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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
2
×C
20
Direct product G=N×Q with N=
A
4
and Q=
C
2
×C
20
d
ρ
Label
ID
A
4
×C
2
×C
20
120
A4xC2xC20
480,1126
Semidirect products G=N:Q with N=
A
4
and Q=
C
2
×C
20
extension
φ:Q→Out N
d
ρ
Label
ID
A
4
⋊
1
(C
2
×C
20
) =
C
20
×S
4
φ:
C
2
×C
20
/
C
20
→
C
2
⊆ Out
A
4
60
3
A4:1(C2xC20)
480,1014
A
4
⋊
2
(C
2
×C
20
) =
C
10
×A
4
⋊C
4
φ:
C
2
×C
20
/
C
2
×C
10
→
C
2
⊆ Out
A
4
120
A4:2(C2xC20)
480,1022
×
⋊
ℤ
𝔽
○
≀
ℚ
◁