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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
xF
7
Direct product G=NxQ with N=
C
5
and Q=
C
2
xF
7
d
ρ
Label
ID
C
10
xF
7
70
6
C10xF7
420,17
Semidirect products G=N:Q with N=
C
5
and Q=
C
2
xF
7
extension
φ:Q→Aut N
d
ρ
Label
ID
C
5
:
1
(C
2
xF
7
) =
D
5
xF
7
φ:
C
2
xF
7
/
F
7
→
C
2
⊆ Aut
C
5
35
12+
C5:1(C2xF7)
420,16
C
5
:
2
(C
2
xF
7
) =
C
2
xC
5
:F
7
φ:
C
2
xF
7
/
C
2
xC
7
:C
3
→
C
2
⊆ Aut
C
5
70
6+
C5:2(C2xF7)
420,19
x
:
Z
F
o
wr
Q
<