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

Extensions 1→N→G→Q→1 with N=C20 and Q=C4⋊C4

Direct product G=N×Q with N=C20 and Q=C4⋊C4
dρLabelID
C4⋊C4×C20320C4:C4xC20320,879

Semidirect products G=N:Q with N=C20 and Q=C4⋊C4
extensionφ:Q→Aut NdρLabelID
C20⋊(C4⋊C4) = C20⋊(C4⋊C4)φ: C4⋊C4/C2 → C2×C4 ⊆ Aut C2080C20:(C4:C4)320,1050
C20⋊2(C4⋊C4) = C42⋊8F5φ: C4⋊C4/C4 → C4 ⊆ Aut C2080C20:2(C4:C4)320,1026
C20⋊3(C4⋊C4) = C4×C4⋊F5φ: C4⋊C4/C4 → C4 ⊆ Aut C2080C20:3(C4:C4)320,1025
C20⋊4(C4⋊C4) = C20⋊4(C4⋊C4)φ: C4⋊C4/C22 → C22 ⊆ Aut C20320C20:4(C4:C4)320,600
C20⋊5(C4⋊C4) = C20⋊5(C4⋊C4)φ: C4⋊C4/C22 → C22 ⊆ Aut C20320C20:5(C4:C4)320,603
C20⋊6(C4⋊C4) = C20⋊6(C4⋊C4)φ: C4⋊C4/C22 → C22 ⊆ Aut C20320C20:6(C4:C4)320,612
C20⋊7(C4⋊C4) = C20⋊7(C4⋊C4)φ: C4⋊C4/C2×C4 → C2 ⊆ Aut C20320C20:7(C4:C4)320,555
C20⋊8(C4⋊C4) = C42⋊8Dic5φ: C4⋊C4/C2×C4 → C2 ⊆ Aut C20320C20:8(C4:C4)320,562
C20⋊9(C4⋊C4) = C4×C10.D4φ: C4⋊C4/C2×C4 → C2 ⊆ Aut C20320C20:9(C4:C4)320,558
C20⋊10(C4⋊C4) = C4×C4⋊Dic5φ: C4⋊C4/C2×C4 → C2 ⊆ Aut C20320C20:10(C4:C4)320,561
C20⋊11(C4⋊C4) = C5×C42⋊9C4φ: C4⋊C4/C2×C4 → C2 ⊆ Aut C20320C20:11(C4:C4)320,885
C20⋊12(C4⋊C4) = C5×C23.65C23φ: C4⋊C4/C2×C4 → C2 ⊆ Aut C20320C20:12(C4:C4)320,890

Non-split extensions G=N.Q with N=C20 and Q=C4⋊C4
extensionφ:Q→Aut NdρLabelID
C20.1(C4⋊C4) = D10.18D8φ: C4⋊C4/C2 → C2×C4 ⊆ Aut C2080C20.1(C4:C4)320,212
C20.2(C4⋊C4) = C20.C42φ: C4⋊C4/C2 → C2×C4 ⊆ Aut C2080C20.2(C4:C4)320,213
C20.3(C4⋊C4) = M4(2)⋊F5φ: C4⋊C4/C2 → C2×C4 ⊆ Aut C20408C20.3(C4:C4)320,237
C20.4(C4⋊C4) = M4(2)⋊4F5φ: C4⋊C4/C2 → C2×C4 ⊆ Aut C20808C20.4(C4:C4)320,240
C20.5(C4⋊C4) = C4⋊C4.9F5φ: C4⋊C4/C2 → C2×C4 ⊆ Aut C20160C20.5(C4:C4)320,1046
C20.6(C4⋊C4) = M4(2)⋊1F5φ: C4⋊C4/C2 → C2×C4 ⊆ Aut C20408C20.6(C4:C4)320,1065
C20.7(C4⋊C4) = M4(2).1F5φ: C4⋊C4/C2 → C2×C4 ⊆ Aut C20808C20.7(C4:C4)320,1067
