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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
4
.
3
S
4
Direct product G=N×Q with N=
C
5
and Q=
C
4
.
3
S
4
d
ρ
Label
ID
C
5
×C
4
.
3
S
4
80
4
C5xC4.3S4
480,1021
Semidirect products G=N:Q with N=
C
5
and Q=
C
4
.
3
S
4
extension
φ:Q→Aut N
d
ρ
Label
ID
C
5
⋊
1
(C
4
.
3
S
4
) =
GL
2
(𝔽
3
)⋊D
5
φ:
C
4
.
3
S
4
/
GL
2
(𝔽
3
)
→
C
2
⊆ Aut
C
5
80
4+
C5:1(C4.3S4)
480,970
C
5
⋊
2
(C
4
.
3
S
4
) =
C
20
.
3
S
4
φ:
C
4
.
3
S
4
/
C
4
.A
4
→
C
2
⊆ Aut
C
5
80
4+
C5:2(C4.3S4)
480,1032
×
⋊
ℤ
𝔽
○
≀
ℚ
◁