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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=
A
4
⋊Q
8
Direct product G=N×Q with N=
C
5
and Q=
A
4
⋊Q
8
d
ρ
Label
ID
C
5
×A
4
⋊Q
8
120
6
C5xA4:Q8
480,1013
Semidirect products G=N:Q with N=
C
5
and Q=
A
4
⋊Q
8
extension
φ:Q→Aut N
d
ρ
Label
ID
C
5
⋊
1
(A
4
⋊Q
8
) =
A
4
⋊Dic
10
φ:
A
4
⋊Q
8
/
A
4
⋊C
4
→
C
2
⊆ Aut
C
5
120
6-
C5:1(A4:Q8)
480,975
C
5
⋊
2
(A
4
⋊Q
8
) =
C
20
.
1
S
4
φ:
A
4
⋊Q
8
/
C
4
×A
4
→
C
2
⊆ Aut
C
5
120
6-
C5:2(A4:Q8)
480,1024
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○
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