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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=
D
7
and Q=
C
7
⋊C
3
Direct product G=N×Q with N=
D
7
and Q=
C
7
⋊C
3
d
ρ
Label
ID
D
7
×C
7
⋊C
3
42
6
D7xC7:C3
294,9
Semidirect products G=N:Q with N=
D
7
and Q=
C
7
⋊C
3
extension
φ:Q→Out N
d
ρ
Label
ID
D
7
⋊
1
(C
7
⋊C
3
) =
C
7
⋊
3
F
7
φ:
C
7
⋊C
3
/
C
7
→
C
3
⊆ Out
D
7
42
6
D7:1(C7:C3)
294,11
D
7
⋊
2
(C
7
⋊C
3
) =
C
7
⋊
4
F
7
φ:
C
7
⋊C
3
/
C
7
→
C
3
⊆ Out
D
7
14
6
D7:2(C7:C3)
294,12
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⋊
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𝔽
○
≀
ℚ
◁