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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
×D
4
Direct product G=N×Q with N=
A
4
and Q=
C
5
×D
4
d
ρ
Label
ID
C
5
×D
4
×A
4
60
6
C5xD4xA4
480,1127
Semidirect products G=N:Q with N=
A
4
and Q=
C
5
×D
4
extension
φ:Q→Out N
d
ρ
Label
ID
A
4
⋊
1
(C
5
×D
4
) =
C
5
×C
4
⋊S
4
φ:
C
5
×D
4
/
C
20
→
C
2
⊆ Out
A
4
60
6
A4:1(C5xD4)
480,1015
A
4
⋊
2
(C
5
×D
4
) =
C
5
×A
4
⋊D
4
φ:
C
5
×D
4
/
C
2
×C
10
→
C
2
⊆ Out
A
4
60
6
A4:2(C5xD4)
480,1023
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⋊
ℤ
𝔽
○
≀
ℚ
◁