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

Extensions 1→N→G→Q→1 with N=C4 and Q=C42⋊C2

Direct product G=N×Q with N=C4 and Q=C42⋊C2
dρLabelID
C4×C42⋊C264C4xC4^2:C2128,1002

Semidirect products G=N:Q with N=C4 and Q=C42⋊C2
extensionφ:Q→Aut NdρLabelID
C4⋊1(C42⋊C2) = C43⋊9C2φ: C42⋊C2/C42 → C2 ⊆ Aut C464C4:1(C4^2:C2)128,1025
C4⋊2(C42⋊C2) = C23.226C24φ: C42⋊C2/C22⋊C4 → C2 ⊆ Aut C464C4:2(C4^2:C2)128,1076
C4⋊3(C42⋊C2) = C23.236C24φ: C42⋊C2/C4⋊C4 → C2 ⊆ Aut C464C4:3(C4^2:C2)128,1086
C4⋊4(C42⋊C2) = C23.167C24φ: C42⋊C2/C22×C4 → C2 ⊆ Aut C464C4:4(C4^2:C2)128,1017

Non-split extensions G=N.Q with N=C4 and Q=C42⋊C2
extensionφ:Q→Aut NdρLabelID
C4.1(C42⋊C2) = C4×C4≀C2φ: C42⋊C2/C42 → C2 ⊆ Aut C432C4.1(C4^2:C2)128,490
C4.2(C42⋊C2) = D4.C42φ: C42⋊C2/C42 → C2 ⊆ Aut C432C4.2(C4^2:C2)128,491
C4.3(C42⋊C2) = C4×D4⋊C4φ: C42⋊C2/C42 → C2 ⊆ Aut C464C4.3(C4^2:C2)128,492
C4.4(C42⋊C2) = C4×Q8⋊C4φ: C42⋊C2/C42 → C2 ⊆ Aut C4128C4.4(C4^2:C2)128,493
C4.5(C42⋊C2) = D4⋊C42φ: C42⋊C2/C42 → C2 ⊆ Aut C464C4.5(C4^2:C2)128,494
C4.6(C42⋊C2) = Q8⋊C42φ: C42⋊C2/C42 → C2 ⊆ Aut C4128C4.6(C4^2:C2)128,495
C4.7(C42⋊C2) = C2.(C8⋊8D4)φ: C42⋊C2/C42 → C2 ⊆ Aut C4128C4.7(C4^2:C2)128,665
C4.8(C42⋊C2) = C2.(C8⋊7D4)φ: C42⋊C2/C42 → C2 ⊆ Aut C464C4.8(C4^2:C2)128,666
C4.9(C42⋊C2) = C2.(C8⋊D4)φ: C42⋊C2/C42 → C2 ⊆ Aut C4128C4.9(C4^2:C2)128,667
C4.10(C42⋊C2) = C2.(C8⋊2D4)φ: C42⋊C2/C42 → C2 ⊆ Aut C464C4.10(C4^2:C2)128,668
C4.11(C42⋊C2) = C42.428D4φ: C42⋊C2/C42 → C2 ⊆ Aut C432C4.11(C4^2:C2)128,669
C4.12(C42⋊C2) = C42.107D4φ: C42⋊C2/C42 → C2 ⊆ Aut C432C4.12(C4^2:C2)128,670
C4.13(C42⋊C2) = C42⋊14Q8φ: C42⋊C2/C42 → C2 ⊆ Aut C4128C4.13(C4^2:C2)128,1027
C4.14(C42⋊C2) = C23.201C24φ: C42⋊C2/C42 → C2 ⊆ Aut C464C4.14(C4^2:C2)128,1051
C4.15(C42⋊C2) = C23.202C24φ: C42⋊C2/C42 → C2 ⊆ Aut C4128C4.15(C4^2:C2)128,1052
C4.16(C42⋊C2) = C42.260C23φ: C42⋊C2/C42 → C2 ⊆ Aut C464C4.16(C4^2:C2)128,1654
