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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=
C
5
and Q=
S
4
Direct product G=N×Q with N=
C
5
and Q=
S
4
d
ρ
Label
ID
C
5
×S
4
20
3
C5xS4
120,37
Semidirect products G=N:Q with N=
C
5
and Q=
S
4
extension
φ:Q→Aut N
d
ρ
Label
ID
C
5
⋊S
4
=
C
5
⋊S
4
φ:
S
4
/
A
4
→
C
2
⊆ Aut
C
5
20
6+
C5:S4
120,38
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𝔽
○
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ℚ
◁