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

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

Direct product G=N×Q with N=C4 and Q=C4⋊1D4
dρLabelID
C4×C4⋊1D464C4xC4:1D4128,1038

Semidirect products G=N:Q with N=C4 and Q=C4⋊1D4
extensionφ:Q→Aut NdρLabelID
C4⋊1(C4⋊1D4) = C43⋊15C2φ: C4⋊1D4/C42 → C2 ⊆ Aut C464C4:1(C4:1D4)128,1599
C4⋊2(C4⋊1D4) = C42⋊20D4φ: C4⋊1D4/C2×D4 → C2 ⊆ Aut C464C4:2(C4:1D4)128,1273

Non-split extensions G=N.Q with N=C4 and Q=C4⋊1D4
extensionφ:Q→Aut NdρLabelID
C4.1(C4⋊1D4) = C4⋊D16φ: C4⋊1D4/C42 → C2 ⊆ Aut C464C4.1(C4:1D4)128,978
C4.2(C4⋊1D4) = C4⋊Q32φ: C4⋊1D4/C42 → C2 ⊆ Aut C4128C4.2(C4:1D4)128,979
C4.3(C4⋊1D4) = C16⋊5D4φ: C4⋊1D4/C42 → C2 ⊆ Aut C464C4.3(C4:1D4)128,980
C4.4(C4⋊1D4) = C8.21D8φ: C4⋊1D4/C42 → C2 ⊆ Aut C464C4.4(C4:1D4)128,981
C4.5(C4⋊1D4) = C16⋊3D4φ: C4⋊1D4/C42 → C2 ⊆ Aut C464C4.5(C4:1D4)128,982
C4.6(C4⋊1D4) = C8.7D8φ: C4⋊1D4/C42 → C2 ⊆ Aut C464C4.6(C4:1D4)128,983
C4.7(C4⋊1D4) = C42⋊31D4φ: C4⋊1D4/C42 → C2 ⊆ Aut C464C4.7(C4:1D4)128,1389
C4.8(C4⋊1D4) = C42.196D4φ: C4⋊1D4/C42 → C2 ⊆ Aut C464C4.8(C4:1D4)128,1390
C4.9(C4⋊1D4) = C43⋊12C2φ: C4⋊1D4/C42 → C2 ⊆ Aut C464C4.9(C4:1D4)128,1590
C4.10(C4⋊1D4) = C42⋊19Q8φ: C4⋊1D4/C42 → C2 ⊆ Aut C4128C4.10(C4:1D4)128,1600
C4.11(C4⋊1D4) = C2×C8⋊5D4φ: C4⋊1D4/C42 → C2 ⊆ Aut C464C4.11(C4:1D4)128,1875
C4.12(C4⋊1D4) = C2×C8⋊4D4φ: C4⋊1D4/C42 → C2 ⊆ Aut C464C4.12(C4:1D4)128,1876
C4.13(C4⋊1D4) = C2×C4⋊Q16φ: C4⋊1D4/C42 → C2 ⊆ Aut C4128C4.13(C4:1D4)128,1877
C4.14(C4⋊1D4) = C2×C8.12D4φ: C4⋊1D4/C42 → C2 ⊆ Aut C464C4.14(C4:1D4)128,1878
C4.15(C4⋊1D4) = C2×C8⋊3D4φ: C4⋊1D4/C42 → C2 ⊆ Aut C464C4.15(C4:1D4)128,1880
C4.16(C4⋊1D4) = C2×C8.2D4φ: C4⋊1D4/C42 → C2 ⊆ Aut C464C4.16(C4:1D4)128,1881
C4.17(C4⋊1D4) = M4(2)⋊12D4φ: C4⋊1D4/C2×D4 → C2 ⊆ Aut C432C4.17(C4:1D4)128,697
C4.18(C4⋊1D4) = C42.114D4φ: C4⋊1D4/C2×D4 → C2 ⊆ Aut C464C4.18(C4:1D4)128,698
C4.19(C4⋊1D4) = C42.115D4φ: C4⋊1D4/C2×D4 → C2 ⊆ Aut C432C4.19(C4:1D4)128,699
C4.20(C4⋊1D4) = M4(2).31D4φ: C4⋊1D4/C2×D4 → C2 ⊆ Aut C432C4.20(C4:1D4)128,709
C4.21(C4⋊1D4) = M4(2).32D4φ: C4⋊1D4/C2×D4 → C2 ⊆ Aut C432C4.21(C4:1D4)128,710
C4.22(C4⋊1D4) = M4(2).33D4φ: C4⋊1D4/C2×D4 → C2 ⊆ Aut C464C4.22(C4:1D4)128,711
C4.23(C4⋊1D4) = C42.117D4φ: C4⋊1D4/C2×D4 → C2 ⊆ Aut C4128C4.23(C4:1D4)128,713
C4.24(C4⋊1D4) = C42.118D4φ: C4⋊1D4/C2×D4 → C2 ⊆ Aut C464C4.24(C4:1D4)128,714
C4.25(C4⋊1D4) = C42.119D4φ: C4⋊1D4/C2×D4 → C2 ⊆ Aut C464C4.25(C4:1D4)128,715
C4.26(C4⋊1D4) = C23⋊2D8φ: C4⋊1D4/C2×D4 → C2 ⊆ Aut C464C4.26(C4:1D4)128,731
C4.27(C4⋊1D4) = C23⋊3SD16φ: C4⋊1D4/C2×D4 → C2 ⊆ Aut C464C4.27(C4:1D4)128,732
