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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
×S
3
and Q=
C
16
Direct product G=N×Q with N=
C
5
×S
3
and Q=
C
16
d
ρ
Label
ID
S
3
×C
80
240
2
S3xC80
480,116
Semidirect products G=N:Q with N=
C
5
×S
3
and Q=
C
16
extension
φ:Q→Out N
d
ρ
Label
ID
(C
5
×S
3
)⋊C
16
=
S
3
×C
5
⋊C
16
φ:
C
16
/
C
4
→
C
4
⊆ Out
C
5
×S
3
240
8
(C5xS3):C16
480,239
(C
5
×S
3
)⋊
2
C
16
=
S
3
×C
5
⋊
2
C
16
φ:
C
16
/
C
8
→
C
2
⊆ Out
C
5
×S
3
240
4
(C5xS3):2C16
480,8
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⋊
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𝔽
○
≀
ℚ
◁