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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=
A
4
⋊C
4
Direct product G=N×Q with N=
C
5
and Q=
A
4
⋊C
4
d
ρ
Label
ID
C
5
×A
4
⋊C
4
60
3
C5xA4:C4
240,104
Semidirect products G=N:Q with N=
C
5
and Q=
A
4
⋊C
4
extension
φ:Q→Aut N
d
ρ
Label
ID
C
5
⋊(A
4
⋊C
4
) =
A
4
⋊F
5
φ:
A
4
⋊C
4
/
A
4
→
C
4
⊆ Aut
C
5
20
12+
C5:(A4:C4)
240,192
C
5
⋊
2
(A
4
⋊C
4
) =
A
4
⋊Dic
5
φ:
A
4
⋊C
4
/
C
2
×A
4
→
C
2
⊆ Aut
C
5
60
6-
C5:2(A4:C4)
240,107
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⋊
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𝔽
○
≀
ℚ
◁