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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=
A
4
and Q=
C
5
×S
3
Direct product G=N×Q with N=
A
4
and Q=
C
5
×S
3
d
ρ
Label
ID
C
5
×S
3
×A
4
60
6
C5xS3xA4
360,143
Semidirect products G=N:Q with N=
A
4
and Q=
C
5
×S
3
extension
φ:Q→Out N
d
ρ
Label
ID
A
4
⋊(C
5
×S
3
) =
C
5
×C
3
⋊S
4
φ:
C
5
×S
3
/
C
15
→
C
2
⊆ Out
A
4
60
6
A4:(C5xS3)
360,140
×
⋊
ℤ
𝔽
○
≀
ℚ
◁