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

Extensions 1→N→G→Q→1 with N=C2×C10 and Q=C4⋊C4

Direct product G=N×Q with N=C2×C10 and Q=C4⋊C4
dρLabelID
C4⋊C4×C2×C10320C4:C4xC2xC10320,1515

Semidirect products G=N:Q with N=C2×C10 and Q=C4⋊C4
extensionφ:Q→Aut NdρLabelID
(C2×C10)⋊(C4⋊C4) = D10⋊(C4⋊C4)φ: C4⋊C4/C2 → C2×C4 ⊆ Aut C2×C1040(C2xC10):(C4:C4)320,1037
(C2×C10)⋊2(C4⋊C4) = D10⋊6(C4⋊C4)φ: C4⋊C4/C4 → C4 ⊆ Aut C2×C1080(C2xC10):2(C4:C4)320,1103
(C2×C10)⋊3(C4⋊C4) = C22×C4⋊F5φ: C4⋊C4/C4 → C4 ⊆ Aut C2×C1080(C2xC10):3(C4:C4)320,1591
(C2×C10)⋊4(C4⋊C4) = C24.44D10φ: C4⋊C4/C22 → C22 ⊆ Aut C2×C10160(C2xC10):4(C4:C4)320,569
(C2×C10)⋊5(C4⋊C4) = C24.46D10φ: C4⋊C4/C22 → C22 ⊆ Aut C2×C10160(C2xC10):5(C4:C4)320,573
(C2×C10)⋊6(C4⋊C4) = C24.47D10φ: C4⋊C4/C22 → C22 ⊆ Aut C2×C10160(C2xC10):6(C4:C4)320,577
(C2×C10)⋊7(C4⋊C4) = C5×C23.7Q8φ: C4⋊C4/C2×C4 → C2 ⊆ Aut C2×C10160(C2xC10):7(C4:C4)320,881
(C2×C10)⋊8(C4⋊C4) = C5×C23.8Q8φ: C4⋊C4/C2×C4 → C2 ⊆ Aut C2×C10160(C2xC10):8(C4:C4)320,886
(C2×C10)⋊9(C4⋊C4) = C24.62D10φ: C4⋊C4/C2×C4 → C2 ⊆ Aut C2×C10160(C2xC10):9(C4:C4)320,837
(C2×C10)⋊10(C4⋊C4) = C24.64D10φ: C4⋊C4/C2×C4 → C2 ⊆ Aut C2×C10160(C2xC10):10(C4:C4)320,839
(C2×C10)⋊11(C4⋊C4) = C22×C10.D4φ: C4⋊C4/C2×C4 → C2 ⊆ Aut C2×C10320(C2xC10):11(C4:C4)320,1455
(C2×C10)⋊12(C4⋊C4) = C22×C4⋊Dic5φ: C4⋊C4/C2×C4 → C2 ⊆ Aut C2×C10320(C2xC10):12(C4:C4)320,1457

Non-split extensions G=N.Q with N=C2×C10 and Q=C4⋊C4
extensionφ:Q→Aut NdρLabelID
(C2×C10).1(C4⋊C4) = (C22×F5)⋊C4φ: C4⋊C4/C2 → C2×C4 ⊆ Aut C2×C10408+(C2xC10).1(C4:C4)320,204
(C2×C10).2(C4⋊C4) = C22⋊C4.F5φ: C4⋊C4/C2 → C2×C4 ⊆ Aut C2×C10808-(C2xC10).2(C4:C4)320,205
(C2×C10).3(C4⋊C4) = M4(2)⋊3F5φ: C4⋊C4/C2 → C2×C4 ⊆ Aut C2×C10408(C2xC10).3(C4:C4)320,238
(C2×C10).4(C4⋊C4) = M4(2).F5φ: C4⋊C4/C2 → C2×C4 ⊆ Aut C2×C10808(C2xC10).4(C4:C4)320,239
(C2×C10).5(C4⋊C4) = C20⋊C8⋊C2φ: C4⋊C4/C2 → C2×C4 ⊆ Aut C2×C10160(C2xC10).5(C4:C4)320,1034
(C2×C10).6(C4⋊C4) = M4(2)⋊1F5φ: C4⋊C4/C2 → C2×C4 ⊆ Aut C2×C10408(C2xC10).6(C4:C4)320,1065
