C4 ⊆ Aut C10320C10.3(D4:C4)320,211
C10.4(D4⋊C4) = D10.18D8φ: D4⋊C4/D4 → C4 ⊆ Aut C1080C10.4(D4:C4)320,212
C10.5(D4⋊C4) = D10.D8φ: D4⋊C4/D4 → C4 ⊆ Aut C10808-C10.5(D4:C4)320,241
C10.6(D4⋊C4) = D5.D16φ: D4⋊C4/D4 → C4 ⊆ Aut C10808+C10.6(D4:C4)320,242
C10.7(D4⋊C4) = D8.F5φ: D4⋊C4/D4 → C4 ⊆ Aut C101608-C10.7(D4:C4)320,243
C10.8(D4⋊C4) = D40.C4φ: D4⋊C4/D4 → C4 ⊆ Aut C10808+C10.8(D4:C4)320,244
C10.9(D4⋊C4) = D40⋊1C4φ: D4⋊C4/D4 → C4 ⊆ Aut C10808+C10.9(D4:C4)320,245
C10.10(D4⋊C4) = D5.Q32φ: D4⋊C4/D4 → C4 ⊆ Aut C10808-C10.10(D4:C4)320,246
C10.11(D4⋊C4) = Q16.F5φ: D4⋊C4/D4 → C4 ⊆ Aut C101608+C10.11(D4:C4)320,247
C10.12(D4⋊C4) = Dic20.C4φ: D4⋊C4/D4 → C4 ⊆ Aut C101608-C10.12(D4:C4)320,248
C10.13(D4⋊C4) = D10.SD16φ: D4⋊C4/D4 → C4 ⊆ Aut C1080C10.13(D4:C4)320,258
C10.14(D4⋊C4) = Dic5.23D8φ: D4⋊C4/D4 → C4 ⊆ Aut C10160C10.14(D4:C4)320,262
C10.15(D4⋊C4) = Dic5.SD16φ: D4⋊C4/D4 → C4 ⊆ Aut C10160C10.15(D4:C4)320,263
C10.16(D4⋊C4) = (C2×D20)⋊C4φ: D4⋊C4/C4⋊C4 → C2 ⊆ Aut C1080C10.16(D4:C4)320,9
C10.17(D4⋊C4) = C20.47D8φ: D4⋊C4/C4⋊C4 → C2 ⊆ Aut C10320C10.17(D4:C4)320,40
C10.18(D4⋊C4) = D20⋊4C8φ: D4⋊C4/C4⋊C4 → C2 ⊆ Aut C10160C10.18(D4:C4)320,41
C10.19(D4⋊C4) = D40⋊14C4φ: D4⋊C4/C4⋊C4 → C2 ⊆ Aut C10804C10.19(D4:C4)320,46
C10.20(D4⋊C4) = C40.5D4φ: D4⋊C4/C4⋊C4 → C2 ⊆ Aut C10160C10.20(D4:C4)320,49
C10.21(D4⋊C4) = C10.Q32φ: D4⋊C4/C4⋊C4 → C2 ⊆ Aut C10320C10.21(D4:C4)320,50
C10.22(D4⋊C4) = D40.6C4φ: D4⋊C4/C4⋊C4 → C2 ⊆ Aut C10804+C10.22(D4:C4)320,53
C10.23(D4⋊C4) = C40.8D4φ: D4⋊C4/C4⋊C4 → C2 ⊆ Aut C101604-C10.23(D4:C4)320,54
C10.24(D4⋊C4) = D40.5C4φ: D4⋊C4/C4⋊C4 → C2 ⊆ Aut C101604C10.24(D4:C4)320,55
C10.25(D4⋊C4) = D20⋊3C8φ: D4⋊C4/C2×C8 → C2 ⊆ Aut C10160C10.25(D4:C4)320,17
C10.26(D4⋊C4) = C22.2D40φ: D4⋊C4/C2×C8 → C2 ⊆ Aut C1080C10.26(D4:C4)320,28
C10.27(D4⋊C4) = C4.D40φ: D4⋊C4/C2×C8 → C2 ⊆ Aut C10160C10.27(D4:C4)320,43
C10.28(D4⋊C4) = C20.2D8φ: D4⋊C4/C2×C8 → C2 ⊆ Aut C10320C10.28(D4:C4)320,44
C10.29(D4⋊C4) = C40.78D4φ: D4⋊C4/C2×C8 → C2 ⊆ Aut C10320C10.29(D4:C4)320,61
C10.30(D4⋊C4) = D40⋊7C4φ: D4⋊C4/C2×C8 → C2 ⊆ Aut C10160C10.30(D4:C4)320,67
