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

Extensions 1→N→G→Q→1 with N=C8 and Q=C5⋊D4

Direct product G=N×Q with N=C8 and Q=C5⋊D4
dρLabelID
C8×C5⋊D4160C8xC5:D4320,736

Semidirect products G=N:Q with N=C8 and Q=C5⋊D4
extensionφ:Q→Aut NdρLabelID
C8⋊1(C5⋊D4) = C40⋊2D4φ: C5⋊D4/C10 → C22 ⊆ Aut C8160C8:1(C5:D4)320,761
C8⋊2(C5⋊D4) = C40⋊3D4φ: C5⋊D4/C10 → C22 ⊆ Aut C8160C8:2(C5:D4)320,762
C8⋊3(C5⋊D4) = C40⋊11D4φ: C5⋊D4/C10 → C22 ⊆ Aut C8160C8:3(C5:D4)320,781
C8⋊4(C5⋊D4) = C40⋊12D4φ: C5⋊D4/C10 → C22 ⊆ Aut C8160C8:4(C5:D4)320,786
C8⋊5(C5⋊D4) = C40⋊8D4φ: C5⋊D4/C10 → C22 ⊆ Aut C8160C8:5(C5:D4)320,801
C8⋊6(C5⋊D4) = C40⋊9D4φ: C5⋊D4/C10 → C22 ⊆ Aut C8160C8:6(C5:D4)320,803
C8⋊7(C5⋊D4) = C40⋊5D4φ: C5⋊D4/Dic5 → C2 ⊆ Aut C8160C8:7(C5:D4)320,778
C8⋊8(C5⋊D4) = C40⋊15D4φ: C5⋊D4/Dic5 → C2 ⊆ Aut C8160C8:8(C5:D4)320,802
C8⋊9(C5⋊D4) = C40⋊18D4φ: C5⋊D4/Dic5 → C2 ⊆ Aut C8160C8:9(C5:D4)320,755
C8⋊10(C5⋊D4) = C40⋊6D4φ: C5⋊D4/D10 → C2 ⊆ Aut C8160C8:10(C5:D4)320,784
C8⋊11(C5⋊D4) = C40⋊14D4φ: C5⋊D4/D10 → C2 ⊆ Aut C8160C8:11(C5:D4)320,798
C8⋊12(C5⋊D4) = C40⋊D4φ: C5⋊D4/D10 → C2 ⊆ Aut C8160C8:12(C5:D4)320,754
C8⋊13(C5⋊D4) = C40⋊29D4φ: C5⋊D4/C2×C10 → C2 ⊆ Aut C8160C8:13(C5:D4)320,742
C8⋊14(C5⋊D4) = C40⋊30D4φ: C5⋊D4/C2×C10 → C2 ⊆ Aut C8160C8:14(C5:D4)320,741
C8⋊15(C5⋊D4) = C40⋊32D4φ: C5⋊D4/C2×C10 → C2 ⊆ Aut C8160C8:15(C5:D4)320,738

