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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=
Q
8
and Q=
C
7
⋊C
3
Direct product G=N×Q with N=
Q
8
and Q=
C
7
⋊C
3
d
ρ
Label
ID
Q
8
×C
7
⋊C
3
56
6
Q8xC7:C3
168,21
Semidirect products G=N:Q with N=
Q
8
and Q=
C
7
⋊C
3
extension
φ:Q→Out N
d
ρ
Label
ID
Q
8
⋊(C
7
⋊C
3
) =
C
14
.A
4
φ:
C
7
⋊C
3
/
C
7
→
C
3
⊆ Out
Q
8
56
6
Q8:(C7:C3)
168,23
×
⋊
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𝔽
○
≀
ℚ
◁