(C2×C10).7(C4⋊C4) = M4(2).1F5φ: C4⋊C4/C2 → C2×C4 ⊆ Aut C2×C10808(C2xC10).7(C4:C4)320,1067
(C2×C10).8(C4⋊C4) = C40⋊2C8φ: C4⋊C4/C4 → C4 ⊆ Aut C2×C10320(C2xC10).8(C4:C4)320,219
(C2×C10).9(C4⋊C4) = C40⋊1C8φ: C4⋊C4/C4 → C4 ⊆ Aut C2×C10320(C2xC10).9(C4:C4)320,220
(C2×C10).10(C4⋊C4) = C20.26M4(2)φ: C4⋊C4/C4 → C4 ⊆ Aut C2×C10320(C2xC10).10(C4:C4)320,221
(C2×C10).11(C4⋊C4) = Dic5.13D8φ: C4⋊C4/C4 → C4 ⊆ Aut C2×C10320(C2xC10).11(C4:C4)320,222
(C2×C10).12(C4⋊C4) = D10.10D8φ: C4⋊C4/C4 → C4 ⊆ Aut C2×C1080(C2xC10).12(C4:C4)320,231
(C2×C10).13(C4⋊C4) = C20.24C42φ: C4⋊C4/C4 → C4 ⊆ Aut C2×C10804(C2xC10).13(C4:C4)320,233
(C2×C10).14(C4⋊C4) = C20.10C42φ: C4⋊C4/C4 → C4 ⊆ Aut C2×C10160(C2xC10).14(C4:C4)320,234
(C2×C10).15(C4⋊C4) = C20.25C42φ: C4⋊C4/C4 → C4 ⊆ Aut C2×C10804(C2xC10).15(C4:C4)320,235
(C2×C10).16(C4⋊C4) = C22⋊F5⋊C4φ: C4⋊C4/C4 → C4 ⊆ Aut C2×C1080(C2xC10).16(C4:C4)320,255
(C2×C10).17(C4⋊C4) = C10.(C4⋊C8)φ: C4⋊C4/C4 → C4 ⊆ Aut C2×C10320(C2xC10).17(C4:C4)320,256
(C2×C10).18(C4⋊C4) = C22.F5⋊C4φ: C4⋊C4/C4 → C4 ⊆ Aut C2×C10160(C2xC10).18(C4:C4)320,257
(C2×C10).19(C4⋊C4) = C2×C40⋊C4φ: C4⋊C4/C4 → C4 ⊆ Aut C2×C1080(C2xC10).19(C4:C4)320,1057
(C2×C10).20(C4⋊C4) = C2×D5.D8φ: C4⋊C4/C4 → C4 ⊆ Aut C2×C1080(C2xC10).20(C4:C4)320,1058
(C2×C10).21(C4⋊C4) = (C2×C8)⋊6F5φ: C4⋊C4/C4 → C4 ⊆ Aut C2×C10804(C2xC10).21(C4:C4)320,1059
(C2×C10).22(C4⋊C4) = C2×C40.C4φ: C4⋊C4/C4 → C4 ⊆ Aut C2×C10160(C2xC10).22(C4:C4)320,1060
(C2×C10).23(C4⋊C4) = C2×D10.Q8φ: C4⋊C4/C4 → C4 ⊆ Aut C2×C10160(C2xC10).23(C4:C4)320,1061
(C2×C10).24(C4⋊C4) = (C8×D5).C4φ: C4⋊C4/C4 → C4 ⊆ Aut C2×C10804(C2xC10).24(C4:C4)320,1062
(C2×C10).25(C4⋊C4) = C2×C20⋊C8φ: C4⋊C4/C4 → C4 ⊆ Aut C2×C10320(C2xC10).25(C4:C4)320,1085
(C2×C10).26(C4⋊C4) = C2×Dic5⋊C8φ: C4⋊C4/C4 → C4 ⊆ Aut C2×C10320(C2xC10).26(C4:C4)320,1090
(C2×C10).27(C4⋊C4) = C20⋊8M4(2)φ: C4⋊C4/C4 → C4 ⊆ Aut C2×C10160(C2xC10).27(C4:C4)320,1096
(C2×C10).28(C4⋊C4) = C2×D10.3Q8φ: C4⋊C4/C4 → C4 ⊆ Aut C2×C1080(C2xC10).28(C4:C4)320,1100