Non-split extensions G=N.Q with N=C8 and Q=C5⋊D4
extensionφ:Q→Aut NdρLabelID
C8.1(C5⋊D4) = C40.4D4φ: C5⋊D4/C10 → C22 ⊆ Aut C8160C8.1(C5:D4)320,764
C8.2(C5⋊D4) = D8.D10φ: C5⋊D4/C10 → C22 ⊆ Aut C8804C8.2(C5:D4)320,774
C8.3(C5⋊D4) = C40.31D4φ: C5⋊D4/C10 → C22 ⊆ Aut C8160C8.3(C5:D4)320,794
C8.4(C5⋊D4) = Q16.D10φ: C5⋊D4/C10 → C22 ⊆ Aut C81604C8.4(C5:D4)320,806
C8.5(C5⋊D4) = C40.36D4φ: C5⋊D4/C10 → C22 ⊆ Aut C8160C8.5(C5:D4)320,816
C8.6(C5⋊D4) = C40.37D4φ: C5⋊D4/C10 → C22 ⊆ Aut C8160C8.6(C5:D4)320,817
C8.7(C5⋊D4) = D8⋊D10φ: C5⋊D4/C10 → C22 ⊆ Aut C8804+C8.7(C5:D4)320,820
C8.8(C5⋊D4) = C40.31C23φ: C5⋊D4/C10 → C22 ⊆ Aut C81604-C8.8(C5:D4)320,822
C8.9(C5⋊D4) = C5⋊D32φ: C5⋊D4/Dic5 → C2 ⊆ Aut C81604+C8.9(C5:D4)320,77
C8.10(C5⋊D4) = D16.D5φ: C5⋊D4/Dic5 → C2 ⊆ Aut C81604-C8.10(C5:D4)320,78
C8.11(C5⋊D4) = C5⋊SD64φ: C5⋊D4/Dic5 → C2 ⊆ Aut C81604+C8.11(C5:D4)320,79
C8.12(C5⋊D4) = C5⋊Q64φ: C5⋊D4/Dic5 → C2 ⊆ Aut C83204-C8.12(C5:D4)320,80
C8.13(C5⋊D4) = C2×C5⋊D16φ: C5⋊D4/Dic5 → C2 ⊆ Aut C8160C8.13(C5:D4)320,773
C8.14(C5⋊D4) = C2×D8.D5φ: C5⋊D4/Dic5 → C2 ⊆ Aut C8160C8.14(C5:D4)320,775
C8.15(C5⋊D4) = C40.22D4φ: C5⋊D4/Dic5 → C2 ⊆ Aut C8160C8.15(C5:D4)320,782
C8.16(C5⋊D4) = C2×C5⋊SD32φ: C5⋊D4/Dic5 → C2 ⊆ Aut C8160C8.16(C5:D4)320,805
C8.17(C5⋊D4) = C2×C5⋊Q32φ: C5⋊D4/Dic5 → C2 ⊆ Aut C8320C8.17(C5:D4)320,807
C8.18(C5⋊D4) = C40.26D4φ: C5⋊D4/Dic5 → C2 ⊆ Aut C8320C8.18(C5:D4)320,808
C8.19(C5⋊D4) = C40.28D4φ: C5⋊D4/Dic5 → C2 ⊆ Aut C8160C8.19(C5:D4)320,818
C8.20(C5⋊D4) = C40.43D4φ: C5⋊D4/Dic5 → C2 ⊆ Aut C8160C8.20(C5:D4)320,795
C8.21(C5⋊D4) = C40.30C23φ: C5⋊D4/Dic5 → C2 ⊆ Aut C81604C8.21(C5:D4)320,821
C8.22(C5⋊D4) = C40.93D4φ: C5⋊D4/Dic5 → C2 ⊆ Aut C8804C8.22(C5:D4)320,771
C8.23(C5⋊D4) = C10.D16φ: C5⋊D4/D10 → C2 ⊆ Aut C8160C8.23(C5:D4)320,120
C8.24(C5⋊D4) = D8.Dic5φ: C5⋊D4/D10 → C2 ⊆ Aut C8804C8.24(C5:D4)320,121
C8.25(C5⋊D4) = C40.15D4φ: C5⋊D4/D10 → C2 ⊆ Aut C8320C8.25(C5:D4)320,122
C8.26(C5⋊D4) = Q16.Dic5φ: C5⋊D4/D10 → C2 ⊆ Aut C81604C8.26(C5:D4)320,123
C8.27(C5⋊D4) = C40.23D4φ: C5⋊D4/D10 → C2 ⊆ Aut C8804C8.27(C5:D4)320,787
C8.28(C5⋊D4) = D10⋊3Q16φ: C5⋊D4/D10 → C2 ⊆ Aut C8160C8.28(C5:D4)320,815
C8.29(C5⋊D4) = C40.29D4φ: C5⋊D4/D10 → C2 ⊆ Aut C81604C8.29(C5:D4)320,819
C8.30(C5⋊D4) = D8⋊2Dic5φ: C5⋊D4/D10 → C2 ⊆ Aut C8804C8.30(C5:D4)320,124
C8.31(C5⋊D4) = C20.58D8φ: C5⋊D4/D10 → C2 ⊆ Aut C81604C8.31(C5:D4)320,125
C8.32(C5⋊D4) = C40.44D4φ: C5⋊D4/D10 → C2 ⊆ Aut C8804C8.32(C5:D4)320,804
C8.33(C5⋊D4) = C40.D4φ: C5⋊D4/D10 → C2 ⊆ Aut C8804C8.33(C5:D4)320,111
C8.34(C5⋊D4) = C40.92D4φ: C5⋊D4/D10 → C2 ⊆ Aut C81604C8.34(C5:D4)320,119
C8.35(C5⋊D4) = C40.78D4φ: C5⋊D4/C2×C10 → C2 ⊆ Aut C8320C8.35(C5:D4)320,61
C8.36(C5⋊D4) = D40⋊7C4φ: C5⋊D4/C2×C10 → C2 ⊆ Aut C8160C8.36(C5:D4)320,67
C8.37(C5⋊D4) = D40.4C4φ: C5⋊D4/C2×C10 → C2 ⊆ Aut C8804+C8.37(C5:D4)320,74
C8.38(C5⋊D4) = C20.4D8φ: C5⋊D4/C2×C10 → C2 ⊆ Aut C81604-C8.38(C5:D4)320,75
C8.39(C5⋊D4) = C40.82D4φ: C5⋊D4/C2×C10 → C2 ⊆ Aut C8160C8.39(C5:D4)320,743
C8.40(C5⋊D4) = D4.4D20φ: C5⋊D4/C2×C10 → C2 ⊆ Aut C8804+C8.40(C5:D4)320,769
C8.41(C5⋊D4) = D4.5D20φ: C5⋊D4/C2×C10 → C2 ⊆ Aut C81604-C8.41(C5:D4)320,770
C8.42(C5⋊D4) = D40.3C4φ: C5⋊D4/C2×C10 → C2 ⊆ Aut C81602C8.42(C5:D4)320,68
C8.43(C5⋊D4) = D40⋊8C4φ: C5⋊D4/C2×C10 → C2 ⊆ Aut C8804C8.43(C5:D4)320,76
C8.44(C5⋊D4) = D4.3D20φ: C5⋊D4/C2×C10 → C2 ⊆ Aut C8804C8.44(C5:D4)320,768
C8.45(C5⋊D4) = D20.3C8φ: C5⋊D4/C2×C10 → C2 ⊆ Aut C81602C8.45(C5:D4)320,66
C8.46(C5⋊D4) = C8.25D20φ: C5⋊D4/C2×C10 → C2 ⊆ Aut C8804C8.46(C5:D4)320,72
C8.47(C5⋊D4) = C40.50D4φ: C5⋊D4/C2×C10 → C2 ⊆ Aut C8804C8.47(C5:D4)320,772
C8.48(C5⋊D4) = C40.88D4central extension (φ=1)320C8.48(C5:D4)320,59
C8.49(C5⋊D4) = D10⋊1C16central extension (φ=1)160C8.49(C5:D4)320,65
C8.50(C5⋊D4) = C40.9Q8central extension (φ=1)804C8.50(C5:D4)320,69
C8.51(C5⋊D4) = D20.4C8central extension (φ=1)1604C8.51(C5:D4)320,73
C8.52(C5⋊D4) = C40.91D4central extension (φ=1)160C8.52(C5:D4)320,107

׿
×
⋊
ℤ
𝔽
○
≀
ℚ
◁