C20.8(C4⋊C4) = C80⋊4C4φ: C4⋊C4/C4 → C4 ⊆ Aut C20804C20.8(C4:C4)320,185
C20.9(C4⋊C4) = C80⋊5C4φ: C4⋊C4/C4 → C4 ⊆ Aut C20804C20.9(C4:C4)320,186
C20.10(C4⋊C4) = C80⋊2C4φ: C4⋊C4/C4 → C4 ⊆ Aut C20804C20.10(C4:C4)320,187
C20.11(C4⋊C4) = C80⋊3C4φ: C4⋊C4/C4 → C4 ⊆ Aut C20804C20.11(C4:C4)320,188
C20.12(C4⋊C4) = C16.F5φ: C4⋊C4/C4 → C4 ⊆ Aut C201604C20.12(C4:C4)320,189
C20.13(C4⋊C4) = C80.2C4φ: C4⋊C4/C4 → C4 ⊆ Aut C201604C20.13(C4:C4)320,190
C20.14(C4⋊C4) = C42⋊3F5φ: C4⋊C4/C4 → C4 ⊆ Aut C20804C20.14(C4:C4)320,201
C20.15(C4⋊C4) = (C2×C8)⋊F5φ: C4⋊C4/C4 → C4 ⊆ Aut C20804C20.15(C4:C4)320,232
C20.16(C4⋊C4) = C20⋊3M4(2)φ: C4⋊C4/C4 → C4 ⊆ Aut C20160C20.16(C4:C4)320,1019
C20.17(C4⋊C4) = C42.14F5φ: C4⋊C4/C4 → C4 ⊆ Aut C20160C20.17(C4:C4)320,1020
C20.18(C4⋊C4) = C42⋊9F5φ: C4⋊C4/C4 → C4 ⊆ Aut C2080C20.18(C4:C4)320,1027
C20.19(C4⋊C4) = C2×C40⋊C4φ: C4⋊C4/C4 → C4 ⊆ Aut C2080C20.19(C4:C4)320,1057
C20.20(C4⋊C4) = C2×D5.D8φ: C4⋊C4/C4 → C4 ⊆ Aut C2080C20.20(C4:C4)320,1058
C20.21(C4⋊C4) = C2×C40.C4φ: C4⋊C4/C4 → C4 ⊆ Aut C20160C20.21(C4:C4)320,1060
C20.22(C4⋊C4) = C2×D10.Q8φ: C4⋊C4/C4 → C4 ⊆ Aut C20160C20.22(C4:C4)320,1061
C20.23(C4⋊C4) = C20⋊C16φ: C4⋊C4/C4 → C4 ⊆ Aut C20320C20.23(C4:C4)320,196
C20.24(C4⋊C4) = C42.9F5φ: C4⋊C4/C4 → C4 ⊆ Aut C20804C20.24(C4:C4)320,199
C20.25(C4⋊C4) = C42⋊6F5φ: C4⋊C4/C4 → C4 ⊆ Aut C20404C20.25(C4:C4)320,200
C20.26(C4⋊C4) = C10.M5(2)φ: C4⋊C4/C4 → C4 ⊆ Aut C20320C20.26(C4:C4)320,226
C20.27(C4⋊C4) = C40.1C8φ: C4⋊C4/C4 → C4 ⊆ Aut C20804C20.27(C4:C4)320,227
C20.28(C4⋊C4) = D10.3M4(2)φ: C4⋊C4/C4 → C4 ⊆ Aut C2080C20.28(C4:C4)320,230
C20.29(C4⋊C4) = C42.11F5φ: C4⋊C4/C4 → C4 ⊆ Aut C20160C20.29(C4:C4)320,1017
C20.30(C4⋊C4) = (C2×C8)⋊6F5φ: C4⋊C4/C4 → C4 ⊆ Aut C20804C20.30(C4:C4)320,1059
C20.31(C4⋊C4) = (C8×D5).C4φ: C4⋊C4/C4 → C4 ⊆ Aut C20804C20.31(C4:C4)320,1062
C20.32(C4⋊C4) = C8.Dic10φ: C4⋊C4/C22 → C22 ⊆ Aut C20804C20.32(C4:C4)320,45
