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

Extensions 1→N→G→Q→1 with N=C4:C4 and Q=C2

Direct product G=NxQ with N=C4:C4 and Q=C2
dρLabelID
C2xC4:C432C2xC4:C432,23

Semidirect products G=N:Q with N=C4:C4 and Q=C2
extensionφ:Q→Out NdρLabelID
C4:C4:1C2 = D4:C4φ: C2/C1 → C2 ⊆ Out C4:C416C4:C4:1C232,9
C4:C4:2C2 = C4:D4φ: C2/C1 → C2 ⊆ Out C4:C416C4:C4:2C232,28
C4:C4:3C2 = C22:Q8φ: C2/C1 → C2 ⊆ Out C4:C416C4:C4:3C232,29
C4:C4:4C2 = C22.D4φ: C2/C1 → C2 ⊆ Out C4:C416C4:C4:4C232,30
C4:C4:5C2 = C42:2C2φ: C2/C1 → C2 ⊆ Out C4:C416C4:C4:5C232,33
C4:C4:6C2 = C42:C2φ: trivial image16C4:C4:6C232,24
C4:C4:7C2 = C4xD4φ: trivial image16C4:C4:7C232,25

Non-split extensions G=N.Q with N=C4:C4 and Q=C2
extensionφ:Q→Out NdρLabelID
C4:C4.1C2 = Q8:C4φ: C2/C1 → C2 ⊆ Out C4:C432C4:C4.1C232,10
C4:C4.2C2 = C4.Q8φ: C2/C1 → C2 ⊆ Out C4:C432C4:C4.2C232,13
C4:C4.3C2 = C2.D8φ: C2/C1 → C2 ⊆ Out C4:C432C4:C4.3C232,14
C4:C4.4C2 = C42.C2φ: C2/C1 → C2 ⊆ Out C4:C432C4:C4.4C232,32
C4:C4.5C2 = C4:Q8φ: C2/C1 → C2 ⊆ Out C4:C432C4:C4.5C232,35
C4:C4.6C2 = C4xQ8φ: trivial image32C4:C4.6C232,26

׿
x
:
Z
F
o
wr
Q
<