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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=
C
3
⋊C
8
Direct product G=N×Q with N=
C
5
and Q=
C
3
⋊C
8
d
ρ
Label
ID
C
5
×C
3
⋊C
8
120
2
C5xC3:C8
120,1
Semidirect products G=N:Q with N=
C
5
and Q=
C
3
⋊C
8
extension
φ:Q→Aut N
d
ρ
Label
ID
C
5
⋊(C
3
⋊C
8
) =
C
15
⋊C
8
φ:
C
3
⋊C
8
/
C
6
→
C
4
⊆ Aut
C
5
120
4
C5:(C3:C8)
120,7
C
5
⋊
2
(C
3
⋊C
8
) =
C
15
⋊
3
C
8
φ:
C
3
⋊C
8
/
C
12
→
C
2
⊆ Aut
C
5
120
2
C5:2(C3:C8)
120,3
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◁