(C2×C10).29(C4⋊C4) = C24.D10φ: C4⋊C4/C22 → C22 ⊆ Aut C2×C1080(C2xC10).29(C4:C4)320,84
(C2×C10).30(C4⋊C4) = C24.2D10φ: C4⋊C4/C22 → C22 ⊆ Aut C2×C1080(C2xC10).30(C4:C4)320,85
(C2×C10).31(C4⋊C4) = C42⋊1Dic5φ: C4⋊C4/C22 → C22 ⊆ Aut C2×C10804(C2xC10).31(C4:C4)320,89
(C2×C10).32(C4⋊C4) = C20.32C42φ: C4⋊C4/C22 → C22 ⊆ Aut C2×C1080(C2xC10).32(C4:C4)320,90
(C2×C10).33(C4⋊C4) = C20.60(C4⋊C4)φ: C4⋊C4/C22 → C22 ⊆ Aut C2×C10804(C2xC10).33(C4:C4)320,91
(C2×C10).34(C4⋊C4) = M4(2)⋊Dic5φ: C4⋊C4/C22 → C22 ⊆ Aut C2×C10160(C2xC10).34(C4:C4)320,112
(C2×C10).35(C4⋊C4) = C20.33C42φ: C4⋊C4/C22 → C22 ⊆ Aut C2×C1080(C2xC10).35(C4:C4)320,113
(C2×C10).36(C4⋊C4) = (C2×C40)⋊C4φ: C4⋊C4/C22 → C22 ⊆ Aut C2×C10804(C2xC10).36(C4:C4)320,114
(C2×C10).37(C4⋊C4) = C20.34C42φ: C4⋊C4/C22 → C22 ⊆ Aut C2×C10160(C2xC10).37(C4:C4)320,116
(C2×C10).38(C4⋊C4) = C20.51C42φ: C4⋊C4/C22 → C22 ⊆ Aut C2×C10804(C2xC10).38(C4:C4)320,118
(C2×C10).39(C4⋊C4) = C20.64(C4⋊C4)φ: C4⋊C4/C22 → C22 ⊆ Aut C2×C10160(C2xC10).39(C4:C4)320,622
(C2×C10).40(C4⋊C4) = C20.76(C4⋊C4)φ: C4⋊C4/C22 → C22 ⊆ Aut C2×C10160(C2xC10).40(C4:C4)320,625
(C2×C10).41(C4⋊C4) = C42.43D10φ: C4⋊C4/C22 → C22 ⊆ Aut C2×C10160(C2xC10).41(C4:C4)320,626
(C2×C10).42(C4⋊C4) = Dic5⋊5M4(2)φ: C4⋊C4/C22 → C22 ⊆ Aut C2×C10160(C2xC10).42(C4:C4)320,745
(C2×C10).43(C4⋊C4) = C20.51(C4⋊C4)φ: C4⋊C4/C22 → C22 ⊆ Aut C2×C10160(C2xC10).43(C4:C4)320,746
(C2×C10).44(C4⋊C4) = C23.47D20φ: C4⋊C4/C22 → C22 ⊆ Aut C2×C10160(C2xC10).44(C4:C4)320,748
(C2×C10).45(C4⋊C4) = M4(2).Dic5φ: C4⋊C4/C22 → C22 ⊆ Aut C2×C10804(C2xC10).45(C4:C4)320,752
(C2×C10).46(C4⋊C4) = C5×C4.9C42φ: C4⋊C4/C2×C4 → C2 ⊆ Aut C2×C10804(C2xC10).46(C4:C4)320,142
(C2×C10).47(C4⋊C4) = C5×C4.10C42φ: C4⋊C4/C2×C4 → C2 ⊆ Aut C2×C10804(C2xC10).47(C4:C4)320,143
(C2×C10).48(C4⋊C4) = C5×C42⋊6C4φ: C4⋊C4/C2×C4 → C2 ⊆ Aut C2×C1080(C2xC10).48(C4:C4)320,144
(C2×C10).49(C4⋊C4) = C5×C23.9D4φ: C4⋊C4/C2×C4 → C2 ⊆ Aut C2×C1080(C2xC10).49(C4:C4)320,147
(C2×C10).50(C4⋊C4) = C5×C22.C42φ: C4⋊C4/C2×C4 → C2 ⊆ Aut C2×C10160(C2xC10).50(C4:C4)320,148
