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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=
D
4
.A
4
Direct product G=N×Q with N=
C
5
and Q=
D
4
.A
4
d
ρ
Label
ID
C
5
×D
4
.A
4
80
4
C5xD4.A4
480,1132
Semidirect products G=N:Q with N=
C
5
and Q=
D
4
.A
4
extension
φ:Q→Aut N
d
ρ
Label
ID
C
5
⋊
1
(D
4
.A
4
) =
SL
2
(𝔽
3
).
11
D
10
φ:
D
4
.A
4
/
C
2
×SL
2
(𝔽
3
)
→
C
2
⊆ Aut
C
5
80
4
C5:1(D4.A4)
480,1040
C
5
⋊
2
(D
4
.A
4
) =
D
20
.A
4
φ:
D
4
.A
4
/
C
4
.A
4
→
C
2
⊆ Aut
C
5
80
4-
C5:2(D4.A4)
480,1043
×
⋊
ℤ
𝔽
○
≀
ℚ
◁