C20.33(C4⋊C4) = C40.2Q8φ: C4⋊C4/C22 → C22 ⊆ Aut C20320C20.33(C4:C4)320,47
C20.34(C4⋊C4) = C10.SD32φ: C4⋊C4/C22 → C22 ⊆ Aut C20320C20.34(C4:C4)320,48
C20.35(C4⋊C4) = C40.7Q8φ: C4⋊C4/C22 → C22 ⊆ Aut C201604C20.35(C4:C4)320,51
C20.36(C4⋊C4) = C40.6Q8φ: C4⋊C4/C22 → C22 ⊆ Aut C20804C20.36(C4:C4)320,52
C20.37(C4⋊C4) = C20.31C42φ: C4⋊C4/C22 → C22 ⊆ Aut C20320C20.37(C4:C4)320,87
C20.38(C4⋊C4) = (C2×C20).Q8φ: C4⋊C4/C22 → C22 ⊆ Aut C20160C20.38(C4:C4)320,88
C20.39(C4⋊C4) = C20.32C42φ: C4⋊C4/C22 → C22 ⊆ Aut C2080C20.39(C4:C4)320,90
C20.40(C4⋊C4) = M4(2)⋊Dic5φ: C4⋊C4/C22 → C22 ⊆ Aut C20160C20.40(C4:C4)320,112
C20.41(C4⋊C4) = C20.33C42φ: C4⋊C4/C22 → C22 ⊆ Aut C2080C20.41(C4:C4)320,113
C20.42(C4⋊C4) = (C2×C40)⋊C4φ: C4⋊C4/C22 → C22 ⊆ Aut C20804C20.42(C4:C4)320,114
C20.43(C4⋊C4) = C23.9D20φ: C4⋊C4/C22 → C22 ⊆ Aut C20804C20.43(C4:C4)320,115
C20.44(C4⋊C4) = M4(2)⋊4Dic5φ: C4⋊C4/C22 → C22 ⊆ Aut C20804C20.44(C4:C4)320,117
C20.45(C4⋊C4) = C2×C10.D8φ: C4⋊C4/C22 → C22 ⊆ Aut C20320C20.45(C4:C4)320,589
C20.46(C4⋊C4) = C2×C20.Q8φ: C4⋊C4/C22 → C22 ⊆ Aut C20320C20.46(C4:C4)320,590
C20.47(C4⋊C4) = C20.47(C4⋊C4)φ: C4⋊C4/C22 → C22 ⊆ Aut C20160C20.47(C4:C4)320,591
C20.48(C4⋊C4) = C20.48(C4⋊C4)φ: C4⋊C4/C22 → C22 ⊆ Aut C20320C20.48(C4:C4)320,604
C20.49(C4⋊C4) = C42.43D10φ: C4⋊C4/C22 → C22 ⊆ Aut C20160C20.49(C4:C4)320,626
C20.50(C4⋊C4) = Dic5⋊5M4(2)φ: C4⋊C4/C22 → C22 ⊆ Aut C20160C20.50(C4:C4)320,745
C20.51(C4⋊C4) = C20.51(C4⋊C4)φ: C4⋊C4/C22 → C22 ⊆ Aut C20160C20.51(C4:C4)320,746
C20.52(C4⋊C4) = C23.47D20φ: C4⋊C4/C22 → C22 ⊆ Aut C20160C20.52(C4:C4)320,748
C20.53(C4⋊C4) = M4(2).Dic5φ: C4⋊C4/C22 → C22 ⊆ Aut C20804C20.53(C4:C4)320,752
C20.54(C4⋊C4) = C80⋊13C4φ: C4⋊C4/C2×C4 → C2 ⊆ Aut C20320C20.54(C4:C4)320,62
C20.55(C4⋊C4) = C80⋊14C4φ: C4⋊C4/C2×C4 → C2 ⊆ Aut C20320C20.55(C4:C4)320,63
C20.56(C4⋊C4) = C80.6C4φ: C4⋊C4/C2×C4 → C2 ⊆ Aut C201602C20.56(C4:C4)320,64