C4.17(C42⋊C2) = C42.261C23φ: C42⋊C2/C42 → C2 ⊆ Aut C464C4.17(C4^2:C2)128,1655
C4.18(C42⋊C2) = C23.36D8φ: C42⋊C2/C22⋊C4 → C2 ⊆ Aut C464C4.18(C4^2:C2)128,555
C4.19(C42⋊C2) = C24.157D4φ: C42⋊C2/C22⋊C4 → C2 ⊆ Aut C464C4.19(C4^2:C2)128,556
C4.20(C42⋊C2) = C24.69D4φ: C42⋊C2/C22⋊C4 → C2 ⊆ Aut C464C4.20(C4^2:C2)128,557
C4.21(C42⋊C2) = C24.70D4φ: C42⋊C2/C22⋊C4 → C2 ⊆ Aut C432C4.21(C4^2:C2)128,558
C4.22(C42⋊C2) = C2.D8⋊4C4φ: C42⋊C2/C22⋊C4 → C2 ⊆ Aut C4128C4.22(C4^2:C2)128,650
C4.23(C42⋊C2) = C4.Q8⋊9C4φ: C42⋊C2/C22⋊C4 → C2 ⊆ Aut C4128C4.23(C4^2:C2)128,651
C4.24(C42⋊C2) = C4.Q8⋊10C4φ: C42⋊C2/C22⋊C4 → C2 ⊆ Aut C4128C4.24(C4^2:C2)128,652
C4.25(C42⋊C2) = C2.D8⋊5C4φ: C42⋊C2/C22⋊C4 → C2 ⊆ Aut C4128C4.25(C4^2:C2)128,653
C4.26(C42⋊C2) = M4(2).3Q8φ: C42⋊C2/C22⋊C4 → C2 ⊆ Aut C432C4.26(C4^2:C2)128,654
C4.27(C42⋊C2) = C23.227C24φ: C42⋊C2/C22⋊C4 → C2 ⊆ Aut C464C4.27(C4^2:C2)128,1077
C4.28(C42⋊C2) = C24.208C23φ: C42⋊C2/C22⋊C4 → C2 ⊆ Aut C464C4.28(C4^2:C2)128,1078
C4.29(C42⋊C2) = C23.229C24φ: C42⋊C2/C22⋊C4 → C2 ⊆ Aut C464C4.29(C4^2:C2)128,1079
C4.30(C42⋊C2) = C42.262C23φ: C42⋊C2/C22⋊C4 → C2 ⊆ Aut C432C4.30(C4^2:C2)128,1656
C4.31(C42⋊C2) = C42.98D4φ: C42⋊C2/C4⋊C4 → C2 ⊆ Aut C464C4.31(C4^2:C2)128,534
C4.32(C42⋊C2) = C42.99D4φ: C42⋊C2/C4⋊C4 → C2 ⊆ Aut C4128C4.32(C4^2:C2)128,535
C4.33(C42⋊C2) = C42.100D4φ: C42⋊C2/C4⋊C4 → C2 ⊆ Aut C464C4.33(C4^2:C2)128,536
C4.34(C42⋊C2) = C42.101D4φ: C42⋊C2/C4⋊C4 → C2 ⊆ Aut C4128C4.34(C4^2:C2)128,537
C4.35(C42⋊C2) = C42.102D4φ: C42⋊C2/C4⋊C4 → C2 ⊆ Aut C432C4.35(C4^2:C2)128,538
C4.36(C42⋊C2) = D4⋊C4⋊C4φ: C42⋊C2/C4⋊C4 → C2 ⊆ Aut C464C4.36(C4^2:C2)128,657
C4.37(C42⋊C2) = C4.67(C4×D4)φ: C42⋊C2/C4⋊C4 → C2 ⊆ Aut C464C4.37(C4^2:C2)128,658
C4.38(C42⋊C2) = C4.68(C4×D4)φ: C42⋊C2/C4⋊C4 → C2 ⊆ Aut C4128C4.38(C4^2:C2)128,659
C4.39(C42⋊C2) = C2.(C4×Q16)φ: C42⋊C2/C4⋊C4 → C2 ⊆ Aut C4128C4.39(C4^2:C2)128,660
C4.40(C42⋊C2) = M4(2).24D4φ: C42⋊C2/C4⋊C4 → C2 ⊆ Aut C432C4.40(C4^2:C2)128,661