(C2×C10).51(C4⋊C4) = C5×M4(2)⋊4C4φ: C4⋊C4/C2×C4 → C2 ⊆ Aut C2×C10804(C2xC10).51(C4:C4)320,149
(C2×C10).52(C4⋊C4) = C5×C4⋊M4(2)φ: C4⋊C4/C2×C4 → C2 ⊆ Aut C2×C10160(C2xC10).52(C4:C4)320,924
(C2×C10).53(C4⋊C4) = C5×C42.6C22φ: C4⋊C4/C2×C4 → C2 ⊆ Aut C2×C10160(C2xC10).53(C4:C4)320,925
(C2×C10).54(C4⋊C4) = C5×C23.25D4φ: C4⋊C4/C2×C4 → C2 ⊆ Aut C2×C10160(C2xC10).54(C4:C4)320,928
(C2×C10).55(C4⋊C4) = C5×M4(2)⋊C4φ: C4⋊C4/C2×C4 → C2 ⊆ Aut C2×C10160(C2xC10).55(C4:C4)320,929
(C2×C10).56(C4⋊C4) = C5×M4(2).C4φ: C4⋊C4/C2×C4 → C2 ⊆ Aut C2×C10804(C2xC10).56(C4:C4)320,931
(C2×C10).57(C4⋊C4) = C40⋊6C8φ: C4⋊C4/C2×C4 → C2 ⊆ Aut C2×C10320(C2xC10).57(C4:C4)320,15
(C2×C10).58(C4⋊C4) = C40⋊5C8φ: C4⋊C4/C2×C4 → C2 ⊆ Aut C2×C10320(C2xC10).58(C4:C4)320,16
(C2×C10).59(C4⋊C4) = C20.53D8φ: C4⋊C4/C2×C4 → C2 ⊆ Aut C2×C10320(C2xC10).59(C4:C4)320,37
(C2×C10).60(C4⋊C4) = C20.39SD16φ: C4⋊C4/C2×C4 → C2 ⊆ Aut C2×C10320(C2xC10).60(C4:C4)320,38
(C2×C10).61(C4⋊C4) = C42⋊6Dic5φ: C4⋊C4/C2×C4 → C2 ⊆ Aut C2×C1080(C2xC10).61(C4:C4)320,81
(C2×C10).62(C4⋊C4) = (C2×C20)⋊8C8φ: C4⋊C4/C2×C4 → C2 ⊆ Aut C2×C10320(C2xC10).62(C4:C4)320,82
(C2×C10).63(C4⋊C4) = C20.31C42φ: C4⋊C4/C2×C4 → C2 ⊆ Aut C2×C10320(C2xC10).63(C4:C4)320,87
(C2×C10).64(C4⋊C4) = (C2×C20).Q8φ: C4⋊C4/C2×C4 → C2 ⊆ Aut C2×C10160(C2xC10).64(C4:C4)320,88
(C2×C10).65(C4⋊C4) = (C2×C40)⋊15C4φ: C4⋊C4/C2×C4 → C2 ⊆ Aut C2×C10320(C2xC10).65(C4:C4)320,108
(C2×C10).66(C4⋊C4) = C20.39C42φ: C4⋊C4/C2×C4 → C2 ⊆ Aut C2×C10320(C2xC10).66(C4:C4)320,109
(C2×C10).67(C4⋊C4) = C20.40C42φ: C4⋊C4/C2×C4 → C2 ⊆ Aut C2×C10160(C2xC10).67(C4:C4)320,110
(C2×C10).68(C4⋊C4) = C23.9D20φ: C4⋊C4/C2×C4 → C2 ⊆ Aut C2×C10804(C2xC10).68(C4:C4)320,115
(C2×C10).69(C4⋊C4) = M4(2)⋊4Dic5φ: C4⋊C4/C2×C4 → C2 ⊆ Aut C2×C10804(C2xC10).69(C4:C4)320,117
(C2×C10).70(C4⋊C4) = C2×C20⋊3C8φ: C4⋊C4/C2×C4 → C2 ⊆ Aut C2×C10320(C2xC10).70(C4:C4)320,550
(C2×C10).71(C4⋊C4) = C20⋊13M4(2)φ: C4⋊C4/C2×C4 → C2 ⊆ Aut C2×C10160(C2xC10).71(C4:C4)320,551
