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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=
F
5
Direct product G=N×Q with N=
A
4
and Q=
F
5
d
ρ
Label
ID
A
4
×F
5
20
12+
A4xF5
240,193
Semidirect products G=N:Q with N=
A
4
and Q=
F
5
extension
φ:Q→Out N
d
ρ
Label
ID
A
4
⋊F
5
=
A
4
⋊F
5
φ:
F
5
/
D
5
→
C
2
⊆ Out
A
4
20
12+
A4:F5
240,192
×
⋊
ℤ
𝔽
○
≀
ℚ
◁