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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
3
and Q=
C
40
⋊C
4
Direct product G=N×Q with N=
C
3
and Q=
C
40
⋊C
4
d
ρ
Label
ID
C
3
×C
40
⋊C
4
120
4
C3xC40:C4
480,273
Semidirect products G=N:Q with N=
C
3
and Q=
C
40
⋊C
4
extension
φ:Q→Aut N
d
ρ
Label
ID
C
3
⋊
1
(C
40
⋊C
4
) =
C
120
⋊C
4
φ:
C
40
⋊C
4
/
C
8
×D
5
→
C
2
⊆ Aut
C
3
120
4
C3:1(C40:C4)
480,298
C
3
⋊
2
(C
40
⋊C
4
) =
Dic
5
.Dic
6
φ:
C
40
⋊C
4
/
C
4
⋊F
5
→
C
2
⊆ Aut
C
3
120
8
C3:2(C40:C4)
480,235
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⋊
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𝔽
○
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ℚ
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