(C2×C10).72(C4⋊C4) = C2×C10.D8φ: C4⋊C4/C2×C4 → C2 ⊆ Aut C2×C10320(C2xC10).72(C4:C4)320,589
(C2×C10).73(C4⋊C4) = C2×C20.Q8φ: C4⋊C4/C2×C4 → C2 ⊆ Aut C2×C10320(C2xC10).73(C4:C4)320,590
(C2×C10).74(C4⋊C4) = C20.47(C4⋊C4)φ: C4⋊C4/C2×C4 → C2 ⊆ Aut C2×C10160(C2xC10).74(C4:C4)320,591
(C2×C10).75(C4⋊C4) = C2×C20.8Q8φ: C4⋊C4/C2×C4 → C2 ⊆ Aut C2×C10320(C2xC10).75(C4:C4)320,726
(C2×C10).76(C4⋊C4) = C20.65(C4⋊C4)φ: C4⋊C4/C2×C4 → C2 ⊆ Aut C2×C10160(C2xC10).76(C4:C4)320,729
(C2×C10).77(C4⋊C4) = C2×C40⋊6C4φ: C4⋊C4/C2×C4 → C2 ⊆ Aut C2×C10320(C2xC10).77(C4:C4)320,731
(C2×C10).78(C4⋊C4) = C2×C40⋊5C4φ: C4⋊C4/C2×C4 → C2 ⊆ Aut C2×C10320(C2xC10).78(C4:C4)320,732
(C2×C10).79(C4⋊C4) = C23.22D20φ: C4⋊C4/C2×C4 → C2 ⊆ Aut C2×C10160(C2xC10).79(C4:C4)320,733
(C2×C10).80(C4⋊C4) = C2×C40.6C4φ: C4⋊C4/C2×C4 → C2 ⊆ Aut C2×C10160(C2xC10).80(C4:C4)320,734
(C2×C10).81(C4⋊C4) = C2×C20.53D4φ: C4⋊C4/C2×C4 → C2 ⊆ Aut C2×C10160(C2xC10).81(C4:C4)320,750
(C2×C10).82(C4⋊C4) = C23.Dic10φ: C4⋊C4/C2×C4 → C2 ⊆ Aut C2×C10804(C2xC10).82(C4:C4)320,751
(C2×C10).83(C4⋊C4) = C2×C10.10C42φ: C4⋊C4/C2×C4 → C2 ⊆ Aut C2×C10320(C2xC10).83(C4:C4)320,835
(C2×C10).84(C4⋊C4) = C5×C8⋊2C8central extension (φ=1)320(C2xC10).84(C4:C4)320,139
(C2×C10).85(C4⋊C4) = C5×C8⋊1C8central extension (φ=1)320(C2xC10).85(C4:C4)320,140
(C2×C10).86(C4⋊C4) = C5×C22.7C42central extension (φ=1)320(C2xC10).86(C4:C4)320,141
(C2×C10).87(C4⋊C4) = C5×C22.4Q16central extension (φ=1)320(C2xC10).87(C4:C4)320,145
(C2×C10).88(C4⋊C4) = C5×C4.C42central extension (φ=1)160(C2xC10).88(C4:C4)320,146
(C2×C10).89(C4⋊C4) = C10×C2.C42central extension (φ=1)320(C2xC10).89(C4:C4)320,876
(C2×C10).90(C4⋊C4) = C10×C4⋊C8central extension (φ=1)320(C2xC10).90(C4:C4)320,923
(C2×C10).91(C4⋊C4) = C10×C4.Q8central extension (φ=1)320(C2xC10).91(C4:C4)320,926
(C2×C10).92(C4⋊C4) = C10×C2.D8central extension (φ=1)320(C2xC10).92(C4:C4)320,927
(C2×C10).93(C4⋊C4) = C10×C8.C4central extension (φ=1)160(C2xC10).93(C4:C4)320,930

׿
×
⋊
ℤ
𝔽
○
≀
ℚ
◁