C4.41(C42⋊C2) = C23.237C24φ: C42⋊C2/C4⋊C4 → C2 ⊆ Aut C4128C4.41(C4^2:C2)128,1087
C4.42(C42⋊C2) = C23.238C24φ: C42⋊C2/C4⋊C4 → C2 ⊆ Aut C4128C4.42(C4^2:C2)128,1088
C4.43(C42⋊C2) = C24.212C23φ: C42⋊C2/C4⋊C4 → C2 ⊆ Aut C464C4.43(C4^2:C2)128,1089
C4.44(C42⋊C2) = C42.678C23φ: C42⋊C2/C4⋊C4 → C2 ⊆ Aut C464C4.44(C4^2:C2)128,1657
C4.45(C42⋊C2) = C8.16C42φ: C42⋊C2/C22×C4 → C2 ⊆ Aut C4324C4.45(C4^2:C2)128,479
C4.46(C42⋊C2) = C23.5C42φ: C42⋊C2/C22×C4 → C2 ⊆ Aut C4324C4.46(C4^2:C2)128,489
C4.47(C42⋊C2) = C4×C4.Q8φ: C42⋊C2/C22×C4 → C2 ⊆ Aut C4128C4.47(C4^2:C2)128,506
C4.48(C42⋊C2) = C4×C2.D8φ: C42⋊C2/C22×C4 → C2 ⊆ Aut C4128C4.48(C4^2:C2)128,507
C4.49(C42⋊C2) = C8⋊C42φ: C42⋊C2/C22×C4 → C2 ⊆ Aut C4128C4.49(C4^2:C2)128,508
C4.50(C42⋊C2) = C4×C8.C4φ: C42⋊C2/C22×C4 → C2 ⊆ Aut C464C4.50(C4^2:C2)128,509
C4.51(C42⋊C2) = C8.6C42φ: C42⋊C2/C22×C4 → C2 ⊆ Aut C464C4.51(C4^2:C2)128,510
C4.52(C42⋊C2) = C24.133D4φ: C42⋊C2/C22×C4 → C2 ⊆ Aut C464C4.52(C4^2:C2)128,539
C4.53(C42⋊C2) = C23.22D8φ: C42⋊C2/C22×C4 → C2 ⊆ Aut C464C4.53(C4^2:C2)128,540
C4.54(C42⋊C2) = C24.67D4φ: C42⋊C2/C22×C4 → C2 ⊆ Aut C464C4.54(C4^2:C2)128,541
C4.55(C42⋊C2) = C24.19Q8φ: C42⋊C2/C22×C4 → C2 ⊆ Aut C432C4.55(C4^2:C2)128,542
C4.56(C42⋊C2) = C24.9Q8φ: C42⋊C2/C22×C4 → C2 ⊆ Aut C432C4.56(C4^2:C2)128,543
C4.57(C42⋊C2) = C42.55Q8φ: C42⋊C2/C22×C4 → C2 ⊆ Aut C4128C4.57(C4^2:C2)128,566
C4.58(C42⋊C2) = C42.56Q8φ: C42⋊C2/C22×C4 → C2 ⊆ Aut C4128C4.58(C4^2:C2)128,567
C4.59(C42⋊C2) = C42.24Q8φ: C42⋊C2/C22×C4 → C2 ⊆ Aut C4128C4.59(C4^2:C2)128,568
C4.60(C42⋊C2) = C42.322D4φ: C42⋊C2/C22×C4 → C2 ⊆ Aut C464C4.60(C4^2:C2)128,569
C4.61(C42⋊C2) = C42.104D4φ: C42⋊C2/C22×C4 → C2 ⊆ Aut C464C4.61(C4^2:C2)128,570
C4.62(C42⋊C2) = C8⋊C4⋊17C4φ: C42⋊C2/C22×C4 → C2 ⊆ Aut C4164C4.62(C4^2:C2)128,573
C4.63(C42⋊C2) = C23.165C24φ: C42⋊C2/C22×C4 → C2 ⊆ Aut C464C4.63(C4^2:C2)128,1015
