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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=
C
3
xC
24
Direct product G=NxQ with N=
C
5
and Q=
C
3
xC
24
d
ρ
Label
ID
C
3
xC
120
360
C3xC120
360,38
Semidirect products G=N:Q with N=
C
5
and Q=
C
3
xC
24
extension
φ:Q→Aut N
d
ρ
Label
ID
C
5
:(C
3
xC
24
) =
C
3
2
xC
5
:C
8
φ:
C
3
xC
24
/
C
3
xC
6
→
C
4
⊆ Aut
C
5
360
C5:(C3xC24)
360,52
C
5
:
2
(C
3
xC
24
) =
C
3
2
xC
5
:
2
C
8
φ:
C
3
xC
24
/
C
3
xC
12
→
C
2
⊆ Aut
C
5
360
C5:2(C3xC24)
360,33
x
:
Z
F
o
wr
Q
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