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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
and Q=
Q
8
2
Direct product G=N×Q with N=
C
5
and Q=
Q
8
2
d
ρ
Label
ID
C
5
×Q
8
2
320
C5xQ8^2
320,1560
Semidirect products G=N:Q with N=
C
5
and Q=
Q
8
2
extension
φ:Q→Aut N
d
ρ
Label
ID
C
5
⋊
1
(Q
8
2
) =
Q
8
×Dic
10
φ:
Q
8
2
/
C
4
×Q
8
→
C
2
⊆ Aut
C
5
320
C5:1(Q8^2)
320,1238
C
5
⋊
2
(Q
8
2
) =
Dic
10
⋊
9
Q
8
φ:
Q
8
2
/
C
4
⋊Q
8
→
C
2
⊆ Aut
C
5
320
C5:2(Q8^2)
320,1394
×
⋊
ℤ
𝔽
○
≀