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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
3
⋊C
32
Direct product G=N×Q with N=
C
5
and Q=
C
3
⋊C
32
d
ρ
Label
ID
C
5
×C
3
⋊C
32
480
2
C5xC3:C32
480,1
Semidirect products G=N:Q with N=
C
5
and Q=
C
3
⋊C
32
extension
φ:Q→Aut N
d
ρ
Label
ID
C
5
⋊(C
3
⋊C
32
) =
C
15
⋊C
32
φ:
C
3
⋊C
32
/
C
24
→
C
4
⊆ Aut
C
5
480
4
C5:(C3:C32)
480,6
C
5
⋊
2
(C
3
⋊C
32
) =
C
15
⋊
3
C
32
φ:
C
3
⋊C
32
/
C
48
→
C
2
⊆ Aut
C
5
480
2
C5:2(C3:C32)
480,3
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≀
ℚ
◁