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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
×Q
8
and Q=
C
3
2
Direct product G=N×Q with N=
C
5
×Q
8
and Q=
C
3
2
d
ρ
Label
ID
Q
8
×C
3
×C
15
360
Q8xC3xC15
360,117
Semidirect products G=N:Q with N=
C
5
×Q
8
and Q=
C
3
2
extension
φ:Q→Out N
d
ρ
Label
ID
(C
5
×Q
8
)⋊C
3
2
=
C
15
×SL
2
(𝔽
3
)
φ:
C
3
2
/
C
3
→
C
3
⊆ Out
C
5
×Q
8
120
2
(C5xQ8):C3^2
360,89
×
⋊
ℤ
𝔽
○
≀
ℚ
◁