C20.57(C4⋊C4) = C40.Q8φ: C4⋊C4/C2×C4 → C2 ⊆ Aut C20804C20.57(C4:C4)320,71
C20.58(C4⋊C4) = C42⋊6Dic5φ: C4⋊C4/C2×C4 → C2 ⊆ Aut C2080C20.58(C4:C4)320,81
C20.59(C4⋊C4) = C42⋊1Dic5φ: C4⋊C4/C2×C4 → C2 ⊆ Aut C20804C20.59(C4:C4)320,89
C20.60(C4⋊C4) = C20.60(C4⋊C4)φ: C4⋊C4/C2×C4 → C2 ⊆ Aut C20804C20.60(C4:C4)320,91
C20.61(C4⋊C4) = C20.39C42φ: C4⋊C4/C2×C4 → C2 ⊆ Aut C20320C20.61(C4:C4)320,109
C20.62(C4⋊C4) = C20⋊13M4(2)φ: C4⋊C4/C2×C4 → C2 ⊆ Aut C20160C20.62(C4:C4)320,551
C20.63(C4⋊C4) = C42⋊9Dic5φ: C4⋊C4/C2×C4 → C2 ⊆ Aut C20320C20.63(C4:C4)320,563
C20.64(C4⋊C4) = C20.64(C4⋊C4)φ: C4⋊C4/C2×C4 → C2 ⊆ Aut C20160C20.64(C4:C4)320,622
C20.65(C4⋊C4) = C20.65(C4⋊C4)φ: C4⋊C4/C2×C4 → C2 ⊆ Aut C20160C20.65(C4:C4)320,729
C20.66(C4⋊C4) = C2×C40⋊6C4φ: C4⋊C4/C2×C4 → C2 ⊆ Aut C20320C20.66(C4:C4)320,731
C20.67(C4⋊C4) = C2×C40⋊5C4φ: C4⋊C4/C2×C4 → C2 ⊆ Aut C20320C20.67(C4:C4)320,732
C20.68(C4⋊C4) = C23.Dic10φ: C4⋊C4/C2×C4 → C2 ⊆ Aut C20804C20.68(C4:C4)320,751
C20.69(C4⋊C4) = C20⋊3C16φ: C4⋊C4/C2×C4 → C2 ⊆ Aut C20320C20.69(C4:C4)320,20
C20.70(C4⋊C4) = C40.7C8φ: C4⋊C4/C2×C4 → C2 ⊆ Aut C20802C20.70(C4:C4)320,21
C20.71(C4⋊C4) = C40.88D4φ: C4⋊C4/C2×C4 → C2 ⊆ Aut C20320C20.71(C4:C4)320,59
C20.72(C4⋊C4) = C40.9Q8φ: C4⋊C4/C2×C4 → C2 ⊆ Aut C20804C20.72(C4:C4)320,69
C20.73(C4⋊C4) = (C2×C20)⋊8C8φ: C4⋊C4/C2×C4 → C2 ⊆ Aut C20320C20.73(C4:C4)320,82
C20.74(C4⋊C4) = (C2×C40)⋊15C4φ: C4⋊C4/C2×C4 → C2 ⊆ Aut C20320C20.74(C4:C4)320,108
C20.75(C4⋊C4) = C2×C20⋊3C8φ: C4⋊C4/C2×C4 → C2 ⊆ Aut C20320C20.75(C4:C4)320,550
C20.76(C4⋊C4) = C20.76(C4⋊C4)φ: C4⋊C4/C2×C4 → C2 ⊆ Aut C20160C20.76(C4:C4)320,625
C20.77(C4⋊C4) = C2×C20.8Q8φ: C4⋊C4/C2×C4 → C2 ⊆ Aut C20320C20.77(C4:C4)320,726
C20.78(C4⋊C4) = C23.22D20φ: C4⋊C4/C2×C4 → C2 ⊆ Aut C20160C20.78(C4:C4)320,733
C20.79(C4⋊C4) = C2×C40.6C4φ: C4⋊C4/C2×C4 → C2 ⊆ Aut C20160C20.79(C4:C4)320,734