C4.64(C42⋊C2) = C24.192C23φ: C42⋊C2/C22×C4 → C2 ⊆ Aut C464C4.64(C4^2:C2)128,1046
C4.65(C42⋊C2) = C42.677C23φ: C42⋊C2/C22×C4 → C2 ⊆ Aut C432C4.65(C4^2:C2)128,1652
C4.66(C42⋊C2) = C42.259C23φ: C42⋊C2/C22×C4 → C2 ⊆ Aut C432C4.66(C4^2:C2)128,1653
C4.67(C42⋊C2) = C42⋊4C8central extension (φ=1)128C4.67(C4^2:C2)128,476
C4.68(C42⋊C2) = C43.C2central extension (φ=1)128C4.68(C4^2:C2)128,477
C4.69(C42⋊C2) = (C4×C8)⋊12C4central extension (φ=1)128C4.69(C4^2:C2)128,478
C4.70(C42⋊C2) = C8×C22⋊C4central extension (φ=1)64C4.70(C4^2:C2)128,483
C4.71(C42⋊C2) = C23.36C42central extension (φ=1)64C4.71(C4^2:C2)128,484
C4.72(C42⋊C2) = C23.17C42central extension (φ=1)64C4.72(C4^2:C2)128,485
C4.73(C42⋊C2) = C8×C4⋊C4central extension (φ=1)128C4.73(C4^2:C2)128,501
C4.74(C42⋊C2) = C4⋊C8⋊13C4central extension (φ=1)128C4.74(C4^2:C2)128,502
C4.75(C42⋊C2) = C4⋊C8⋊14C4central extension (φ=1)128C4.75(C4^2:C2)128,503
C4.76(C42⋊C2) = C42.13C8central extension (φ=1)64C4.76(C4^2:C2)128,894
C4.77(C42⋊C2) = C42.6C8central extension (φ=1)64C4.77(C4^2:C2)128,895
C4.78(C42⋊C2) = C8.12M4(2)central extension (φ=1)64C4.78(C4^2:C2)128,896
C4.79(C42⋊C2) = C43⋊2C2central extension (φ=1)64C4.79(C4^2:C2)128,1030
C4.80(C42⋊C2) = C2×C42.12C4central extension (φ=1)64C4.80(C4^2:C2)128,1649
C4.81(C42⋊C2) = C2×C42.6C4central extension (φ=1)64C4.81(C4^2:C2)128,1650
C4.82(C42⋊C2) = C2×C42.7C22central extension (φ=1)64C4.82(C4^2:C2)128,1651
C4.83(C42⋊C2) = (C2×D4).24Q8central stem extension (φ=1)324C4.83(C4^2:C2)128,544
C4.84(C42⋊C2) = (C2×C8).103D4central stem extension (φ=1)324C4.84(C4^2:C2)128,545
C4.85(C42⋊C2) = (C2×C42)⋊C4central stem extension (φ=1)164C4.85(C4^2:C2)128,559
C4.86(C42⋊C2) = C8.(C4⋊C4)central stem extension (φ=1)324C4.86(C4^2:C2)128,565
C4.87(C42⋊C2) = C8.5M4(2)central stem extension (φ=1)164C4.87(C4^2:C2)128,897
C4.88(C42⋊C2) = C8.19M4(2)central stem extension (φ=1)324C4.88(C4^2:C2)128,898

׿
×
⋊
ℤ
𝔽
○
≀
ℚ
◁