C4.28(C4⋊1D4) = C23⋊2Q16φ: C4⋊1D4/C2×D4 → C2 ⊆ Aut C464C4.28(C4:1D4)128,733
C4.29(C4⋊1D4) = C42⋊9D4φ: C4⋊1D4/C2×D4 → C2 ⊆ Aut C416C4.29(C4:1D4)128,734
C4.30(C4⋊1D4) = C42.129D4φ: C4⋊1D4/C2×D4 → C2 ⊆ Aut C432C4.30(C4:1D4)128,735
C4.31(C4⋊1D4) = C42⋊10D4φ: C4⋊1D4/C2×D4 → C2 ⊆ Aut C432C4.31(C4:1D4)128,736
C4.32(C4⋊1D4) = C42.130D4φ: C4⋊1D4/C2×D4 → C2 ⊆ Aut C432C4.32(C4:1D4)128,737
C4.33(C4⋊1D4) = M4(2).4D4φ: C4⋊1D4/C2×D4 → C2 ⊆ Aut C432C4.33(C4:1D4)128,750
C4.34(C4⋊1D4) = M4(2).5D4φ: C4⋊1D4/C2×D4 → C2 ⊆ Aut C432C4.34(C4:1D4)128,751
C4.35(C4⋊1D4) = M4(2).6D4φ: C4⋊1D4/C2×D4 → C2 ⊆ Aut C464C4.35(C4:1D4)128,752
C4.36(C4⋊1D4) = C42⋊19D4φ: C4⋊1D4/C2×D4 → C2 ⊆ Aut C464C4.36(C4:1D4)128,1272
C4.37(C4⋊1D4) = C42.167D4φ: C4⋊1D4/C2×D4 → C2 ⊆ Aut C464C4.37(C4:1D4)128,1274
C4.38(C4⋊1D4) = M4(2)⋊7D4φ: C4⋊1D4/C2×D4 → C2 ⊆ Aut C432C4.38(C4:1D4)128,1883
C4.39(C4⋊1D4) = M4(2)⋊8D4φ: C4⋊1D4/C2×D4 → C2 ⊆ Aut C464C4.39(C4:1D4)128,1884
C4.40(C4⋊1D4) = M4(2)⋊9D4φ: C4⋊1D4/C2×D4 → C2 ⊆ Aut C432C4.40(C4:1D4)128,1885
C4.41(C4⋊1D4) = M4(2)⋊10D4φ: C4⋊1D4/C2×D4 → C2 ⊆ Aut C432C4.41(C4:1D4)128,1886
C4.42(C4⋊1D4) = M4(2)⋊11D4φ: C4⋊1D4/C2×D4 → C2 ⊆ Aut C432C4.42(C4:1D4)128,1887
C4.43(C4⋊1D4) = M4(2).20D4φ: C4⋊1D4/C2×D4 → C2 ⊆ Aut C464C4.43(C4:1D4)128,1888
C4.44(C4⋊1D4) = C42⋊9C8central extension (φ=1)128C4.44(C4:1D4)128,574
C4.45(C4⋊1D4) = C42.25Q8central extension (φ=1)128C4.45(C4:1D4)128,575
C4.46(C4⋊1D4) = C42.324D4central extension (φ=1)64C4.46(C4:1D4)128,580
C4.47(C4⋊1D4) = C42.106D4central extension (φ=1)64C4.47(C4:1D4)128,581
C4.48(C4⋊1D4) = C42.325D4central extension (φ=1)64C4.48(C4:1D4)128,686
C4.49(C4⋊1D4) = C42.109D4central extension (φ=1)64C4.49(C4:1D4)128,687
C4.50(C4⋊1D4) = C43⋊C2central extension (φ=1)32C4.50(C4:1D4)128,694
C4.51(C4⋊1D4) = C42⋊8D4central extension (φ=1)32C4.51(C4:1D4)128,695
C4.52(C4⋊1D4) = C42.326D4central extension (φ=1)32C4.52(C4:1D4)128,706
C4.53(C4⋊1D4) = C42.116D4central extension (φ=1)32C4.53(C4:1D4)128,707
C4.54(C4⋊1D4) = C42⋊16D4central extension (φ=1)64C4.54(C4:1D4)128,1129
C4.55(C4⋊1D4) = C42.360D4central extension (φ=1)64C4.55(C4:1D4)128,1879
C4.56(C4⋊1D4) = C42.247D4central extension (φ=1)64C4.56(C4:1D4)128,1882
C4.57(C4⋊1D4) = C42⋊2D4central stem extension (φ=1)164C4.57(C4:1D4)128,742
C4.58(C4⋊1D4) = (C2×C8).2D4central stem extension (φ=1)324C4.58(C4:1D4)128,749
C4.59(C4⋊1D4) = C24.11Q8central stem extension (φ=1)164C4.59(C4:1D4)128,823
C4.60(C4⋊1D4) = C42.10D4central stem extension (φ=1)324C4.60(C4:1D4)128,830

׿
×
⋊
ℤ
𝔽
○
≀
ℚ
◁