C20.80(C4⋊C4) = C2×C20.53D4φ: C4⋊C4/C2×C4 → C2 ⊆ Aut C20160C20.80(C4:C4)320,750
C20.81(C4⋊C4) = C5×C4.9C42φ: C4⋊C4/C2×C4 → C2 ⊆ Aut C20804C20.81(C4:C4)320,142
C20.82(C4⋊C4) = C5×C42⋊6C4φ: C4⋊C4/C2×C4 → C2 ⊆ Aut C2080C20.82(C4:C4)320,144
C20.83(C4⋊C4) = C5×C22.4Q16φ: C4⋊C4/C2×C4 → C2 ⊆ Aut C20320C20.83(C4:C4)320,145
C20.84(C4⋊C4) = C5×C22.C42φ: C4⋊C4/C2×C4 → C2 ⊆ Aut C20160C20.84(C4:C4)320,148
C20.85(C4⋊C4) = C5×M4(2)⋊4C4φ: C4⋊C4/C2×C4 → C2 ⊆ Aut C20804C20.85(C4:C4)320,149
C20.86(C4⋊C4) = C5×C8.Q8φ: C4⋊C4/C2×C4 → C2 ⊆ Aut C20804C20.86(C4:C4)320,170
C20.87(C4⋊C4) = C5×C16⋊3C4φ: C4⋊C4/C2×C4 → C2 ⊆ Aut C20320C20.87(C4:C4)320,171
C20.88(C4⋊C4) = C5×C16⋊4C4φ: C4⋊C4/C2×C4 → C2 ⊆ Aut C20320C20.88(C4:C4)320,172
C20.89(C4⋊C4) = C5×C8.4Q8φ: C4⋊C4/C2×C4 → C2 ⊆ Aut C201602C20.89(C4:C4)320,173
C20.90(C4⋊C4) = C5×C42⋊8C4φ: C4⋊C4/C2×C4 → C2 ⊆ Aut C20320C20.90(C4:C4)320,883
C20.91(C4⋊C4) = C5×C4⋊M4(2)φ: C4⋊C4/C2×C4 → C2 ⊆ Aut C20160C20.91(C4:C4)320,924
C20.92(C4⋊C4) = C5×C42.6C22φ: C4⋊C4/C2×C4 → C2 ⊆ Aut C20160C20.92(C4:C4)320,925
C20.93(C4⋊C4) = C10×C4.Q8φ: C4⋊C4/C2×C4 → C2 ⊆ Aut C20320C20.93(C4:C4)320,926
C20.94(C4⋊C4) = C10×C2.D8φ: C4⋊C4/C2×C4 → C2 ⊆ Aut C20320C20.94(C4:C4)320,927
C20.95(C4⋊C4) = C5×M4(2)⋊C4φ: C4⋊C4/C2×C4 → C2 ⊆ Aut C20160C20.95(C4:C4)320,929
C20.96(C4⋊C4) = C5×M4(2).C4φ: C4⋊C4/C2×C4 → C2 ⊆ Aut C20804C20.96(C4:C4)320,931
C20.97(C4⋊C4) = C5×C22.7C42central extension (φ=1)320C20.97(C4:C4)320,141
C20.98(C4⋊C4) = C5×C4⋊C16central extension (φ=1)320C20.98(C4:C4)320,168
C20.99(C4⋊C4) = C5×C8.C8central extension (φ=1)802C20.99(C4:C4)320,169
C20.100(C4⋊C4) = C10×C4⋊C8central extension (φ=1)320C20.100(C4:C4)320,923
C20.101(C4⋊C4) = C5×C23.25D4central extension (φ=1)160C20.101(C4:C4)320,928
C20.102(C4⋊C4) = C10×C8.C4central extension (φ=1)160C20.102(C4:C4)320,930

׿
×
⋊
ℤ
𝔽
○
≀
ℚ
◁