Home
About
Cn
Dn
Sn
An
Degree
Linear
Irr Reps
Characters
x
:
.
o
wr

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

Direct product G=NxQ with N=D4 and Q=C4:C4
dρLabelID
D4xC4:C464D4xC4:C4128,1080

Semidirect products G=N:Q with N=D4 and Q=C4:C4
extensionφ:Q→Out NdρLabelID
D4:1(C4:C4) = C42.98D4φ: C4:C4/C2xC4 → C2 ⊆ Out D464D4:1(C4:C4)128,534
D4:2(C4:C4) = C42.102D4φ: C4:C4/C2xC4 → C2 ⊆ Out D432D4:2(C4:C4)128,538
D4:3(C4:C4) = C4wrC2:C4φ: C4:C4/C2xC4 → C2 ⊆ Out D432D4:3(C4:C4)128,591
D4:4(C4:C4) = C2.(C4xD8)φ: C4:C4/C2xC4 → C2 ⊆ Out D464D4:4(C4:C4)128,594
D4:5(C4:C4) = D4:(C4:C4)φ: C4:C4/C2xC4 → C2 ⊆ Out D464D4:5(C4:C4)128,596
D4:6(C4:C4) = C23.231C24φ: trivial image64D4:6(C4:C4)128,1081

Non-split extensions G=N.Q with N=D4 and Q=C4:C4
extensionφ:Q→Out NdρLabelID
D4.1(C4:C4) = C42.100D4φ: C4:C4/C2xC4 → C2 ⊆ Out D464D4.1(C4:C4)128,536
D4.2(C4:C4) = C8oD4:C4φ: C4:C4/C2xC4 → C2 ⊆ Out D4324D4.2(C4:C4)128,546
D4.3(C4:C4) = C4oD4.4Q8φ: C4:C4/C2xC4 → C2 ⊆ Out D464D4.3(C4:C4)128,547
D4.4(C4:C4) = C4oD4.5Q8φ: C4:C4/C2xC4 → C2 ⊆ Out D464D4.4(C4:C4)128,548
D4.5(C4:C4) = C42:9(C2xC4)φ: C4:C4/C2xC4 → C2 ⊆ Out D432D4.5(C4:C4)128,592
D4.6(C4:C4) = M4(2).41D4φ: C4:C4/C2xC4 → C2 ⊆ Out D4164D4.6(C4:C4)128,593
D4.7(C4:C4) = M4(2).42D4φ: C4:C4/C2xC4 → C2 ⊆ Out D432D4.7(C4:C4)128,598
D4.8(C4:C4) = C42.674C23φ: trivial image64D4.8(C4:C4)128,1638
D4.9(C4:C4) = C4oD4.7Q8φ: trivial image64D4.9(C4:C4)128,1644
D4.10(C4:C4) = C4oD4.8Q8φ: trivial image64D4.10(C4:C4)128,1645
D4.11(C4:C4) = M4(2).29C23φ: trivial image324D4.11(C4:C4)128,1648

׿
x
:
Z
F
o
wr
Q
<