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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=
C
5
and Q=
A
4
:Q
8
Direct product G=NxQ with N=
C
5
and Q=
A
4
:Q
8
d
ρ
Label
ID
C
5
xA
4
:Q
8
120
6
C5xA4:Q8
480,1013
Semidirect products G=N:Q with N=
C
5
and Q=
A
4
:Q
8
extension
φ:Q→Aut N
d
ρ
Label
ID
C
5
:
1
(A
4
:Q
8
) =
A
4
:Dic
10
φ:
A
4
:Q
8
/
A
4
:C
4
→
C
2
⊆ Aut
C
5
120
6-
C5:1(A4:Q8)
480,975
C
5
:
2
(A
4
:Q
8
) =
C
20
.
1
S
4
φ:
A
4
:Q
8
/
C
4
xA
4
→
C
2
⊆ Aut
C
5
120
6-
C5:2(A4:Q8)
480,1024
x
:
Z
F
o
wr
Q
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