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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
2
4
Direct product G=N×Q with N=
C
5
×S
3
and Q=
C
2
4
d
ρ
Label
ID
S
3
×C
2
3
×C
10
240
S3xC2^3xC10
480,1211
Semidirect products G=N:Q with N=
C
5
×S
3
and Q=
C
2
4
extension
φ:Q→Out N
d
ρ
Label
ID
(C
5
×S
3
)⋊C
2
4
=
S
3
×C
2
3
×D
5
φ:
C
2
4
/
C
2
3
→
C
2
⊆ Out
C
5
×S
3
120
(C5xS3):C2^4
480,1207
×
⋊
ℤ
𝔽
○
≀
ℚ
◁