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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=
C
8
.A
4
Direct product G=N×Q with N=
C
5
and Q=
C
8
.A
4
d
ρ
Label
ID
C
5
×C
8
.A
4
160
2
C5xC8.A4
480,660
Semidirect products G=N:Q with N=
C
5
and Q=
C
8
.A
4
extension
φ:Q→Aut N
d
ρ
Label
ID
C
5
⋊(C
8
.A
4
) =
SL
2
(𝔽
3
).F
5
φ:
C
8
.A
4
/
SL
2
(𝔽
3
)
→
C
4
⊆ Aut
C
5
160
8+
C5:(C8.A4)
480,964
C
5
⋊
2
(C
8
.A
4
) =
SL
2
(𝔽
3
).Dic
5
φ:
C
8
.A
4
/
C
4
.A
4
→
C
2
⊆ Aut
C
5
160
4
C5:2(C8.A4)
480,267
×
⋊
ℤ
𝔽
○
≀
ℚ
◁