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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=
S
3
xC
14
Direct product G=NxQ with N=
C
5
and Q=
S
3
xC
14
d
ρ
Label
ID
S
3
xC
70
210
2
S3xC70
420,37
Semidirect products G=N:Q with N=
C
5
and Q=
S
3
xC
14
extension
φ:Q→Aut N
d
ρ
Label
ID
C
5
:
1
(S
3
xC
14
) =
S
3
xC
7
xD
5
φ:
S
3
xC
14
/
S
3
xC
7
→
C
2
⊆ Aut
C
5
105
4
C5:1(S3xC14)
420,27
C
5
:
2
(S
3
xC
14
) =
C
14
xD
15
φ:
S
3
xC
14
/
C
42
→
C
2
⊆ Aut
C
5
210
2
C5:2(S3xC14)
420,39
x
:
Z
F
o
wr
Q
<