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

Extensions 1→N→G→Q→1 with N=Q8 and Q=C5⋊D4

Direct product G=N×Q with N=Q8 and Q=C5⋊D4
dρLabelID
Q8×C5⋊D4160Q8xC5:D4320,1487

Semidirect products G=N:Q with N=Q8 and Q=C5⋊D4
extensionφ:Q→Out NdρLabelID
Q8⋊1(C5⋊D4) = Dic5⋊5SD16φ: C5⋊D4/Dic5 → C2 ⊆ Out Q8160Q8:1(C5:D4)320,790
Q8⋊2(C5⋊D4) = D10⋊8SD16φ: C5⋊D4/D10 → C2 ⊆ Out Q8160Q8:2(C5:D4)320,797
Q8⋊3(C5⋊D4) = D20⋊7D4φ: C5⋊D4/D10 → C2 ⊆ Out Q8160Q8:3(C5:D4)320,799
Q8⋊4(C5⋊D4) = D20⋊18D4φ: C5⋊D4/D10 → C2 ⊆ Out Q8408+Q8:4(C5:D4)320,825
Q8⋊5(C5⋊D4) = (C5×Q8)⋊13D4φ: C5⋊D4/C2×C10 → C2 ⊆ Out Q8160Q8:5(C5:D4)320,854
Q8⋊6(C5⋊D4) = (C5×D4)⋊14D4φ: C5⋊D4/C2×C10 → C2 ⊆ Out Q8160Q8:6(C5:D4)320,865
Q8⋊7(C5⋊D4) = 2+ 1+4⋊D5φ: C5⋊D4/C2×C10 → C2 ⊆ Out Q8408+Q8:7(C5:D4)320,868
Q8⋊8(C5⋊D4) = C10.452- 1+4φ: trivial image160Q8:8(C5:D4)320,1489
Q8⋊9(C5⋊D4) = C10.1072- 1+4φ: trivial image160Q8:9(C5:D4)320,1503
Q8⋊10(C5⋊D4) = C10.1482+ 1+4φ: trivial image160Q8:10(C5:D4)320,1506

Non-split extensions G=N.Q with N=Q8 and Q=C5⋊D4
extensionφ:Q→Out NdρLabelID
Q8.1(C5⋊D4) = (C5×Q8).D4φ: C5⋊D4/Dic5 → C2 ⊆ Out Q8160Q8.1(C5:D4)320,793
Q8.2(C5⋊D4) = Dic5⋊3Q16φ: C5⋊D4/Dic5 → C2 ⊆ Out Q8320Q8.2(C5:D4)320,809
Q8.3(C5⋊D4) = (C2×Q16)⋊D5φ: C5⋊D4/Dic5 → C2 ⊆ Out Q8160Q8.3(C5:D4)320,812
Q8.4(C5⋊D4) = M4(2).D10φ: C5⋊D4/Dic5 → C2 ⊆ Out Q8808+Q8.4(C5:D4)320,826
Q8.5(C5⋊D4) = M4(2).13D10φ: C5⋊D4/Dic5 → C2 ⊆ Out Q8808-Q8.5(C5:D4)320,827
Q8.6(C5⋊D4) = M4(2).15D10φ: C5⋊D4/Dic5 → C2 ⊆ Out Q8808+Q8.6(C5:D4)320,830
Q8.7(C5⋊D4) = M4(2).16D10φ: C5⋊D4/Dic5 → C2 ⊆ Out Q81608-Q8.7(C5:D4)320,831
Q8.8(C5⋊D4) = D10⋊5Q16φ: C5⋊D4/D10 → C2 ⊆ Out Q8160Q8.8(C5:D4)320,813
Q8.9(C5⋊D4) = D20.17D4φ: C5⋊D4/D10 → C2 ⊆ Out Q8160Q8.9(C5:D4)320,814
Q8.10(C5⋊D4) = D20.38D4φ: C5⋊D4/D10 → C2 ⊆ Out Q8808-Q8.10(C5:D4)320,828
Q8.11(C5⋊D4) = D20.39D4φ: C5⋊D4/D10 → C2 ⊆ Out Q8808+Q8.11(C5:D4)320,829
Q8.12(C5⋊D4) = D20.40D4φ: C5⋊D4/D10 → C2 ⊆ Out Q8808-Q8.12(C5:D4)320,832
Q8.13(C5⋊D4) = (C2×C10)⋊8Q16φ: C5⋊D4/C2×C10 → C2 ⊆ Out Q8160Q8.13(C5:D4)320,855
Q8.14(C5⋊D4) = (C5×D4).32D4φ: C5⋊D4/C2×C10 → C2 ⊆ Out Q8160Q8.14(C5:D4)320,866
Q8.15(C5⋊D4) = 2+ 1+4.D5φ: C5⋊D4/C2×C10 → C2 ⊆ Out Q8808-Q8.15(C5:D4)320,869
Q8.16(C5⋊D4) = 2- 1+4⋊2D5φ: C5⋊D4/C2×C10 → C2 ⊆ Out Q8808+Q8.16(C5:D4)320,872
Q8.17(C5⋊D4) = 2- 1+4.2D5φ: C5⋊D4/C2×C10 → C2 ⊆ Out Q8808-Q8.17(C5:D4)320,873
Q8.18(C5⋊D4) = D20.32C23φ: trivial image808+Q8.18(C5:D4)320,1507
Q8.19(C5⋊D4) = D20.33C23φ: trivial image808-Q8.19(C5:D4)320,1508
Q8.20(C5⋊D4) = D20.34C23φ: trivial image808+Q8.20(C5:D4)320,1509
Q8.21(C5⋊D4) = D20.35C23φ: trivial image1608-Q8.21(C5:D4)320,1510

׿
×
⋊
ℤ
𝔽
○
≀
ℚ
◁