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C
n
D
n
S
n
A
n
Degree
Linear
Irr Reps
Characters
x
:
.
o
wr
Extensions
1→N→G→Q→1 with N=
D
4
and Q=
C
2
Direct product G=NxQ with N=
D
4
and Q=
C
2
d
ρ
Label
ID
C
2
xD
4
8
C2xD4
16,11
Semidirect products G=N:Q with N=
D
4
and Q=
C
2
extension
φ:Q→Out N
d
ρ
Label
ID
D
4
:C
2
=
D
8
φ:
C
2
/
C
1
→
C
2
⊆ Out
D
4
8
2+
D4:C2
16,7
D
4
:
2
C
2
=
C
4
oD
4
φ: trivial image
8
2
D4:2C2
16,13
Non-split extensions G=N.Q with N=
D
4
and Q=
C
2
extension
φ:Q→Out N
d
ρ
Label
ID
D
4
.C
2
=
SD
16
φ:
C
2
/
C
1
→
C
2
⊆ Out
D
4
8
2
D4.C2
16,8
x
:
Z
F
o
wr
Q
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