C10.31(D4⋊C4) = D40.3C4φ: D4⋊C4/C2×C8 → C2 ⊆ Aut C101602C10.31(D4:C4)320,68
C10.32(D4⋊C4) = D40.4C4φ: D4⋊C4/C2×C8 → C2 ⊆ Aut C10804+C10.32(D4:C4)320,74
C10.33(D4⋊C4) = C20.4D8φ: D4⋊C4/C2×C8 → C2 ⊆ Aut C101604-C10.33(D4:C4)320,75
C10.34(D4⋊C4) = D40⋊8C4φ: D4⋊C4/C2×C8 → C2 ⊆ Aut C10804C10.34(D4:C4)320,76
C10.35(D4⋊C4) = C20.39C42φ: D4⋊C4/C2×C8 → C2 ⊆ Aut C10320C10.35(D4:C4)320,109
C10.36(D4⋊C4) = C20.31C42φ: D4⋊C4/C2×D4 → C2 ⊆ Aut C10320C10.36(D4:C4)320,87
C10.37(D4⋊C4) = C20.57D8φ: D4⋊C4/C2×D4 → C2 ⊆ Aut C10160C10.37(D4:C4)320,92
C10.38(D4⋊C4) = C4⋊C4⋊Dic5φ: D4⋊C4/C2×D4 → C2 ⊆ Aut C1080C10.38(D4:C4)320,95
C10.39(D4⋊C4) = C20.9D8φ: D4⋊C4/C2×D4 → C2 ⊆ Aut C10160C10.39(D4:C4)320,102
C10.40(D4⋊C4) = C20.10D8φ: D4⋊C4/C2×D4 → C2 ⊆ Aut C10320C10.40(D4:C4)320,105
C10.41(D4⋊C4) = C10.D16φ: D4⋊C4/C2×D4 → C2 ⊆ Aut C10160C10.41(D4:C4)320,120
C10.42(D4⋊C4) = D8.Dic5φ: D4⋊C4/C2×D4 → C2 ⊆ Aut C10804C10.42(D4:C4)320,121
C10.43(D4⋊C4) = C40.15D4φ: D4⋊C4/C2×D4 → C2 ⊆ Aut C10320C10.43(D4:C4)320,122
C10.44(D4⋊C4) = Q16.Dic5φ: D4⋊C4/C2×D4 → C2 ⊆ Aut C101604C10.44(D4:C4)320,123
C10.45(D4⋊C4) = D8⋊2Dic5φ: D4⋊C4/C2×D4 → C2 ⊆ Aut C10804C10.45(D4:C4)320,124
C10.46(D4⋊C4) = C20.58D8φ: D4⋊C4/C2×D4 → C2 ⊆ Aut C101604C10.46(D4:C4)320,125
C10.47(D4⋊C4) = C5×D4⋊C8central extension (φ=1)160C10.47(D4:C4)320,130
C10.48(D4⋊C4) = C5×C22.SD16central extension (φ=1)80C10.48(D4:C4)320,132
C10.49(D4⋊C4) = C5×C4.D8central extension (φ=1)160C10.49(D4:C4)320,136
C10.50(D4⋊C4) = C5×C4.10D8central extension (φ=1)320C10.50(D4:C4)320,137
C10.51(D4⋊C4) = C5×C22.4Q16central extension (φ=1)320C10.51(D4:C4)320,145
C10.52(D4⋊C4) = C5×C2.D16central extension (φ=1)160C10.52(D4:C4)320,162
C10.53(D4⋊C4) = C5×C2.Q32central extension (φ=1)320C10.53(D4:C4)320,163
C10.54(D4⋊C4) = C5×D8.C4central extension (φ=1)1602C10.54(D4:C4)320,164
C10.55(D4⋊C4) = C5×D8⋊2C4central extension (φ=1)804C10.55(D4:C4)320,165
C10.56(D4⋊C4) = C5×M5(2)⋊C2central extension (φ=1)804C10.56(D4:C4)320,166
C10.57(D4⋊C4) = C5×C8.17D4central extension (φ=1)1604C10.57(D4:C4)320,167

׿
×
⋊
ℤ
𝔽
○
≀
ℚ
◁