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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=
D
5
Direct product G=N×Q with N=
A
4
and Q=
D
5
d
ρ
Label
ID
D
5
×A
4
20
6+
D5xA4
120,39
Semidirect products G=N:Q with N=
A
4
and Q=
D
5
extension
φ:Q→Out N
d
ρ
Label
ID
A
4
⋊D
5
=
C
5
⋊S
4
φ:
D
5
/
C
5
→
C
2
⊆ Out
A
4
20
6+
A4:D5
120,38
×
⋊
ℤ
𝔽
○
≀
ℚ
◁