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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
2
xS
4
Direct product G=NxQ with N=
C
5
and Q=
C
2
xS
4
d
ρ
Label
ID
C
10
xS
4
30
3
C10xS4
240,196
Semidirect products G=N:Q with N=
C
5
and Q=
C
2
xS
4
extension
φ:Q→Aut N
d
ρ
Label
ID
C
5
:
1
(C
2
xS
4
) =
D
5
xS
4
φ:
C
2
xS
4
/
S
4
→
C
2
⊆ Aut
C
5
20
6+
C5:1(C2xS4)
240,194
C
5
:
2
(C
2
xS
4
) =
C
2
xC
5
:S
4
φ:
C
2
xS
4
/
C
2
xA
4
→
C
2
⊆ Aut
C
5
30
6+
C5:2(C2xS4)
240,197
x
:
Z
F
o
wr
Q
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