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C
n
D
n
S
n
A
n
Degree
Linear
Irr Reps
Characters
×
⋊
.
○
≀
Extensions
1→N→G→Q→1 with N=
C
5
2
and Q=
D
7
Direct product G=N×Q with N=
C
5
2
and Q=
D
7
d
ρ
Label
ID
D
7
×C
5
2
175
D7xC5^2
350,5
Semidirect products G=N:Q with N=
C
5
2
and Q=
D
7
extension
φ:Q→Aut N
d
ρ
Label
ID
C
5
2
⋊
1
D
7
=
C
5
×D
35
φ:
D
7
/
C
7
→
C
2
⊆ Aut
C
5
2
70
2
C5^2:1D7
350,7
C
5
2
⋊
2
D
7
=
C
5
⋊D
35
φ:
D
7
/
C
7
→
C
2
⊆ Aut
C
5
2
175
C5^2:2D7
350,9
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⋊
ℤ
𝔽
○
≀
ℚ
◁